Department of Mathematics and Statistics, Binghamton University

Course Description

2015-02-26T16:48:10-04:00

Course Description

The page stores an independent copy of the course description section of the University Bulletin.

MATH 105, BEGINNING ALGEBRA

Basic concepts and techniques of algebra including a review of real numbers, fractions, equations, inequalities, problem solving, graphs, functions, solving systems of linear equations, exponents, polynomials and factoring polynomials. College credit given only to students with deficiencies in the mathematics admission requirement. Not open to students who have credit for any higher-numbered mathematics course. fall only

MATH 106, INTERMEDIATE ALGEBRA

Basic concepts and techniques of algebra, rational functions and expressions, problem solving, radicals, rational exponents, complex numbers, quadratic equations and functions, exponential and logarithmic functions, sequences and series. College credit given only to students with deficiencies in the mathematics admission requirement. Not open to students who have credit for any higher-numbered mathematics course. every sem.

MATH 107, BASIC INTEGRATED MATHEMATICS

Development of basic algebraic skills with some geometry. The course is designed as a bridge between high school mathematics and elementary statistics. It is not adequate preparation for calculus. Prerequisites: two years of high school math. Not open for credit to students who have credit for Math 147. every sem.

MATH 108, ALGEBRA AND TRIGONOMETRY

Topics essential for the study of calculus, including elements of trigonometry, complex numbers, logarithms and basic algebra. Skill development in algebraic and trigonometric manipulations. Not open for credit to students who have credit for Math 221. every sem.

MATH 130, MATHEMATICS IN ACTION

Emphasizes the real-world significance of mathematics and applications of several areas of mathematics. Topics covered include design of street networks, planning and scheduling, weighted voting systems, fair division and apportionment, measuring populations and the universe, symmetries, fractals and statistics. Provides students with an experience in quantitative reasoning and data analysis through mathematical modeling of some real-life problems including a hands-on approach. Further emphasis is on illustrating the importance, relevance and currency of mathematics in the modern world. every sem.

MATH 147, ELEMENTARY STATISTICS

Classification of data, frequency distributions, probability and the normal curve, elementary sampling theory. Not open to students who have credit for any other course in statistics. Prerequisite: MATH 107. every sem.

MATH 148, ELEMENTARY STATISTICS FOR BIOLOGISTS

Elementary Statistics for Biologists. Data analysis, probability, normal curve, regression, confidence intervals, hypothesis testing. This course will emphasize applications to biology. Not open to students who have credit for any other course in statistics. Prerequisite: MATH 107. every sem.

MATH 220, CALCULUS FOR BUSINESS AND MANAGEMENT

Elements of calculus; emphasis on maximum and minimum problems. Primarily for School of Management students, who may satisfy their mathematics requirement with either MATH 220 or 221, and for economics majors in the BS specialization in financial economics. Not equivalent to MATH 221 as prerequisite for MATH 222. Prerequisite: MATH 108 or equivalent. every sem.

MATH 221, CALCULUS I

Differentiation and integration of elementary functions. Prerequisite: MATH 108 or equivalent. every sem.

MATH 222, CALCULUS II

Techniques and application of integration. Sequences and series. Prerequisite: MATH 221. every sem.

MATH 304, LINEAR ALGEBRA

Vector spaces, linear transformations, determinants, characteristic values. Prerequisite: MATH 221. every sem.

MATH 314, DISCRETE MATHEMATICS

Logic, sets, relations, functions. Induction, recursion, counting methods. Graphs, trees. Some abstract algebra. Prerequisite: MATH 221. every sem.

MATH 323, CALCULUS III

Calculus of functions of several variables. Prerequisite: MATH 222. every sem.

MATH 327, PROBABILITY WITH STATISTICAL METHODS

Development of probabilistic concepts in discrete and absolutely continuous cases. Classical combinatorial methods, independence, random variables, distributions, moments, transformations, conditioning, confidence intervals, estimation. Open to Watson School students only. Does not serve as a prerequisite for MATH 448 or for any actuarial science courses. Prerequisite: MATH 222 or consent of department. every sem.

MATH 330, NUMBER SYSTEMS

Careful discussion of the real numbers, the rational numbers and the integers, including a thorough study of induction and recursion. Countable and uncountable sets. The methodology of mathematics: basic logic, the use of quantifiers, equivalence relations, sets and functions. Methods of proof in mathematics. Training in how to discover and write proofs. Prerequisite: MATH 222. every sem.

MATH 346, INTRODUCTION TO FINANCIAL MATHEMATICS

Interest theory, annuities, amortization, bonds, portfolio insurance, Derivative markets. The material will focus on the actuarial mathematics requirements for the Exam FM. Prerequisite: MATH 222. every sem.

MATH 356, MATHEMATICAL MODELING

Mathematical structures that allow people to describe and discuss naturally occurring phenomena. Possible topics include functions as models, recurrence relations, networks and graph theory, linear programming, discrete probability models, Markov chains, Monte Carlo simulations, random walks, queuing theory, recursive game theory. For each topic, we will discuss the mathematics rigorously and then analyze some real-world applications. Prerequisites: MATH 304 and either MATH 314 or MATH 330. spring only

MATH 371, ORDINARY DIFFERENTIAL EQUATIONS

Ordinary differential equations. Emphasis on applications to problems in physics, chemistry, biology, economics, etc. Prerequisite: MATH 222. fall only

MATH 372, DYNAMICAL SYSTEMS

Introduction to ordinary differential equations using linear algebra and geometry. The emphasis is on understanding long-term features of the solutions, rather than on solving the equations analytically. Topics include mathematical modeling; linear systems of differential equations; non-linear systems; stability of equilibria and periodic orbits; numeric methods; chaotic systems. Prerequisites: MATH 222 and MATH 304. every sem.

MATH 375, COMPLEX VARIABLES

Analytic functions. Cauchy's integral theorem, power series. Prerequisite: MATH 323. spring only

MATH 381, GRAPH THEORY

Directed and undirected graphs, trees, connectivity, Eulerian and Hamiltonian graphs, planar graphs, coloring of graphs, graph parameters, optimization and graph algorithms. Prerequisites: MATH 304, and either MATH 314 or 330, or consent of department. spring only

MATH 386, COMBINATORICS

Topics from among counting techniques, generating function and recurrence relations, pigeonhole principle, Ramsey's Theorem, Latin squares, combinatorial designs. Prerequisites: MATH 304 and either MATH 314 or 330, or consent of department. fall only

MATH 391, PRACTICUM IN COLLEGE TEACHING

Independent study through teaching in particular mathematics course. Various assignments closely directed by instructor in course, including development of syllabi and other course materials; construction and reading of examinations; lecturing and/or discussion leadership; laboratory supervision; academic counseling of student. May be repeated for total of no more than eight credits. Credits may not be earned in conjunction with course in which student is currently enrolled. Does not satisfy major or Harpur College Distribution requirements. Prerequisite: consent of instructor. Pass/Fail only. var. cr.

MATH 401, MODERN ALGEBRA I

Groups, rings, integral domains, fields. Prerequisites: MATH 304 and 330, or consent of department. fall only

MATH 402, MODERN ALGEBRA II

Further study of topics in MATH 401. Vector spaces, modules, lattices, Galois theory. Prerequisite: MATH 401. spring only

MATH 404, ADVANCED LINEAR ALGEBRA

Modules, normal forms of linear transformations, quadratic forms. Prerequisites: MATH 304 and 330, or consent of department. spring only

MATH 407, INTRODUCTION TO THE THEORY OF NUMBERS

Classical number theory. Divisibility, prime numbers, quadratic reciprocity, Diophantine equations. Prerequisite: MATH 330 or consent of department. offered as needed

MATH 447, INTRODUCTION TO PROBABILITY AND STATISTICS I

Basic concepts of probability, univariate and multivariate distributions, distribution theory, central limit theorem. Prerequisite: MATH 323 or consent of department. every sem.

MATH 448, INTRODUCTION TO PROBABILITY AND STATISTICS II

Estimation, confidence intervals and hypothesis testing. Introduction to linear models, categorical data and nonparametric statistics. Prerequisite: MATH 447. every sem.

MATH 449, PROBLEM SOLVING IN ACTUARIAL SCIENCE

Prerequisite: Math 447 or consent of department. spring only

MATH 450, ACTUARIAL MATHEMATICS I

Markov chains, Poisson processes, survival models, life tables, life insurance, life annuities. The material will focus on the actuarial mathematics requirements for the Exam MLC. Prerequisites: MATH 330, MATH 346 and MATH 447. fall only

MATH 452, ACTUARIAL MATHEMATICS II

Benefit premiums, benefit reserves, multiple life functions, multiple decrement functions. The material will focus on the actuarial mathematics requirements for the Exam MLC. Prerequisite: MATH 222, MATH 304 and MATH 450. spring only

MATH 454, FINANCIAL MATHEMATICS

Interest rate models, principle of no arbitrage, fundamental theorem of asset pricing, evaluation of derivatives, put-call parity, European put and call options, binomial models, Black-Scholes option-pricing model, American options, option Greeks, exotic options, lognormal distribution, diffusion process, Ito's lemma, simulation and delta-hedging. The material will focus on the requirements for the Exam MFE. Prerequisites/Co-requisites: MATH 346, MATH 447 or equivalent. every spring

MATH 461, TOPOLOGY

Study of topological spaces. Metric spaces, separation properties, connectivity, compactness. Prerequisites: MATH 304, 323 and 330, or consent of department. fall only

MATH 465, FOUNDATIONS OF GEOMETRY

Postulational treatment of geometric systems, including projective, affine and non-Euclidean geometries. Prerequisites: MATH 304 and 330, or consent of department. offered as needed

MATH 471, PARTIAL DIFFERENTIAL EQUATIONS

Vector calculus, Fourier series, partial differential equations, with emphasis on applications. Prerequisite: MATH 371 or 372. spring only

MATH 472, PDE AND MATHEMATICAL ANALYSIS

Partial differential equations of mathematics, including first order equations, second order equations of potential theory, wave propagation, and heat flow, and higher order equations. We solve these equations by means of classical Fourier analysis, functional analysis, generalized functions and variational principles. Topics vary year by year. Prerequisites: MATH 330 and either MATH 371 or MATH 372 or equivalent. every spring

MATH 478, REAL ANALYSIS I

Geometry and topology of Rn, functions and limits, calculus of functions on Rn and higher dimensional spaces. Prerequisites: MATH 304, 323 and 330, or consent of department. fall only

MATH 479, REAL ANALYSIS II

Sequences and series of functions, more advanced study of differentiation and integration. Prerequisite: MATH 478. spring only

MATH 480, SEMINAR IN ALGEBRA

spring only, var. cr.

MATH 488, TOPICS IN HIGHER MATHEMATICS

Some topics in higher mathematics not normally part of regular curriculum. Prerequisites: consent of department. May be repeated for credit. offered as needed

MATH 489, PROBLEM SOLVING

Problem solving is a part of mathematics organized around methods rather than theorems. For this reason it is somewhat amorphous, and difficult to study, but the ideas are applicable to almost any part of mathematics. For purposes of this class, there is a distinction between problems and exercises. An exercise is a question that tests mastery of a narrowly focused technique. In a problem, by contrast, the technique to be used is not immediately apparent. Problems are sometimes open-ended, poorly-defined, or even unsolvable. The objective of the course is to introduce students to a variety of mathematical knowledge and techniques useful for mathematical problem solving and not always covered in other courses. This course will be run partly in a seminar format; students will be expected to regularly present their own work to the class. Students will be expected to participate in the William Lowell Putnam Mathematical Competition (which is held on the first Saturday in December). Prerequisites: consent of department. fall only

MATH 497, INDEPENDENT WORK

Individual study under direct supervision of faculty member. Prerequisites: consent of department. May be repeated for credit with maximum of eight credit hours of MATH 497 allowed toward major requirements. var. cr.

MATH 498, HONORS STUDY IN MATHEMATICS

Independent studies/research open only to students who have been accepted in the mathematics honors program. May be repeated for credit, with maximum of four credit hours of MATH 498 allowed toward major requirements. Prerequisite: consent of department.

Linear Algebra - Math 304

2021-06-30T10:50:30-04:00

Linear Algebra - Math 304

Spring 2021 - Course Coordinator: Prof. Alex Feingold

Sec	Instructor	Office	Email(*)	Meets	Room
1	Matthew Haulmark	online	Haulmark	MWF:8:00-9:30	online
2	Michael Dobbins	online	Dobbins	MWF:8:00-9:30	online
3	David Biddle	online	Biddle	MWF:9:40-11:10	online
4
5	Christopher Eppolito	online	Eppolito	MWF:11:20-12:50	online
6	Alex Feingold	online	Feingold	MWF:1:10-2:40	online
7	Thomas Kilcoyne	online	Kilcoyne	MWF:2:50-4:20	online
8	Thomas Kilcoyne	online	Kilcoyne	MWF:4:40-6:10	online

(*): To send an email to your instructor, click on the link in the Email column of the table.

If a section has its own detailed syllabus webpage, a link to that page will be provided under the Instructor column of the table above.

Each instructor should provide their students with a Zoom link to the recurring class meetings which begin on Friday, Feb 12, and end on Monday, May 17, 2021.

Below is a partial syllabus with information for all sections that you should know. Your instructor may have a more detailed syllabus about how your section will be run.

Textbook

``Linear Algebra” by Jim Hefferon, Fourth Edition, available as a free download here:

Linear Algebra by Jim Hefferon.

On can buy a cheap printed version and access more free resources at the textbook's official website.

Here are also some additional books that students and instructors may find helpful.

A First Course in Linear Algebra by Robert A. Beezer

Elementary Linear Algebra by K.R. Matthews

Linear Algebra by D. Cherney, T. Denton, R. Thomas, and A. Waldron

Approximate Exam Schedule (Each section instructor will decide when it is appropriate to give Exams 1, 2, 3.)

Exam 1: The week of March 8-12.

Exam 2: The week of April 12-16.

Exam 3: The week of May 10-14.

Final Exam: Tuesday, May 25, 8:00 - 10:00 AM Online.

Grades

Remote format of the course requires steps to combat academic dishonesty and to protect the honest students from unfair competition. Details about how quizzes and exams will be administered so as to achieve that goal will be announced by your instructor. Your instructor may decide to use: (1) Limited time to answer each question, (2) Visual observation of you during the exam through Zoom, (3) Oral exams in place of, or in addition to, written exams. Some advice about preparing for oral exams is available through the following link:

How to study for oral exams

The course total will be determined as follows:

Quizzes: 20%

Exam 1: 20%

Exam 2: 20%

Exam 3: 20%

WebWork Homework (common for all sections): 5%

Final Exam: 15%

At the end of the course, your grade in the course will be determined by your instructor based on your course total and the following approximate scale. (Borderline cases will be decided by other factors such as attendance or participation.)

A 90%, A- 85%, B+ 80%, B 75%, B- 70%, C+ 65%, C 55%, C- 50%, D 45%

Homework

Online homework will be done using WebWork. The server address is

https://webwork.math.binghamton.edu/webwork2/304Spring2021/

For students, your WebWork account username is the pre@ portion of your binghamton.edu e-mail account. Your initial password is the same as the username. For example, if your Binghamton e-mail account is xyzw77@binghamton.edu then your username is: xyzw77 and your initial temporary password is: xyzw77

Make sure to change your password as soon as possible to a secure password, and save that choice where it will not be lost.

Important: Besides the WebWork homework sets, you should do problems from the book, as selected by your instructor, see an approximate schedule below. This part of the homework will not be graded, but it will be important to your success in the course.

Expected workload

You are expected to spend about 12.5 hours per week on average for this class, including participation in Zoom lectures, watching instructional videos, solving homework problems (graded and ungraded), reviewing the material, and preparing for the tests. Expect the work load to be higher than average in the weeks before the exams.

Expected behavior in class

During online classes all students are expected to participate in a way that maximizes their learning and minimizes disruptions for their classmates. Your instructor has the final word on the use of video and audio in the general Zoom sessions, break-out rooms, and online office hours. If you have any concerns, limitations, or circumstances, please communicate with your instructor to find the most appropriate solution.

Academic Code of Honor

For all graded assignments and exams, you are not allowed to use any help not explicitly authorized by your instructor. This includes, but is not limited to, problem-solving websites, notes, help from other people, etc. All instances of academic dishonesty will be investigated, penalized, and referred to the appropriate University officials for maximal possible punishment. In other words, don't even think of trying to cheat.

Getting Help

If you fall behind in class, or need extra help to learn the material, talk to your instructor as soon as you can. They should be able to help you and also point you to other resources. We also encourage you to talk to your classmates, and, in particular, to form informal study groups to prepare for the exams.

Disability Information

If you have a disability for which you are or may be requesting an accommodation, please contact both your instructor and the Services for Students with Disabilities office (119 University Union, 607-777-2686) as early in the term as possible. Note: extended time for the examinations may not automatically apply to the interview-style exams, but we will work with you to provide reasonable accommodations that are appropriate for your situation.

Topics	Text	Problems
Introduction, preview, examples; linear combination	Ch. 1, I.1	1:I.1.17,19,21
Gaussian elimination (reduction)	Ch. 1, I.1	1:I.1.22,24,27,32
(Augmented) matrix of a system, solution set	Ch. 1, I.2	1:I.2.15,16,17,18,21,25
Basic logic: statements, connectives, quantifiers	Appendix
Set theory, general functions	Appendix
Homogeneous and non-homogeneous systems (no formal induction in Lemma 3.6)	Ch. 1, I.3	1:I.3.15,17,18,20,21,24
Points, vectors, lines, planes	Ch. 1, II.1	1:II.1.1,2,3,4,7
Distance, dot product, angles, Cauchy-Schwarz and Triangle Inequalities	Ch. 1, II.2	1:II.2.11,12,14,16,17,21,22
Gauss-Jordan reduction, reduced row echelon form	Ch. 1, III.1	1:III.1.8,9,10,12,13,14,15
Linear combination lemma, uniqueness of RREF (no proofs of 2.5, 2.6)	Ch. 1, III.2	1:III.2.11,14,20,21,24
Review	Ch. 1; Appendix	Student's_Guide; Sample_Problems; Solutions
Matrix operations, including the transpose. Linear system as a matrix equation	Matthews 2.1	3:III.1.13,14,15,16
Linear maps (transformations) given by matrices	Matthews 2.2	3:III.1.19; 3:III.2.12,17,30
Vector spaces: definition, examples	Ch. 2, I.1	2:I.1.17,18,19,21,22,29,30
Linear maps between vector spaces	Ch. 3, II.1	3:II.1.18,19,20,22,24,25,26,28
Subspaces. Span	Ch. 2, I.2	2:I.2.20,21,23,25,26,29,44,45
Linear independence	Ch. 2, II.1	2:II.1.21,22,25,28
Properties of linear independence	Ch. 2, II.1	2:II.1.29,30,32,33
Basis of a vector space	Ch. 2, III.1	2:III.1.20,21,22,23,24,25,26,30,31,34
Dimension of a vector space	Ch. 2, III.2	2:III.2.15,16,17,18,19,20,21,24,25,28
Column space, row space, rank	Ch. 2, III.3	2:III.3.17,18,19,20,21,23,29,32,39
Range space and Kernel (Null space)	Ch. 3, II.2	3:II.2.21,23,24,26,31,35
Review		Student's_Guide; Sample_Problems; Solutions
Invertible matrices: definition, equivalent conditions; inverse matrix	Ch.3, IV.4	3:IV.4.13,14,15,16,17,18,19,26,29 InvertibleMatrices_1 InvertibleMatrices_2 InvertibleMatrices_3 InvertibleMatrices_4 InvertibleMatrices_5
Elementary matrices. Row reduction using elementary matrices	Ch. 3, IV.3; CDTW Ch. 2, 2.3	3:IV.3.24,25,32 ElementaryMatrices_1 ElementaryMatrices_2 ElementaryMatrices_3
Determinant of a matrix, properties	Ch. 4, I.1, I.2	4:I.1.1,3,4,6,9; 4:I.2.8,9,12,13,15,18 Determinants_1 Determinants_2 Determinants_3 Determinants_4 Determinants_5 Determinants_6
More on Determinants	Ch. 4, II.1, III.1	4:III.1.11,14,16,17,20,21,22 Determinants_7(Cramer) Determinants_8(Adjoint)
Matrix of a linear transformation, matrix of the composition, inverse	Ch. 3, III.1, IV.2	3:III.1.13,17,18,19,21,23 Matrix_of_Transformation_1
Change of basis, similar matrices	Ch. 3, V.1, V.2; Ch. 5, II.1	3:V.1.7,9,10,12; 5:II.1.5,8,11,13,14 Matrix_of_Transformation_2 Matrix_of_Transformation_3 Matrix_of_Transformation_4 Similar_Matrices
Complex numbers	Matthews 5.1–5.6	Matthews 5.8.1,2,5,6,7,9 Complex_Numbers_1 Complex_Numbers_2 Complex_Numbers_3 Complex_Numbers_4 Complex_Numbers_5
Eigenvectors, eigenvalues, eigenspaces for matrices and linear operators. Characteristic polynomial	Matthews 6.1, 6.2; Ch. 5, II.3	5:II.3.23,24,25,26,27,28,29,30,31 Eigenvectors_1 Eigenvectors_2 Eigenvectors_3 Eigenvectors_4 Eigenvectors_5
Diagonalization of matrices	Ch. 5, II.2, II.3	5:II.3.22,33,36,46 Diagonalization_1 Diagonalization_2 Diagonalization_3 Diagonalization_4 Diagonalization_5 Diagonalization_6
Orthogonal and orthonormal bases of $R^n$ and its subspaces; orthogonal matrices	Ch. 3, VI.1, VI.2	3:VI.1.6,7,17,19; 3:VI.2.10 Orthogonal_1 Orthogonal_2 Orthogonal_3 Orthogonal_4
Orthogonal complement of a subspace, orthogonal projection	Ch. 3, VI.3	3:VI.3.11,12,13,14,26,27 Complements_1 Complements_2 Complements_3 Complements_4 Complements_5
Gram-Schmidt process; orthogonal diagonalization of matrices	Ch. 3, VI.2	3:VI.2.13,15,17,18,19,22 GramSchmidt_1 GramSchmidt_2 OrthogonalDiagonalization_1 OrthogonalDiagonalization_2
Review for Final Exam		Student's_Guide; Sample_Book_Problems; Sample_Problems; Solutions

Linear Algebra - Math 304

2020-12-21T15:36:54-04:00

Linear Algebra - Math 304

Fall 2020 - Course Coordinator: Prof. Alexander Borisov

Sec	Instructor	Office	Email(*)	Meets	Room
1	Alexander Borisov	online	borisov	MWF:8:00-9:30	online
2	Seunghun Lee	online	shlee	MWF:9:40-11:10	online
3	Fikreab Solomon Admasu	online	fsolomon	MWF:11:20-12:50	online
4	Quincy Loney	online	quincy	MWF:1:10-2:40	online
5	Eugenia Sapir	online	sapir	MWF:2:50-4:20	online
6	Vaidehee Thatte	online	thatte	MWF:4:40-6:10	online

(*): Each email address in this table is of the form xxx@math.binghamton.edu but that should happen automatically if you just click on the link.

If a section has its own detailed syllabus webpage, a link to that page will be provided under the Instructor column of the table above.

Below is a partial syllabus with information for all sections that you should know. Your instructor may have a more detailed syllabus about how your section will be run.

Textbook

``Linear Algebra” by Jim Hefferon, Fourth Edition, available as a free download here:

Linear Algebra by Jim Hefferon.

On can buy a cheap printed version and access more free resources at the textbook's official website.

Here are also some additional books that students and instructors may find helpful.

A First Course in Linear Algebra by Robert A. Beezer

Elementary Linear Algebra by K.R. Matthews

Linear Algebra by D. Cherney, T. Denton, R. Thomas, and A. Waldron

Exam Schedule

Midterm Examination 1: Week of September 21

Midterm Examination 2: Week of October 19

Midterm Examination 3: Week of November 30

Final Exam: December 8-10

Grades

Remote format of the course requires radical steps to combat academic dishonesty and to protect the honest students from unfair competition. To do this, we will have a grading system based primarily on oral examinations.

How to study for oral exams

The midterm and the final examinations will be interview-style (oral) on Zoom, recorded. Each examination will be scheduled for 15-20 minutes, though it may take longer or shorter. The examinations will be scheduled outside of the instructional time, at a time that works for you and your instructor. All examinations will be cumulative. For each examination you will receive a letter grade: A=100%, B=75%, C=50%, D=25%, or F=0%. Final examination grade will not count directly, but will automatically replace one of the midterm grades, to maximize your course total. (If the final examination grade is lower than all your midterm grades, your course total will not change).

The course total will be determined as follows:

WebWork Homework (common for all sections): 3%

Section-specific Homework/Quizzes: 7%

Midterm 1: 20%

Midterm 2: 30%

Midterm 3: 40%

At the end of the course, your grade in the course will be determined by your instructor based primarily on your course total and the following scale (approximate, subject to adjustments):

A 90%, A- 85%, B+ 77.5%, B 72.5%, B- 67.5%, C+ 60%, C 55%, C- 50%, D 37.5%

Homework

Online homework will be done using WebWork. The server address is

https://webwork.math.binghamton.edu/webwork2/304Fall2020/

Your WebWork account username is the pre@ portion of your binghamton.edu e-mail account. Your initial password is the same as the username. For example, if your Binghamton e-mail account is xyzw77@binghamton.edu then your username: xyzw77 and your password: xyzw77

Make sure to change your password as soon as possible to a secure password, and save that choice where it will not be lost.

Expected workload

Expected behavior in class

Academic Code of Honor

For all graded assignments and exams, you are not allowed to use any help, that was not explicitly authorized by your instructor. This includes, but is not limited to problem-solving websites, notes, help from other people, etc. All instances of academic dishonesty will be investigated, penalized, and referred to the appropriate University officials for maximal possible punishment. In other words, don't even think of trying to cheat.

Getting Help

Disability Information

Tentative Schedule

Unless otherwise specified, the Text is the Jim Hefferon's book and the exercises are from there, in the format “Chapter:Section.Subsection.ProblemNumber”. It is subject to change and adjustment at your instructor's discretion. The Problems are for practice only and are not to be turned in. There will be separate weekly graded homework through WebWork. Instructional videos for the second half of the semester is supplementary material, not intended to replace the regular lectures.

Week	Dates	Topics	Text	Problems
1	Aug 26, 28	Introduction, preview, examples; linear combination	Ch. 1, I.1	1:I.1.17,19,21
1	Aug 26, 28	Gaussian elimination (reduction)	Ch. 1, I.1	1:I.1.22,24,27,32
2	Aug 31 - Sep 4	(Augmented) matrix of a system, solution set	Ch. 1, I.2	1:I.2.15,16,17,18,21,25
		Logical statements, basic constructions, quantifiers	Appendix
		Induction (informal), sets, functions	Appendix
3	Sep 7- 11	Homogeneous and non-homogeneous systems (no formal induction in Lemma 3.6)	Ch. 1, I.3	1:I.3.15,17,18,20,21,24
		Points, vectors, lines, planes	Ch. 1, II.1	1:II.1.1,2,3,4,7
		Distance, dot product, angles, Cauchy-Schwarz and Triangle Inequalities	Ch. 1, II.2	1:II.2.11,12,14,16,17,21,22
4	Sep 14-18	Gauss-Jordan reduction, reduced row echelon form	Ch. 1, III.1	1:III.1.8,9,10,12,13,14,15
		Linear combination lemma, uniqueness of RREF (no proofs of 2.5, 2.6)	Ch. 1, III.2	1:III.2.11,14,20,21,24
		Review for Examination 1	Ch. 1; Appendix	Student's_Guide; Sample_Problems; Solutions
5 Exam 1 week	Sep 21-25	Matrix operations, including the transpose. Linear system as a matrix equation	Matthews 2.1	3:III.1.13,14,15,16
		Linear maps (transformations) given by matrices	Matthews 2.2	3:III.1.19; 3:III.2.12,17,30
		Vector spaces: definition, examples	Ch. 2, I.1	2:I.1.17,18,19,21,22,29,30
6	Sep 28 - Oct 2	Linear maps between vector spaces	Ch. 3, II.1	3:II.1.18,19,20,22,24,25,26,28
		Subspaces. Span	Ch. 2, I.2	2:I.2.20,21,23,25,26,29,44,45
		Linear independence	Ch. 2, II.1	2:II.1.21,22,25,28
7	Oct 5-9	Properties of linear independence	Ch. 2, II.1	2:II.1.29,30,32,33
		Basis of a vector space	Ch. 2, III.1	2:III.1.20,21,22,23,24,25,26,30,31,34
		Dimension of a vector space	Ch. 2, III.2	2:III.2.15,16,17,18,19,20,21,24,25,28
8	Oct 12-16	Column space, row space, rank	Ch. 2, III.3	2:III.3.17,18,19,20,21,23,29,32,39
		Range space and Kernel (Null space)	Ch. 3, II.2	3:II.2.21,23,24,26,31,35
		Review for Examination 2		Student's_Guide; Sample_Problems; Solutions
9 Exam 2 week	Oct 19-23	Review for Examination 2
		Invertible matrices: definition, equivalent conditions; inverse matrix	Ch.3, IV.4	3:IV.4.13,14,15,16,17,18,19,26,29 InvertibleMatrices_1 InvertibleMatrices_2 InvertibleMatrices_3 InvertibleMatrices_4 InvertibleMatrices_5
		Elementary matrices. Row reduction using elementary matrices	Ch. 3, IV.3; CDTW Ch. 2, 2.3	3:IV.3.24,25,32 ElementaryMatrices_1 ElementaryMatrices_2 ElementaryMatrices_3
10	Oct 26-30	Determinant of a matrix, properties	Ch. 4, I.1, I.2	4:I.1.1,3,4,6,9; 4:I.2.8,9,12,13,15,18 Determinants_1 Determinants_2 Determinants_3 Determinants_4 Determinants_5 Determinants_6
		More on Determinants	Ch. 4, II.1, III.1	4:III.1.11,14,16,17,20,21,22 Determinants_7(Cramer) Determinants_8(Adjoint)
		Matrix of a linear transformation, matrix of the composition, inverse	Ch. 3, III.1, IV.2	3:III.1.13,17,18,19,21,23 Matrix_of_Transformation_1
11	Nov 2-6	Change of basis, similar matrices	Ch. 3, V.1, V.2; Ch. 5, II.1	3:V.1.7,9,10,12; 5:II.1.5,8,11,13,14 Matrix_of_Transformation_2 Matrix_of_Transformation_3 Matrix_of_Transformation_4 Similar_Matrices
		Complex numbers	Matthews 5.1–5.6	Matthews 5.8.1,2,5,6,7,9 Complex_Numbers_1 Complex_Numbers_2 Complex_Numbers_3 Complex_Numbers_4 Complex_Numbers_5
		Review of the Material
12	Nov 9-13	Eigenvectors, eigenvalues, eigenspaces for matrices and linear operators. Characteristic polynomial	Matthews 6.1, 6.2; Ch. 5, II.3	5:II.3.23,24,25,26,27,28,29,30,31 Eigenvectors_1 Eigenvectors_2 Eigenvectors_3 Eigenvectors_4 Eigenvectors_5
		Diagonalization of matrices	Ch. 5, II.2, II.3	5:II.3.22,33,36,46 Diagonalization_1 Diagonalization_2 Diagonalization_3 Diagonalization_4 Diagonalization_5 Diagonalization_6
		Review of the Material
13	Nov 16-20	Orthogonal and orthonormal bases of $R^n$ and its subspaces; orthogonal matrices	Ch. 3, VI.1, VI.2	3:VI.1.6,7,17,19; 3:VI.2.10 Orthogonal_1 Orthogonal_2 Orthogonal_3 Orthogonal_4
		Orthogonal complement of a subspace, orthogonal projection	Ch. 3, VI.3	3:VI.3.11,12,13,14,26,27 Complements_1 Complements_2 Complements_3 Complements_4 Complements_5
		Gram-Schmidt process; orthogonal diagonalization of matrices	Ch. 3, VI.2	3:VI.2.13,15,17,18,19,22 GramSchmidt_1 GramSchmidt_2 OrthogonalDiagonalization_1 OrthogonalDiagonalization_2
14	Nov 23 -27	NO CLASS
		NO CLASSES - Thanksgiving Break
		NO CLASSES - Thanksgiving Break
15 Exam 3 week	Nov 30 - Dec 4	Review for Examination 3		Student's_Guide; Sample_Book_Problems; Sample_Problems; Solutions
		Review for the Final Examination
		Review for the Final Examination
16 Finals week	Dec 7	Review for the Final Examination
16 Finals week	Dec 8-11	FINAL EXAMINATIONS

Sample Exams and Other Study Materials

IMPORTANT: Please note that the sample exams below are traditional written exams. Our interview-style exams will focus more on understanding and less on calculations.

Examination 1

Sample_1,Answers_1; Sample_2,Answers_2; Sample_3,Answers_3

Examination 2

Being cumulative, Examination 2 will cover all the material of Examination 1 as well as additional topics:

Sample_1,Answers_1; Sample_2,Answers_2; Some_Practice_Problems, Answers

Examination 3 and Final Examination

Being cumulative, Examination 3 and Final Examination will cover all the material of Examinations 1 and 2 as well as additional topics:

Sample_1, Answers_1; Sample_2, Answers_2; Sample_3, Answers_3

The following sample exams are traditional cumulative final exams. They are adapted, with permission, from the collection of Dr. Inna Sysoeva

Sample_1, Answers_1; Sample_2, Answers_2; Sample_3, Answers_3; Sample_4, Answers_4; Sample_5, Answers_5 |

Syllabi from previous semesters

The syllabus for Math 304 in Fall 2019 is available through this link:

Spring 2020 page

The syllabus for Math 304 in Fall 2019 is available through this link:

Fall 2019 page

The syllabus for Math 304 in Spring 2019 is available through this link:

Math 304 Syllabus for Spring 2019

The syllabus for Math 304 in Fall 2018 is available through this link:

Fall 2018 page

Linear Algebra - Math 304

2020-08-21T17:45:49-04:00

Linear Algebra - Math 304

Spring 2020 - Course Coordinator: Prof. Alexander Borisov

Sec	Instructor	Office	Phone	Email(*)	Meets	Room
1	Alexander Borisov	WH-109	777-2764	borisov	MWF:8:00-9:30	SL-302
2	Casey Donoven	WH-202	777-2982	cdonoven	MWF:8:00-9:30	WH-G002
3	David Biddle	WH-126		biddle	MWF:9:40-11:10	AA-G021
4	Charles (Matt) Evans	WH-380		evans	MWF:11:20-12:50	LH-12
5	David Biddle	WH-126		biddle	MWF:11:20-12:50	AA-G021
6	Alex Feingold	WH-115	777-2465	alex	MWF:1:10-2:40	SL-302
7	Thomas Kilcoyne	WH-336		kilcoyne	MWF:2:50-4:20	LH-12
8	Thomas Kilcoyne	WH-336		kilcoyne	MWF:4:40-6:10	LH-12

(*): Each email address in this table is of the form xxx@math.binghamton.edu but that should happen automatically if you just click on the link.

If a section has its own detailed syllabus webpage, a link to that page will be provided under the Instructor column of the table above.

Below is a partial syllabus with information for all sections that you should know. Your instructor may have a more detailed syllabus about how your section will be run.

Important: Syllabus Adjustments due to the Coronavirus Epidemic

Syllabus Addition for MATH 304, due to the Online Instruction Mode

The following changes will be implemented in all sections of MATH 304, effective 03/19/2020.

1) Instead of the regular classes, the instructors will be holding online office hours, using Zoom or alternative software. These online office hours will be held during the regular instructional times. Additional online office hours may be scheduled as needed. In addition to the recommended textbook reading, there will be links to videos posted online. You are responsible for learning the material on your own, and using the online office hours to clarify any questions that you may have.

2) Instead of the in-class quizzes you will be getting homework assignments, through WebWork, MyCourses, or other system, at your instructor's discretion. These assignments are on top of the regular WebWork homework, and they will differ by section and may have shorter deadlines.

3) Midterm examinations and final examination will be conducted in a various remote formats, depending on the section. Your instructor will provide you with the details.

4) Since we are unable to hold a common in-class final examination, the one-letter-grade rule from the original syllabus will not apply.

5) It is your responsibility to inform your instructor of any circumstances that hinder or jeopardize your participation in the course, including any computer-related issues. The instructors and the course coordinator will do their best to help you learn and have a successful semester.

Consider the current situation, as unfortunate as it is, as an opportunity to develop a valuable skill of learning independently. It is, actually, one of the main goals of college education, much more important than any specific knowledge in any course.

Textbook

``Linear Algebra” by Jim Hefferon, Third Edition, available as a free download here:

Linear Algebra by Jim Hefferon.

Students can also buy a cheap printed version from the link on the author's website.

Here are also some additional books that students and instructors may find helpful.

A First Course in Linear Algebra by Robert A. Beezer

Elementary Linear Algebra by K.R. Matthews

Linear Algebra by D. Cherney, T. Denton, R. Thomas, and A. Waldron

Exam Schedule

Only the Final Exam will be common to all sections, but we expect each section will administer other exams on the same day, three times during the semester, as follows:

Exam 1: February 17 or 19 (depending on section)

Exam 2: March 18 This Exam will have to be given online since all classes March 17, 18 have been cancelled.

Exam 3: April 22 or April 24, depending on your section. This Exam will have to be given online.

Final Exam: Thursday, May 7, 8:00-10:00 AM, will be given online.

Arrangements for online exams will be announced soon. It is your instructor's responsibility to find a way to administer such exams, get the results and return the graded exam results.

Grade Distribution and Policies

The course total will be determined as follows:

Homework: 5%

Quizzes: 20% (the number and scope to be determined by your instructor)

Exam 1, 2, and 3: 15% each

Final Exam: 30%

The general grade cutoffs are going to be the following:

90% A; 80% B; 70% C; 60% D; and proportional cutoffs for A-,B+,B-,C+, and C-.

These cutoffs may be relaxed at the end of the semester, and may also differ a bit from section to section.

This rule from the original syllabus will not apply: (Additionally, the following one-letter-grade rule will apply: the grade in the course cannot exceed the grade on the final examination by more than one letter grade. For example, if you get a grade of B- on the final, the highest grade you can get in the course is A-. Note that the rule only works one way: even if you get an A on the final, you may still, theoretically, fail the course. The purpose of this rule is to bring some uniformity to the grading, considering that each section will have their own exams, quizzes, and cutoffs.)

Homework

Online homework will be done using WebWork. The server address is

https://webwork.math.binghamton.edu/webwork2/304Spring2020/

Make sure to change your password as soon as possible to a secure password, and save that choice where it will not be lost.

Besides the online homework sets, you should do problems from the book, as selected by your instructor, see an approximate schedule below. This part of the homework will not be graded, but it will be paramount to your success in the course.

Expected workload outside of the classroom

This class is scheduled to meet three times per week for 90 minutes each time. In addition to attending all classes, you should expect to need 8 to 10 hours per week outside of the class meetings to study the material and do homework.

Expected behavior in class

During classes all students are expected to behave according to university rules. Your instructor makes the final decisions about what to allow in the classroom, regarding in particular cell phone and laptop use, and food and beverage consumption. If you have any temporary of permanent needs that may necessitate an exception, it is your responsibility to discuss the matter with your instructor in advance.

Disability Information

Announcements

January 22 First Day of Classes: After meeting your instructor you should have been given this webpage address to check for the syllabus and instructions. Step 1: Read the entire syllabus, including the detailed syllabus for your section. Step 2: Set up your WebWork account for doing homework assignments. Step 3: Attend all classes and keep up with all homework corresponding to your section lectures.

February 11: Prof. Borisov will hold a review for all MATH 304 students on Sunday, Feb. 16, at 1:00-3:00 pm, in LH-14. The review session will be based entirely on student's questions, the posted sample exams or any other sources.

March 16: Today the administration announced that all classes (in person and online) have been cancelled for March 17 and 18, so that online only classes will begin March 19. That prevents having the scheduled March 18 Exam 2 in class. Each instructor will tell their students how Exam 2 will be handled.

March 30: Lectures of Prof. Feingold (Section 6) recorded on Panopto as well as written lecture notes are available through links on his webpage: Feingold Section 6 Webpage. These recordings are 90-minute class lectures presented online including interactions with students, and the written lecture notes are copies of the pages shown during the lectures.

Tentative Schedule

Unless otherwise specified, the Text is the Jim Hefferon's book and the exercises are from there, in the format “Chapter:Section.Subsection.ProblemNumber”. It is subject to change and adjustment at your instructor's discretion. NOTE: The Problems are for practice only and are not to be turned in. There will be separate weekly GRADED HOMEWORK through WebWork. Many of the examination problems will be similar to these practice problems and/or the WebWork problems.

Week	Dates	Topics	Text	Problems
1	Jan 22, 24	Introduction, preview, examples; linear combination	Ch. 1, I.1	1:I.1.17,1.19,1.21
1	Jan 22, 24	Gaussian elimination (reduction)	Ch. 1, I.1	1:I.1.22,24,27,32
2	Jan 27-31	(Augmented) matrix of a system, solution set	Ch. 1, I.2	1:I.2.15,16,17,18,20,23
		Logical statements, basic constructions, quantifiers	A-1, A-2
		Induction (informal), sets, functions	A-3, A-4
3	Feb 3-7	Homogeneous and non-homogeneous systems (no formal induction in Lemma 3.6)	Ch. 1, I.3	1:I.3.15,17,18,20,21,24
		Points, vectors, lines, planes	Ch. 1, II.1	1:II.1.1,2,3,4,7
		Distance, dot product, angles, Cauchy-Schwarz and Triangle Inequalities	Ch. 1, II.2	1:II.2.11,12,14,16,17,21,22
4	Feb 10-14	Gauss-Jordan reduction, reduced row echelon form	Ch. 1, III.1	1:III.1.8,9,10,12,13,14,15
		Linear combination lemma, uniqueness of RREF (skip proofs of 2.5, 2.6)	Ch. 1, III.2	1:III.2.11,14,20,21,24
		Review for Examination 1	Ch. 1; Appendix	Sample_1,Answers_1; Sample_2,Answers_2; Sample_3,Answers_3
5	Feb 17-21	Examination 1	Jan 22 – Feb 14
		Matrix operations, including the transpose. Linear system as a matrix equation	Matthews 2.1	3:III.1.12,13,14,15
		Linear maps (transformations) given by matrices	Matthews 2.2	3:III.1.18; 3:III.2.17,30
6	Feb 24-28	Vector spaces: definition, examples	Ch. 2, I.1	2:I.1.17,18,19,21,22,29,30
		Subspaces. Span	Ch. 2, I.2	2:I.2.20,21,23,25,29,44
		Linear independence	Ch. 2, II.1	2:II.1.20,21,24,27
7	Mar 2,4	Properties of linear independence	Ch. 2, II.1	2:II.1.28,29,31,32
7	Mar 2,4	Basis of a vector space	Ch. 2, III.1	2:III.1.18,19,20,21,22,23,24,28,29,32
–	Mar 6	No class	Winter Break
8	Mar 9-13	Dimension of a vector space	Ch. 2, III.2	2:III.2.16,17,18,19,22,23,26,29
		Column space, row space, rank	Ch. 2, III.3	2:III.3.17,18,19,20,21,23,29,32,39
		Range space and null space	Ch. 3, II.2	3:II.2.21,23,24,26,31,35
9	Mar 16-20	Review for Examination 2		Sample_1,Answers_1; Sample_2,Answers_2; Some_Practice_Problems, Answers
		Examination 2	Feb 19 – Mar 16
		Invertible matrices: definition, equivalent conditions; inverse matrix	Ch.3, IV.4	3:IV.4.13,14,15,16,17,18,19,26,29 InvertibleMatrices_1 InvertibleMatrices_2 InvertibleMatrices_3 InvertibleMatrices_4 InvertibleMatrices_5
10	Mar 23-27	Elementary matrices. Row reduction using elementary matrices	Ch. 3, IV.3; CDTW Ch. 2, 2.3	3:IV.3.24,25,34; ElementaryMatrices_1 ElementaryMatrices_2 ElementaryMatrices_3
		Determinant of a matrix, properties	Ch. 4, I.1, I.2	4:I.1.1,3,4,6,9; 4:I.2.8,9,12,13,15,18 Determinants_1 Determinants_2 Determinants_3 Determinants_4 Determinants_5 Determinants_6
		More on Determinants	Ch. 4, II.1, III.1	4:III.1.11,14,16,17,20,21,22 Determinants_7(Cramer) Determinants_8(Adjoint)
11	Mar 30-Apr 3	Linear maps (transformations) between general vector spaces	Ch. 3, II.1	3:II.1.18,19,20,25,26,28
		Matrix of a linear transformation, matrix of the composition, inverse	Ch. 3, III.1, IV.2	3:III.1.12,14,15,18,19,20,21,22,26,29 Matrix_of_Transformation_1
		Change of basis, similar matrices	Ch. 3, V.1, V.2; Ch. 4, I.1	3:V.1.7,9,10,11; 4:I.1.5,8,11,13,14 Matrix_of_Transformation_2 Matrix_of_Transformation_3 Matrix_of_Transformation_4 Similar_Matrices
–	Apr 4-12	No Class	Spring Break
12	Apr 13-17	Complex numbers	Matthews 5.1–5.6	Matthews 5.8.1,2,5,6,7,9 Complex_Numbers_1 Complex_Numbers_2 Complex_Numbers_3 Complex_Numbers_4 Complex_Numbers_5
		Eigenvectors, eigenvalues, eigenspaces for matrices and linear operators. Characteristic polynomial	Matthews 6.1, 6.2; Ch. 5, II.3	5:II.3.23,26,27,28,29,30,33 Eigenvectors_1 Eigenvectors_2 Eigenvectors_3 Eigenvectors_4 Eigenvectors_5
		Diagonalization of matrices	Ch. 5, II.2, II.3	5:II.3.21,32,35,40,41,44 Diagonalization_1 Diagonalization_2 Diagonalization_3 Diagonalization_4 Diagonalization_5 Diagonalization_6
13	Apr 20-24	Review for Examination 3		Sample_1, Answers_1; Sample_2, Answers_2; Sample_3, Answers_3
		Examination 3	Mar 20 – Apr 20
		Orthogonal and orthonormal bases of $R^n$ and its subspaces; orthogonal matrices	Ch. 3, VI.1, VI.2	3:VI.1.6,7,17,19; 3:VI.2,10,11,12; Orthogonal_1 Orthogonal_2 Orthogonal_3 Orthogonal_4
14	Apr 27-May 1	Orthogonal complement of a subspace, orthogonal projection	Ch. 3, VI.3	3:VI.3.11,12,13,14,26,27 Complements_1 Complements_2 Complements_3 Complements_4 Complements_5
		Gram-Schmidt process; orthogonal diagonalization of matrices	Ch. 3, VI.2	3:VI.2,13,15,17,18,19,22; GramSchmidt_1 GramSchmidt_2 OrthogonalDiagonalization_1 OrthogonalDiagonalization_2
		Review for the Final Examination
15	May 4	Review for the Final Examination		Sample exams are adapted, with permission, from the collection of Dr. Inna Sysoeva Sample_1, Answers_1; Sample_2, Answers_2; Sample_3, Answers_3; Sample_4, Answers_4; Sample_5, Answers_5
15	Thu. May 7	8:00-10:00 am GW 69EX	Cumulative Final Exam

—-

Syllabi from previous semesters

The syllabus for Math 304 in Fall 2019 is available through this link:

Fall 2019 page

The syllabus for Math 304 in Spring 2019 is available through this link:

Math 304 Syllabus for Spring 2019

The syllabus for Math 304 in Fall 2018 is available through this link:

Fall 2018 page

Section 3 - Math 304: Linear Algebra - Fall 2014

2017-01-05T18:20:20-04:00

Final Exam Week Office Hours

Monday 11-2pm, Wednesday 9-11am and 2-3pm, Thursday 11-2pm

Section Grade

70% of the final grade is reserved for two midterms and a final exam while the remaining 30% is earned in class. In section 3, 20 of the 30 percentage points are earned through weekly quizzes administered on Thursdays and 10 of the 30 percentage points are earned through class participation and homework.

Homework will be assigned every Monday, Wednesday, and Friday. Homework will be randomly collected and only a limited number of questions will be graded. The selected questions will be graded on a scale of 0, 1, or 2 points. Homework will only be collected on the third MWF after it has been assigned; ie homework assigned on a Monday will typically be collected the following Monday.

To earn credit, homework must be professional: clean paper (not torn from a notebook), not obviously a first draft (a minimal number of scratch-outs), and laid out in a coherent manner with enough space for instructor comments. I will not be collecting assignments all the time, but with clear solutions to assigned problems you will have excellent review material.

Section grades will be recorded using blackboard.
———————————————————————————————————————————————

Quiz Announcements

Review Quiz: Thursday 12/11.- Solution
Quiz 10: Thursday 12/4 on Sections 5.3 and 5.4.
Quiz 9: Monday 11/24 on Sections 5.1-5.2.- Solution
Quiz 8: Monday 11/17 on Section 4.8.- Solution
Quiz 7: Thursday 10/30 on Sections 4.1-4.4.- Solution
Quiz 6: Thursday 10/23 on Sections 3.6-3.8.- Solution
Quiz 5: Friday 10/17 on Sections 3.4-3.5.- Solution
Quiz 4: Monday 10/13 on Sections 3.1-3.3.- Solution
Quiz 3: Wednesday 9/24 on Sections 2.1-2.4. - Solution
Quiz 2: Thursday 9/18 on Chapter 1. - Solution
Quiz 1: Thursday 9/11 on Sections 1.1-1.3. - Solution

Assigned Homework

12/8: Homework 27 PDF - Solutions Part I - Part II
12/3: Homework 26 PDF - Solutions Part I - Part II
11/26: Homework 25 PDF - Solutions Part I - Part II
11/24: Homework 24 PDF - Solutions
11/21: Homework 23 PDF - Solutions
11/19: Homework 22 PDF - Solutions
11/17: Homework 21 PDF - Solutions
11/14: Homework 20 PDF - Solutions
11/12: Homework 19 PDF - Solutions
11/10: Homework 18 PDF - Solutions

Suggested Homework

Bonus Homework Assignment 11/20 - Solution
Bonus Homework Assignment 11/13 - Solution
All questions in section 4.9.
All questions in section 3.8.
Bonus True/False Quiz: Monday 11/1 - Solution
Bonus Quiz 10/16 - Solution
Bonus Quiz 10/9 - Solution
All questions in section 2.10.
To supplement sections 2.1-2.5: Schaum's page 33, 1.54, 1.55, 1.67-1.79.
All questions in section 1.7.
Solutions from Thursday 9/11 PDF
To supplement sections 1.1-1.3: Schaum's page 101, 2.70-2.82.

Linear Algebra - Math 304

2026-03-14T16:50:24-04:00

Linear Algebra - Math 304

Spring 2026 -- Course Coordinator: Alex Feingold

Sections

Sec	Instructor	Office	Email(*)	Meets	Room
1	Emmanuel Adara	WH-322	Adara	MWF: 8:00-9:30	CW-109
2	Sarah Lamoureux	WH-330	Lamoureux	MWF: 8:00-9:30	CW-213
3	Sarah Lamoureux	WH-330	Lamoureux	MWF: 9:45-11:15	CW-213
4	Stefan Viola	WH-326	Viola	MWF: 9:45-11:15	LN-2403
5	Stefan Viola	WH-326	Viola	MWF: 11:45-1:15	LN-2403
6	Alex Feingold	WH-115	Feingold	MWF: 1:30-3:00	CW-206 (Changed on Feb. 16)
7	Tara Koskulitz	WH-326	Koskulitz	MWF: 1:30-3:00	WH-G002
8	Tara Koskulitz	WH-326	Koskulitz	MWF: 3:15-4:45	WH-G002

(*): To send an email to your instructor, click on the link in the Email column of the table.

Below is a partial syllabus with information for all sections that you should know. Your instructor may have a more detailed syllabus about how your section will be run.

Textbook (Required)

Linear Algebra and Its Applications, 6/e, by Lay/McDonald, Pearson+ etext

This course is participating in Binghamton University’s Inclusive Access Program, and your access code will be delivered via the B&N Course Materials link in Brightspace.

You should not purchase access to your Pearson materials unless you have opted out of Binghamton University’s Inclusive Access Program. If you plan to opt out, please do not use the access code that was distributed to you via the B&N Course Materials link through your Brightspace course. If you plan to opt out, but cannot immediately purchase access to your course materials, please use Pearson’s Temporary Access which can be located via your link to MyLab, Mastering, or Revel. Otherwise, please follow the 2-part directions below.

(1) To get started, go to your Brightspace course, and click on the content area for the B&N Course Materials link. Navigate to the Courseware product you'd like to access and click “Reveal access code”. Write down your access code or copy & paste it into a separate word/text file.

(2) Now that you’ve acquired your access code, navigate back to your Brightspace course, and go to the Pearson Access link (MyLab/Mastering/Revel) in your Brightspace course to begin the registration process. When prompted, type in the Access Code you copied/saved and complete your registration process.

The following more detailed instructions have been provided by a Pearson representative. Images of the webpages for each step are available from a pdf file here.

Click Course Tools → Course Materials - B&N First Day

Click Reveal Access Code

Click Copy (under Copy Code)

Navigate back to your MATH 304 course. Scroll to the bottom. Click Course Materials.

Click the Pearson link

Click Access Code

Paste the access code you copied earlier and click Finish

Click Go to My Course

You have successfully enrolled in your course! Please ensure you have access to the eText and Study Plan.

We would like to thank Marissa Rivera, a Pearson representative, who held virtual office hours at the beginning of the semester to help students having trouble accessing the textbook and MyLab homework system.

Additional Textbooks and Resources (Supplemental)

Here are a few additional books that students and instructors may find helpful.

Linear Algebra by Jim Hefferon. One can access additional free resources at the textbook's official website.

A First Course in Linear Algebra by Robert A. Beezer

Elementary Linear Algebra by K.R. Matthews

Linear Algebra by D. Cherney, T. Denton, R. Thomas, and A. Waldron

There are also resources for Linear Algebra on the internet, which may supplement the textbook and homework. For example, the following link takes you to a free website with exercises and feedback on your answers: MathMatize by Jonathan Herman

Approximate Exam Schedule

Each section instructor will decide when it is appropriate to give Exams 1, 2, 3.

Exam 1: The week of February 16, 2026.

Exam 2: The week of March 16, 2026. (Note: The withdraw deadline is March 24.)

Exam 3: The week of April 27, 2026.

Final Exam: Common exam for all sections: Wednesday, May 13, 2026, 8:00 - 10:00 AM, GW-69EX.

Anyone with an illness or special situation that would interfere with taking an exam must contact their instructor as soon as possible (before the exam is best) to explain the situation and schedule a make-up exam if the instructor agrees. Not feeling prepared for an exam is not a valid excuse to miss it. Personal medical information does not need to be given, but some form of verification would help your instructor make an informed decision.

Anyone with a final exam conflict must contact their instructor to make an arrangement.

Additional information about the Final Exam procedures:

You should plan to be at the exam location 15 to 20 minutes before the exam starts. You will be told when you can enter the room and where to sit. Exams will be placed on the seats spaced apart, and students from each section should be sitting together in the same area. That way you can have questions answered by your familiar instructor.

You need to bring only writing instruments (pencils and erasers are recommended). No cellphones, earbuds, smart watches, laptops or other electronic devices will be allowed during the exam, and you may be asked to produce a university ID card to prove your identity. Students who come late will not receive any extra time at the end. Students who have accommodations from the SSD will take this exam at the University Testing Center as scheduled starting at the same time as everyone else.

Having a ride that wants to leave early is NOT a reason for missing the final exam, and will not get a make-up exam or an incomplete.

ONLY A COMPLETE CANCELLATION OF ALL EXAMS BY THE ADMINISTRATION WOULD CHANGE THESE ARRANGEMENTS.

Grades

The course total will be determined as follows:

Quizzes: 15% (Quizzes should be given approximately once per week except in weeks when an exam is given.)

Exam 1: 15%

Exam 2: 15%

Exam 3: 15%

Final Exam: 30%

MyLab Assignments (Common for all sections): 10%

Important: To truly master the material in the course, it is recommended that in addition to the assigned MyLab problems, you should do additional exercises at the end of each section. These will not be graded, but they could be important to your success in the course.

Quizzes are important for students to keep up with the progress of the course and to provide timely feedback on how the material is being absorbed. By ``Assessment Day” enough quizzes should have been taken to evaluate each student's progress and make a risk assessment for early warning about problems.

A 90%, A- 85%, B+ 80%, B 75%, B- 70%, C+ 65%, C 60%, C- 55%, D 50%

Health and Safety Procedures

Binghamton University follows the recommendations of public health experts to protect the health of students, faculty, staff and the community at large. Safeguarding public health depends on each of us strictly following requirements as they are instituted and for as long as they remain in force. Health and safety standards will be enforced in this course.

Current rules make face coverings optional, but when they are worn, they should completely cover both the nose and mouth while indoors (unless they are eating or alone in a private space like an office). A face shield is not an acceptable substitute. Classroom safety requirements will continue to be based on guidance from public health authorities and will be uniformly applied across campus. If these requirements change, a campus-wide announcement will be made to inform the University.

Expected workload

You are expected to spend about 12.5 hours per week on average for this class, including in-class lectures, watching instructional videos, solving homework problems (graded and ungraded), reviewing the material, and preparing for the tests. Expect the work load to be higher than average in the weeks before the exams.

Expected behavior in class

During classes all students are expected to participate in a way that maximizes their learning and minimizes disruptions for their classmates. If you have any concerns, limitations, or circumstances, please communicate with your instructor to find the most appropriate solution.

Academic Code of Honor

For all graded assignments and exams, you are not allowed to use any help not explicitly authorized by your instructor. This includes, but is not limited to, problem-solving websites, notes, help from other people, ChatGPT or other AI programs, etc. All instances of academic dishonesty will be investigated, penalized, and referred to the appropriate University officials for maximal possible punishment. Cheating will not be tolerated.

Getting Help

Disability Information

If you have a disability for which you are or may be requesting an accommodation, please contact both your instructor and the Services for Students with Disabilities office (SSD) (119 University Union, 607-777-2686) as early in the term as possible. Note: extended time for the examinations usually requires special scheduling at the University Testing Center (UTC), and must be arranged by your instructor.

Attendance Policy

The following is a quote from the Binghamton University Catalog concerning attendance policy. Based on this university policy, any student who misses more than 25 percent of the scheduled class meetings of Math 304 (without prior approval from their instructor for the missed classes) may be given a grade of F for the course. Classes missed for religious holidays do not count towards that 25 percent, but excessive time taken for travel or personal convenience may be counted.

VII.B.2. Student Attendance and Classroom Discipline

Reporting Absences

``Students are expected to attend all scheduled classes, laboratories, and discussions. Instructors may establish their own attendance criteria for a course. They may establish the number of unexcused absences permitted to receive credit for the course and the number of absences, after which the final grade may be adjusted downward. In such cases, the instructor is expected to stipulate such requirements in the syllabus and make the syllabus available to students at or near the beginning of classes. In the absence of such statements, instructors have the right to deny a student the privilege of taking the final examination or of receiving credit for the course or may prescribe other academic penalties if the student misses more than 25 percent of the total class sessions. Excessive tardiness may count as an absence” (Policies and Procedures Section of the Binghamton University Academic Guide).

Topics Corresponding to Chapters in our Textbook

Some instructors may follow the textbook more closely than others. Instructors who use their own lecture notes may have exams with different contents than the topics listed below. Be sure to listen to your instructor so you know what topics will be covered on your section exams. Only the final exam will be a common exam for all sections.

Topics for Exam 1	Chapter
Systems of Linear Equations	1.1
Row Reduction and Echelon Forms	1.2
Vector Equations	1.3
Matrix Equations	1.4
Solution Sets of Linear Systems	1.5
Linear Independence	1.7
Linear Transformations	1.8
Standard Matrix for a Linear Transformation	1.9
Matrix Operations	2.1
Invertible Matrices	2.2
Invertible Matrix Theorem	2.3
Topics for Exam 2
Determinants	3.1
Properties of Determinants	3.2
Applications of Determinants (Not responsible for Cramer's Rule or Adjugates)	3.3
Abstract Vector Spaces	4.1
Fundamental Subspaces	4.2
Bases	4.3
Coordinate Systems	4.4
Dimension	4.5
Change of Basis Matrices	4.6
Topics for Exam 3
Eigenvalues and Eigenvectors	5.1
Characteristic Equations	5.2
Diagonalization	5.3
Matrix for a Linear Transformation	5.4
Complex Eigendata	5.5
Inner Products	6.1
Orthogonal Sets	6.2
Orthogonal Projections	6.3
Gram-Schmidt	6.4
Additional Topics
Inner Product Spaces	6.7
Symmetric Matrices	7.1

Syllabi from previous semesters

The syllabus for Math 304 in Fall 2025 is available through this link:

Fall 2025 page

The syllabus for Math 304 in Spring 2025 is available through this link:

Spring 2025 page

The syllabus for Math 304 in Fall 2024 is available through this link:

Fall 2024 page

The syllabus for Math 304 in Spring 2024 is available through this link:

Spring 2024 page

The syllabus for Math 304 in Fall 2023 is available through this link:

Fall 2023 page

The syllabus for Math 304 in Spring 2023 is available through this link:

Spring 2023 page

The syllabus for Math 304 in Fall 2022 is available through this link:

Fall 2022 page

The syllabus for Math 304 in Spring 2022 is available through this link:

Spring 2022 page

The syllabus for Math 304 in Fall 2021 is available through this link:

Fall 2021 page

The syllabus for Math 304 in Spring 2021 is available through this link:

Spring 2021 page

Linear Algebra - Math 304

2025-05-16T14:00:04-04:00

Linear Algebra - Math 304

Spring 2025 -- Course Coordinator: Alex Feingold

1	Stefan Viola	WH-316	Viola	MWF: 8:00-9:30	CW-305
2	Quincy Loney	WH-332	Loney	MWF: 8:00-9:30	WH-G002
3	Quincy Loney	WH-332	Loney	MWF: 9:40-11:10	WH-G002
4	Tan Nhat Tran	WH-209	Tran	MWF: 11:20-12:50	CW-329
5	Stefan Viola	WH-316	Viola	MWF: 11:20-12:50	LH-11
6	Alex Feingold	WH-115	Feingold	MWF: 1:10-2:40	WH-G002
7	Tara Koskulitz	WH-316	Koskulitz	MWF: 2:50-4:20	WH-G002
8	Tara Koskulitz	WH-316	Koskulitz	MWF: 4:30-6:00	WH-G002

(*): To send an email to your instructor, click on the link in the Email column of the table.

Below is a partial syllabus with information for all sections that you should know. Your instructor may have a more detailed syllabus about how your section will be run.

Textbook (Required)

Linear Algebra and Its Applications, 6/e, by Lay/McDonald, Pearson+ etext

This course is participating in Binghamton University’s Inclusive Access Program, and your access code will be delivered via the B&N Course Materials link in Brightspace.

The following more detailed instructions have been provided by a Pearson representative. Images of the webpages for each step are available from a pdf file here.

Click Course Tools → Course Materials - B&N First Day

Click Reveal Access Code

Click Copy (under Copy Code)

Navigate back to your MATH 304 course. Scroll to the bottom. Click Course Materials.

Click the Pearson link

Click Access Code

Paste the access code you copied earlier and click Finish

Click Go to My Course

You have successfully enrolled in your course! Please ensure you have access to the eText and Study Plan.

A representative from Pearson will schedule virtual office hours on zoom to help students having problems registering for MyLab. Dates, times and links will be posted here.

Additional Textbooks and Resources (Supplemental)

Here are a few additional books that students and instructors may find helpful.

Linear Algebra by Jim Hefferon. One can access additional free resources at the textbook's official website.

A First Course in Linear Algebra by Robert A. Beezer

Elementary Linear Algebra by K.R. Matthews

Linear Algebra by D. Cherney, T. Denton, R. Thomas, and A. Waldron

Approximate Exam Schedule (Each section instructor will decide when it is appropriate to give Exams 1, 2, 3.)

Exam 1: The week of February 17, 2025.

Exam 2: The week of March 24, 2025.

Exam 3: The week of April 28, 2025.

Final Exam: Common exam for all sections: Friday, May 9, 2025, 12:50 - 2:50 PM, GW-69EX (West Gym).

Anyone with a final exam conflict must contact their instructor to make an arrangement.

Additional information about the Final Exam procedures:

Having a ride that wants to leave early is NOT a reason for missing the final exam, and will not get a make-up exam or an incomplete.

ONLY A COMPLETE CANCELLATION OF ALL EXAMS BY THE ADMINISTRATION WOULD CHANGE THESE ARRANGEMENTS.

Grades

The course total will be determined as follows:

Quizzes: 15% (Quizzes should be given approximately once per week except in weeks when an exam is given.)

Exam 1: 15%

Exam 2: 15%

Exam 3: 15%

Final Exam: 30%

MyLab Assignments (Common for all sections): 10%

A 90%, A- 85%, B+ 80%, B 75%, B- 70%, C+ 65%, C 60%, C- 55%, D 50%

Health and Safety Procedures Due to COVID Pandemic

Expected workload

Expected behavior in class

Academic Code of Honor

For all graded assignments and exams, you are not allowed to use any help not explicitly authorized by your instructor. This includes, but is not limited to, problem-solving websites, notes, help from other people, ChatGPT or other AI programs, etc. All instances of academic dishonesty will be investigated, penalized, and referred to the appropriate University officials for maximal possible punishment. Cheating will not be tolerated.

Getting Help

Disability Information

If you have a disability for which you are or may be requesting an accommodation, please contact both your instructor and the Services for Students with Disabilities (SSD) office (119 University Union, 607-777-2686) as early in the term as possible. Note: extended time for the examinations usually requires special scheduling at the University Testing Center (UTC).

Topics Corresponding to Chapters in our Textbook

Topics for Exam 1	Chapter
Systems of Linear Equations	1.1
Row Reduction and Echelon Forms	1.2
Vector Equations	1.3
Matrix Equations	1.4
Solution Sets of Linear Systems	1.5
Linear Independence	1.7
Linear Transformations	1.8
Standard Matrix for a Linear Transformation	1.9
Matrix Operations	2.1
Invertible Matrices	2.2
Invertible Matrix Theorem	2.3
Topics for Exam 2
Determinants	3.1
Properties of Determinants	3.2
Applications of Determinants (Not responsible for Cramer's Rule or Adjugates)	3.3
Abstract Vector Spaces	4.1
Fundamental Subspaces	4.2
Bases	4.3
Coordinate Systems	4.4
Dimension	4.5
Change of Basis Matrices	4.6
Topics for Exam 3
Eigenvalues and Eigenvectors	5.1
Characteristic Equations	5.2
Diagonalization	5.3
Matrix for a Linear Transformation	5.4
Complex Eigendata	5.5
Inner Products	6.1
Orthogonal Sets	6.2
Orthogonal Projections	6.3
Gram-Schmidt	6.4
Additional Topics
Inner Product Spaces	6.7
Symmetric Matrices	7.1

Syllabi from previous semesters

The syllabus for Math 304 in Spring 2025 is available through this link:

Spring 2025 page

The syllabus for Math 304 in Fall 2024 is available through this link:

Fall 2024 page

The syllabus for Math 304 in Spring 2024 is available through this link:

Spring 2024 page

The syllabus for Math 304 in Fall 2023 is available through this link:

Fall 2023 page

The syllabus for Math 304 in Spring 2023 is available through this link:

Spring 2023 page

The syllabus for Math 304 in Fall 2022 is available through this link:

Fall 2022 page

The syllabus for Math 304 in Spring 2022 is available through this link:

Spring 2022 page

The syllabus for Math 304 in Fall 2021 is available through this link:

Fall 2021 page

The syllabus for Math 304 in Spring 2021 is available through this link:

Spring 2021 page

Linear Algebra - Math 304

2025-12-13T10:19:03-04:00

Linear Algebra - Math 304

Fall 2025 -- Course Coordinator: Alex Feingold

Sec	Instructor	Office	Email(*)	Meets	Room
1	Michael Dobbins	WH-214	Dobbins	MWF: 8:00-9:30	WH-G002
2	Hung Tong-Viet	WH-108	Tong-Viet	MWF: 9:45-11:15	WH-G002
3	Ryan McCulloch	WH-335	McCulloch	MWF: 11:45-1:15	WH-G002
4	Minghao Rostami	WH-128	Rostami	MWF: 1:30-3:00	LN 1406
5	Eugenia Sapir	WH-213	Sapir	MWF: 1:30-3:00	WH-G002
6	Alex Feingold	WH-115	Feingold	MWF: 3:15-4:45	WH-G002
7	Jason Shaw	WH-224	Shaw	MWF: 5:00-6:30	WH-G002

(*): To send an email to your instructor, click on the link in the Email column of the table.

Below is a partial syllabus with information for all sections that you should know. Your instructor may have a more detailed syllabus about how your section will be run.

Textbook (Required)

Linear Algebra and Its Applications, 6/e, by Lay/McDonald, Pearson+ etext

This course is participating in Binghamton University’s Inclusive Access Program, and your access code will be delivered via the B&N Course Materials link in Brightspace.

The following more detailed instructions have been provided by a Pearson representative. Images of the webpages for each step are available from a pdf file here.

Click Course Tools → Course Materials - B&N First Day

Click Reveal Access Code

Click Copy (under Copy Code)

Navigate back to your MATH 304 course. Scroll to the bottom. Click Course Materials.

Click the Pearson link

Click Access Code

Paste the access code you copied earlier and click Finish

Click Go to My Course

You have successfully enrolled in your course! Please ensure you have access to the eText and Study Plan.

Additional Textbooks and Resources (Supplemental)

Here are a few additional books that students and instructors may find helpful.

Linear Algebra by Jim Hefferon. One can access additional free resources at the textbook's official website.

A First Course in Linear Algebra by Robert A. Beezer

Elementary Linear Algebra by K.R. Matthews

Linear Algebra by D. Cherney, T. Denton, R. Thomas, and A. Waldron

Approximate Exam Schedule (Each section instructor will decide when it is appropriate to give Exams 1, 2, 3.)

Exam 1: The week of September 15, 2025.

Exam 2: The week of October 20, 2025.

Exam 3: The week of November 17, 2025.

Final Exam: Common exam for all sections: Tuesday, December 9, 2025, 8:05 - 10:05 PM, GW-69EX (West Gym).

Anyone with a final exam conflict must contact their instructor to make an arrangement.

Additional information about the Final Exam procedures:

Having a ride that wants to leave early is NOT a reason for missing the final exam, and will not get a make-up exam or an incomplete.

ONLY A COMPLETE CANCELLATION OF ALL EXAMS BY THE ADMINISTRATION WOULD CHANGE THESE ARRANGEMENTS.

Grades

The course total will be determined as follows:

Quizzes: 15% (Quizzes should be given approximately once per week except in weeks when an exam is given.)

Exam 1: 15%

Exam 2: 15%

Exam 3: 15%

Final Exam: 30%

MyLab Assignments (Common for all sections): 10%

A 90%, A- 85%, B+ 80%, B 75%, B- 70%, C+ 65%, C 60%, C- 55%, D 50%

Health and Safety Procedures Due to COVID Pandemic

Expected workload

Expected behavior in class

Academic Code of Honor

For all graded assignments and exams, you are not allowed to use any help not explicitly authorized by your instructor. This includes, but is not limited to, problem-solving websites, notes, help from other people, ChatGPT or other AI programs, etc. All instances of academic dishonesty will be investigated, penalized, and referred to the appropriate University officials for maximal possible punishment. Cheating will not be tolerated.

Getting Help

Disability Information

Topics Corresponding to Chapters in our Textbook

Topics for Exam 1	Chapter
Systems of Linear Equations	1.1
Row Reduction and Echelon Forms	1.2
Vector Equations	1.3
Matrix Equations	1.4
Solution Sets of Linear Systems	1.5
Linear Independence	1.7
Linear Transformations	1.8
Standard Matrix for a Linear Transformation	1.9
Matrix Operations	2.1
Invertible Matrices	2.2
Invertible Matrix Theorem	2.3
Topics for Exam 2
Determinants	3.1
Properties of Determinants	3.2
Applications of Determinants (Not responsible for Cramer's Rule or Adjugates)	3.3
Abstract Vector Spaces	4.1
Fundamental Subspaces	4.2
Bases	4.3
Coordinate Systems	4.4
Dimension	4.5
Change of Basis Matrices	4.6
Topics for Exam 3
Eigenvalues and Eigenvectors	5.1
Characteristic Equations	5.2
Diagonalization	5.3
Matrix for a Linear Transformation	5.4
Complex Eigendata	5.5
Inner Products	6.1
Orthogonal Sets	6.2
Orthogonal Projections	6.3
Gram-Schmidt	6.4
Additional Topics
Inner Product Spaces	6.7
Symmetric Matrices	7.1

Syllabi from previous semesters

The syllabus for Math 304 in Spring 2025 is available through this link:

Spring 2025 page

The syllabus for Math 304 in Fall 2024 is available through this link:

Fall 2024 page

The syllabus for Math 304 in Spring 2024 is available through this link:

Spring 2024 page

The syllabus for Math 304 in Fall 2023 is available through this link:

Fall 2023 page

The syllabus for Math 304 in Spring 2023 is available through this link:

Spring 2023 page

The syllabus for Math 304 in Fall 2022 is available through this link:

Fall 2022 page

The syllabus for Math 304 in Spring 2022 is available through this link:

Spring 2022 page

The syllabus for Math 304 in Fall 2021 is available through this link:

Fall 2021 page

The syllabus for Math 304 in Spring 2021 is available through this link:

Spring 2021 page

Linear Algebra - Math 304

2023-07-13T01:28:28-04:00

Linear Algebra - Math 304

Spring 2023 -- Course Coordinator: Quincy Loney

Sec	Instructor	Office	Email(*)	Meets	Room
1	Sarah Lamoureux	WH-326	Lamoureux	MWF: 8:00-9:30	OH-G102
2	Luke Elliott	WH107	Elliott	MWF: 8:00-9:30	CW-204
3	Quincy Loney	WH-332	Loney	MWF: 9:40-11:10	WH-G002
4	Wei Yang	WH-326	Yang	MWF: 11:20-12:50	AA-G007
5	Quincy Loney	WH-332	Loney	MWF: 11:20-12:50	WH-G002
6	Sarah Lamoureux	WH-326	Lamoureux	MWF: 1:10-2:40	CW-321
7	Quincy Loney	WH-332	Loney	MWF: 2:50-4:20	WH-G002
8	Thomas Zaslavsky	WH-216	Zaslavsky	MWF: 4:00-5:30	LH-005

(*): To send an email to your instructor, click on the link in the Email column of the table.

Below is a partial syllabus with information for all sections that you should know. Your instructor may have a more detailed syllabus about how your section will be run.

Textbook (Required)

The Math 304: Linear Algebra zyBook for Spring 2023. To purchase the zyBook for your section:

1. Sign in or create an account at learn.zybooks.com using your binghamton.edu e-mail address.

2. Enter the zyBook code given to you by your instructor.

3. Subscribe for $58.

Additional Textbooks and Resources (Supplemental)

Here are a few additional books that students and instructors may find helpful.

Linear Algebra by Jim Hefferon. One can access additional free resources at the textbook's official website.

A First Course in Linear Algebra by Robert A. Beezer

Elementary Linear Algebra by K.R. Matthews

Linear Algebra by D. Cherney, T. Denton, R. Thomas, and A. Waldron

Three evening exams during the semester, and a Final Exam during final exams week, will be scheduled. Details are as follows:

Exam 1: Wednesday, February 15, LH-1, 8:15-9:45 PM

Exam 2: Wednesday, March 15, LH-1, 8:15-9:45 PM

Exam 3: Wednesday, April 26, LH-1, 8:15-9:45 PM

Final Exam: Tuesday, May 09, LH-1, 8:00-10:00 AM

Anyone with a final exam conflict must contact their instructor to make an arrangement.

Please arrive 10 minutes early for each exam to allow time for seating, and always bring your university ID. No calculators, cellphones or computers will be allowed during exams. A student who needs to leave the exam room during an exam must leave their cellphone in the room. Use of a cellphone to get answers to exam questions during an exam is cheating and will be treated as a violation of university honesty rules.

Grades

The course total will be determined as follows:

Quizzes: 15% (Quizzes should be given approximately once per week except in weeks when an exam is given.)

Exam 1: 15%

Exam 2: 15%

Exam 3: 15%

Final Exam: 30%

zyBook Assignments: 10% (Participation Activities (orange): 5% & Challenge Activities (blue) 5%)

Important: Besides the zyBook Participation and Challenge Activities, you should do the Additional Exercises (black) at the end of each section. This will not be graded, but it could be important to your success in the course.

A 90%, A- 85%, B+ 80%, B 75%, B- 70%, C+ 65%, C 55%, C- 50%, D 45%

Health and Safety Procedures Due to COVID Pandemic

Expected workload

Expected behavior in class

Academic Code of Honor

Getting Help

Disability Information

Topics	Text	Problems
Introduction, preview, examples; linear combination	Hefferon Ch. 1, I.1	1:I.1.17,19,21
Gaussian elimination (reduction)	Hefferon Ch. 1, I.1	1:I.1.22,24,27,32
(Augmented) matrix of a system, solution set	Hefferon Ch. 1, I.2	1:I.2.15,16,17,18,21,25
Basic logic: statements, connectives, quantifiers	Hefferon Appendix
Set theory, general functions	Hefferon Appendix
Homogeneous and non-homogeneous systems (no formal induction in Lemma 3.6)	Hefferon Ch. 1, I.3	1:I.3.15,17,18,20,21,24
Points, vectors, lines, planes	Hefferon Ch. 1, II.1	1:II.1.1,2,3,4,7
Distance, dot product, angles, Cauchy-Schwarz and Triangle Inequalities	Hefferon Ch. 1, II.2	1:II.2.11,12,14,16,17,21,22
Gauss-Jordan reduction, reduced row echelon form	Hefferon Ch. 1, III.1	1:III.1.8,9,10,12,13,14,15
Linear combination lemma, uniqueness of RREF (no proofs of 2.5, 2.6)	Hefferon Ch. 1, III.2	1:III.2.11,14,20,21,24
Matrix operations, including the transpose. Linear system as a matrix equation	Matthews 2.1	3:III.1.13,14,15,16
Linear maps (transformations) given by matrices	Matthews 2.2	3:III.1.19; 3:III.2.12,17,30
Vector spaces: definition, examples	Hefferon Ch. 2, I.1	2:I.1.17,18,19,21,22,29,30
Linear maps between vector spaces	Hefferon Ch. 3, II.1	3:II.1.18,19,20,22,24,25,26,28
Subspaces. Span	Hefferon Ch. 2, I.2	2:I.2.20,21,23,25,26,29,44,45
Linear independence	Hefferon Ch. 2, II.1	2:II.1.21,22,25,28
Properties of linear independence	Hefferon Ch. 2, II.1	2:II.1.29,30,32,33
Basis of a vector space	Hefferon Ch. 2, III.1	2:III.1.20,21,22,23,24,25,26,30,31,34
Dimension of a vector space	Hefferon Ch. 2, III.2	2:III.2.15,16,17,18,19,20,21,24,25,28
Column space, row space, rank	Hefferon Ch. 2, III.3	2:III.3.17,18,19,20,21,23,29,32,39
Range space and Kernel (Null space)	Hefferon Ch. 3, II.2	3:II.2.21,23,24,26,31,35
Invertible matrices: definition, equivalent conditions; inverse matrix	Hefferon Ch.3, IV.4	3:IV.4.13,14,15,16,17,18,19,26,29
Elementary matrices. Row reduction using elementary matrices	Hefferon Ch. 3, IV.3; CDTW Ch. 2, 2.3	3:IV.3.24,25,32
Determinant of a matrix, properties	Hefferon Ch. 4, I.1, I.2	4:I.1.1,3,4,6,9; 4:I.2.8,9,12,13,15,18
More on Determinants	Hefferon Ch. 4, II.1, III.1	4:III.1.11,14,16,17,20,21,22
Matrix of a linear transformation, matrix of the composition, inverse	Hefferon Ch. 3, III.1, IV.2	3:III.1.13,17,18,19,21,23
Change of basis, similar matrices	Hefferon Ch. 3, V.1, V.2; Ch. 5, II.1	3:V.1.7,9,10,12; 5:II.1.5,8,11,13,14
Complex numbers	Matthews 5.1–5.6	Matthews 5.8.1,2,5,6,7,9
Eigenvectors, eigenvalues, eigenspaces for matrices and linear operators. Characteristic polynomial	Matthews 6.1, 6.2; Hefferon Ch. 5, II.3	5:II.3.23,24,25,26,27,28,29,30,31
Diagonalization of matrices	Hefferon Ch. 5, II.2, II.3	5:II.3.22,33,36,46
Orthogonal and orthonormal bases of $R^n$ and its subspaces; orthogonal matrices	Hefferon Ch. 3, VI.1, VI.2	3:VI.1.6,7,17,19; 3:VI.2.10
Orthogonal complement of a subspace, orthogonal projection	Hefferon Ch. 3, VI.3	3:VI.3.11,12,13,14,26,27
Gram-Schmidt process; orthogonal diagonalization of matrices	Hefferon Ch. 3, VI.2	3:VI.2.13,15,17,18,19,22

Linear Algebra - Math 304

2019-01-22T14:42:57-04:00

Linear Algebra - Math 304

Fall 2018

Section	Instructor	Office	Office Hours	Phone	E-mail (Note*)	Meets	Room
1	Daniel Rossi	WH-107	M 1-2, W 11-12, Th 5-6		rossi	8:00-9:30	LH-12
2	Quincy Loney	WH-332	W 11:20-12:50	444-1529	quincy	9:40-11:10	LH-12
3	Adrian Vasiu	WH-111	Tu: 3:20–3:50, Wed: 3:30–5:00, Th: 2–3	777-6036	adrian	11:20-12:50	LH-12
4	Thomas Zaslavsky	WH-216	MWF 3:00-4:15, and by appointment.	777-2201	zaslav	1:10-2:40	LH-12
5	Alex Feingold	WH-115	MWF 1:10-2:10	777-2465	alex	2:50-4:20	LH-12
6	Alex Feingold	WH-115	MWF 1:10-2:10	777-2465	alex	4:40-6:10	LH-12

Click on the section number to get to a web-page for that section (if there is one).

(Note*): Each email address in this table is of the form xxx@math.binghamton.edu but that should happen automatically if you just click on the link.

Here is the detailed syllabus for all sections with course rules that you should know.

Three evening exams during the semester, and a Final Exam during final exams week, will be scheduled. Details are as follows:

Exam 1: Wed, Sept 26, 8:30 - 10:00 PM, LH-1 (Sections 1-4) and LH-14 (Sections 5,6)

Exam 2: Wed, Oct 31, 8:30 - 10:00 PM, LH-1 (Sections 1-4) and LH-14 (Sections 5,6)

Exam 3: Wed, Nov 28, 8:30 - 10:00 PM, LH-1 (Sections 1-4) and LH-14 (Sections 5,6)

Final Exam: Tuesday, Dec. 11, 2018, 10:25 AM - 12:25 PM, GW-69EX (West Gym)

Notes

Here are some short notes for the course written by Prof. Mazur.

Homework

Online homework will be done using WebWork. (Note that this is a new server with the address webwork.math.binghamton.edu/webwork2/Math_304_Fall_2018)

Homework 0, intended to familiarize you with the program, will be posted by the first day of the course.

Your WebWork account username is the pre@ portion of your binghamton.edu e-mail account. Your initial password is the same as the username. Make sure to change it as soon as possible to a secure password, and save that choice where it will not be lost.

For example, if your Binghamton e-mail account is xyzw77@binghamton.edu then

username: xyzw77
password: xyzw77

Login to WebWork now, and change your password. If you registered after August 20, 2018, you have to send an e-mail to alex with subject “WebWork” and provide your first and last name, Binghamton e-mail address and section number in order to have an account on WebWork.

Expected workload outside of the classroom

Expected behaviour in class

During classes students are expected to behave according to university rules. Some students feel free to use their cellphones during class, but most professors find that insulting, and it certainly prevents students from concentrating on the lecture. Any professor who sees a student using a cellphone instead of paying attention can ask the student to put the cellphone away, or can take it until the end of class. Addiction to cellphones is a serious condition affecting many people! It is allowed for students to use cellphones to photograph notes from the board. Some students may use laptop computers to take notes, but they should be careful not to use them for internet browsing during class. Each instructor has the final decision about what to allow in the classroom.

Resources for help with personal problems

The following link to a webpage of the Dean of Students contains important contact information for sources of help if you are having personal problems.

Dean of Students Help Page

Announcements

August 22: First Day of Classes: After meeting your instructor you should have been given this webpage address to check for the syllabus and instructions. Step 1: Read the entire syllabus, including the detailed syllabus at the first link on this page. Step 2: Click on the link for Webworks, set up a secure password and try the Chapter 0 homework assignment, which will get you used to the Webwork system. Step 3: Attend all classes and keep up with all homework corresponding to your section lectures.

September 6: Quiz 1 and its solutions for Sections 5 and 6 (Feingold) can be seen through the following link: Quiz 1 and its solutions.

September 12: Quiz 2 and its solutions for Sections 5 and 6 (Feingold) can be seen through the following link: Quiz 2 and its solutions.

September 18: Quiz 3 and its solutions for Sections 5 and 6 (Feingold) can be seen through the following link: Quiz 3 and its solutions.

September 21: Quiz 4 and its solutions for Sections 5 and 6 (Feingold) can be seen through the following link: Quiz 4 and its solutions.

September 21: A Practice Exam 1 and its solutions for all sections can be seen through the following link: Practice Exam 1 and its solutions.

September 30: Solutions for Exam 1 can be seen through the following link: Exam 1 Solutions. A graph showing the distribution of scores from all sections, and lines indicating the letter grade interpretation of the numerical score, can be found through the following link: Exam 1 Score Distribution and Letter Grade Interpretation. The following table summarizes the letter grade interpretation of the numerical score. Average for all sections was 48.47 out of 75.

Grade	Score Range
A	67 - 75
A-	63 - 66
B+	58 - 62
B	52 - 57
B-	48 - 51
C+	45 - 47
C	40 - 44
C-	35 - 39
D	30 - 34
F	0 - 29

The purpose of these letter grades is to give you an idea of where your score puts you in relation to the rest of the class, and to help you decide whether to withdraw from the course or to work harder. Finally, in order to give students more time to complete the homework assignments from Chapter 2, the deadline for those assignments has been extended until 5:00 PM on Friday, Oct. 5.

October 8: Quiz 5 and its solutions for Sections 5 and 6 (Feingold) can be seen through the following link: Quiz 5 and its solutions.

October 22: Quiz 6 and its solutions for Sections 5 and 6 (Feingold) can be seen through the following link: Quiz 6 and its solutions.

October 24: Some practice problems suggested by Dr. Quincy Loney for Exam 2 (with solutions) can be seen through the following link: Quincy Loney Practice Questions for Exam 2 with Solutions.

October 24: Some practice problems suggested by Dr. Dan Rossi for Exam 2 (without solutions) can be seen through the following link: Dan Rossi Practice Questions for Exam 2.

October 24: A Practice Exam 2 and its solutions written by Prof. Feingold can be seen through the following link: Practice Exam 2 and its solutions.

October 27: Some practice problems suggested by Prof. Adrian Vasiu for Exam 2 (without solutions) can be seen through the following link: Adrian Vasiu Practice Questions for Exam 2.

October 27: Quiz 7 and its solutions for Sections 5 and 6 (Feingold) can be seen through the following link: Quiz 7 and its solutions.

October 29: Dear Students: Exam 2 will consist of 9 problems. You are strongly encouraged to study in detail the Practice Exams 2 posted here and proposed by Professors Feingold and Vasiu. Additional practice problems proposed by Doctors Loney and Rossi are also posted above. We hope very much that you will prepare well for this exam. The instructors of Math 304.

October 30: The solutions to the practice problems suggested by Dr. Dan Rossi for Exam 2 can be seen through the following link: Dan Rossi Practice Solutions for Exam 2.

November 9: Solutions for Exam 2 can be seen through the following link: Exam 2 Solutions. A graph showing the distribution of scores from all sections, and lines indicating the letter grade interpretation of the numerical score, can be found through the following link: Exam 2 Score Distribution and Letter Grade Interpretation. The following table summarizes the letter grade interpretation of the numerical score. Average for all sections was 44.6 out of 75.

Grade	Score Range
A	65 - 75
A-	60 - 64
B+	55 - 59
B	50 - 54
B-	45 - 49
C+	42 - 44
C	37 - 41
C-	32 - 36
D	27 - 31
F	0 - 26

November 18: Quiz 8 and its solutions for Sections 5 and 6 (Feingold) can be seen through the following link: Quiz 8 and its solutions.

November 20: Practice problems for Exam 3 (with some solutions) can be seen through the following link: Exam 3 Practice Problems and some solutions. If some of these problems confuse you, ask your instructor to go over them. That is the purpose of review sessions. The only written solutions made available for these problems are the ones in the file already.

November 27: Quiz 9 and its solutions for Sections 5 and 6 (Feingold) can be seen through the following link: Quiz 9 and its solutions.

December 4: Solutions for Exam 3 can be seen through the following link: Exam 3 Solutions. A graph showing the distribution of scores for Exam 3 from all sections, and lines indicating the letter grade interpretation of the numerical score, can be found through the following link: Exam 3 Score Distribution and Letter Grade Interpretation. The following table summarizes the letter grade interpretation of the numerical score. Average for all sections was 50.39 out of 75.

Grade	Score Range
A	67 - 75
A-	63 - 66
B+	58 - 62
B	52 - 57
B-	48 - 51
C+	45 - 47
C	40 - 44
C-	35 - 39
D	30 - 34
F	0 - 29

December 6: Quiz 10 and its solutions for Sections 5 and 6 (Feingold) can be seen through the following link: Quiz 10 and its solutions. Note: This quiz concerns a Gram-Schmidt orthogonalization process, and a projection to a subspace W using the orthogonal basis of W obtained in part (1), so it is good practice for these topics from Chapter 6.

December 6: Two Math 304 tutors have sent me the following information about a review session planned for this weekend. Jonathan Chen and Rachel Stuttman will hold a review session for the final this Sunday, Dec. 9, 2-5pm in LH-9. All are welcome (no need to sign up ahead of time) and should come with questions.

December 10: Dr. Quincy Loney has provided a long list of True/False questions with answers to help you study for the final exam. The file is available through the following link: Loney True/False Final Exam questions and solutions.

December 18: The following table summarizes the letter grade interpretation of the numerical score for the Final Exam. Average for five out of six sections was 106.5 out of 200.

Grade	Score Range
A	170 - 200
A-	155 - 169
B+	145 - 154
B	135 - 144
B-	125 - 134
C+	115 - 124
C	100 - 114
C-	88 - 99
D	78 - 87
F	0 - 77

The following table summarizes the letter grade interpretation of the numerical score for the Quiz totals. Average for five out of six sections was 44.85 out of 75. Since different sections had different quizzes, administered different ways (not uniformly given or graded), some normalization of the raw scores was used before the numbers were added to the exam scores.

Grade	Score Range
A	65 - 75
A-	60 - 64
B+	55 - 59
B	50 - 54
B-	45 - 49
C+	40 - 44
C	35 - 39
C-	30 - 34
D	25 - 29
F	0 - 24

The following table summarizes the letter grade interpretation of the numerical score for the Course Total Scores. Average for five out of six sections was 300 out of 500.

Grade	Score Range
A	435 - 500
A-	400 - 434
B+	370 - 399
B	340 - 369
B-	310 - 339
C+	285 - 309
C	250 - 284
C-	220 - 249
D	190 - 219
F	0 - 189

Fall 2015 page

Fall 2018 page

Math: Undergraduate Program

2026-03-06T21:47:18-04:00

Undergraduate Program

Start here

This page is for current and incoming Binghamton students who need the practical details of the Mathematics & Statistics majors and minor: forms, policies, and course-planning tools. For an overview of the program and tracks, see the university program page.

If you are:

A prospective student or still exploring whether to study Math/Statistics at Binghamton.

Start with the program overview on the university site. To visit the department and talk with faculty, contact the department secretary.

Thinking about declaring, dropping, or changing a major or minor in Math/Statistics.

Go to Section 3, “Declare, Drop, or Change Major/Minor”.

Already a Math/Statistics major or minor and planning your courses.

Go to Section 5, “Course Selection and Registration”.

Need non-department help? See Harpur Advising (general advising) and Registrar (records/transcripts).

1. Degree Options and Requirements

The Department of Mathematics and Statistics offers seven degree options:

BA and BS in Mathematical Sciences, each with three tracks:
- Mathematics
- Data Science and Statistics (DSS)
- Actuarial Science
Minor in Mathematics

BA vs. BS in Mathematics

Both degrees require the same total credits—the BS simply includes more math courses. Neither is superior; they serve different goals.

BA: Fewer math courses, more flexibility to explore other fields. Often the most efficient path to a double major or dual degree.
BS: More upper-level and proof-oriented coursework. Designed for students aiming at graduate study in mathematics, statistics, or related fields.

For a comprehensive and official description of all program requirements, consult the Academic Guide (BA, BS, Minor).

Be sure to also review the Harpur College requirements and the grade requirements for courses and prerequisites.

2. Combining Math with Other Fields

A math degree pairs naturally with many disciplines. Common combinations include:

Actuarial Science + Economics: These programs heavily overlap.
Mathematics + Computer Science: A math major with a CS minor, or vice versa.

Students can also pursue a double degree across schools—for example, a BS in Business Administration (School of Management) with a BA in Mathematics, or a Watson School CS degree with a math degree. See Harpur's double degree information for details.

For minors outside our department, consult that department for their requirements.

3. Declare, Drop, or Change Major/Minor

You must be admitted to Harpur College of Arts and Sciences before declaring a major in Mathematics and Statistics.

To declare or drop a major or minor, fill in this Google Form.

BS majors: Before declaring, you must meet with a faculty member. If you haven't done so yet but need to declare now, consider declaring a BA first and switching to BS later.

To change from one major to another, drop the old major and declare the new one. Note that you can only hold one major from our department at a time.

4. Forms and Resources

Major and Minor

Major/Minor Declaration, Drop, and Change Form

Course Registration

Math 225/227 Second Half-Semester Signup Form — For registering in 225 or 227 without the 224/226 co-requisite when the stand-alone section doesn't fit your schedule.
Prerequisite Exception Request Form
Request to Take a Graduate Course — You must first obtain the instructor's consent, then visit the math department office for paperwork. To count a graduate course toward your major requirements, email the DUS after you have registered.
Undergraduate Independent Study (Math 497) Form — Find a faculty member willing to supervise, then visit the math department office. Note that there is a limit on how many independent study credits can count toward the major.

5. Course Selection and Registration

Plan your coursework around two things: prerequisites (which are strictly enforced in our department) and semester availability (some courses are only offered in fall or spring). Missing either can delay graduation.

Advice for New Majors

Complete Math 330 (Number Systems) as soon as possible — no later than your fourth semester. Finish Math 304 (Linear Algebra) and Math 323 (Calculus III) before moving to upper-level courses. Plan for about two math courses per semester and meet with your faculty advisor regularly.

For track-specific course planning, see Course Planning by Track.

Getting Into Closed Courses

If a course has a waiting list, add yourself to the waitlist for the section you prefer. When a seat opens, the system emails the student at the top of the list, who has 18 hours to register from the time the email is sent (not when you open it). If you see an open seat but cannot register, it is likely reserved for someone ahead of you on the waitlist — be patient and check your email frequently. Do not try to switch sections while waitlisted; doing so will drop you to the bottom of the list.

If a course is closed with no waiting list, monitor the Schedule of Classes during open registration and self-register if a spot appears.

For additional help, contact the math department secretaries in Whitney Hall. Neither your instructor nor your faculty advisor can place you in a full course.

Useful Resources

Prerequisite Dependency Infographic
Course Planning by Track
Sample 4-Year Plans by Track
Unofficial course schedules for the Department of Mathematics and Statistics
Schedule of Classes — Search for courses by term and subject (Binghamton login required)
Academic Guide — Official course descriptions and program requirements
Past course syllabi by semester

6. Summer and Winter Sessions

The department offers online math courses during summer and winter sessions. All courses are synchronous (live scheduled meetings, not self-paced). See the department course schedule for current offerings and session dates.

Final exams: Some courses require an in-person final exam on campus in Binghamton. The department does not cover travel or lodging costs. A very limited off-campus proctoring exception may be approved in advance. Details and exception request form.

Courses without an in-person final use Zoom with LockDown Browser for exams. No remote/virtual proctoring is available for in-person finals.

7. Information Regarding Calculus

More details about some important Calculus courses

8. Credit Transfer and Exam Credit

Exam Credit (AP / IB / CLEP)

Binghamton's policies and equivalencies are maintained by Harpur Advising:

Transfer Credit from Another Institution

First, check the Pre-Approved Transfer Table — select the institution and course. If your course appears with the correct BU equivalent, you typically do not need a separate petition.

If not pre-approved, get department approval before registering for the course:

Fill out the Harpur Transfer Credit Petition form and save as a PDF (not a photo/screenshot).
Email it to the Director of Undergraduate Studies, Prof. Vladislav Kargin (vkargin@binghamton.edu), and include:
- Current syllabus
- Link to the course catalog or department page
- When you plan to take the course

Online asynchronous courses are generally not approved for transfer.
Upper-level courses (Math 330 and above) are rarely approved for transfer.
Courses from non-US institutions are generally not approved unless part of a regular degree-granting curriculum or an approved Binghamton-affiliated program (e.g., BU study abroad). Standalone summer or winter courses abroad are not accepted.

9. Accelerated (4+1) Programs

Binghamton's 4+1 programs let qualified students earn a bachelor's + master's degree in about five years. See Combined Degree Programs (4+1) for general eligibility and policies.

Math-related options include:

10. Planning for Graduate School

If you are considering graduate school in mathematics, statistics, or a related field, start planning early.

Choose the right courses. Performance in Real Analysis I and II (Math 478/479) is widely used by admissions committees to gauge a student's potential — even for statistics and applied math programs. Beyond Real Analysis, the courses that matter most depend on the discipline you're targeting:

Mathematics: The BS track is strongly recommended. Its required courses (Modern Algebra, Topology, Real Analysis) form the standard preparation.
Statistics or Actuarial Science: A BA may be sufficient, but a BS or additional coursework beyond BA requirements is preferred. Do well in Math 447 (Probability) and Math 448 (Mathematical Statistics).
Data Science: In addition to probability and statistics, consider extra coursework in computer science and computational methods.

Pursue research experience. REU (Research Experiences for Undergraduates) programs are competitive summer research opportunities funded by the NSF and hosted by universities across the country. They strengthen graduate applications significantly and give you a taste of what research is like. Most REU applications are due in January–February for the following summer, so start looking in the fall. Sophomores and juniors are the strongest candidates. You can also approach faculty in our department directly to ask about research projects suitable for undergraduates. See this list of REU programs for current and past opportunities.

Plan your recommendation letters. You will need letters from faculty who know your work well. Think ahead about which courses and professors will give you that opportunity — a professor who taught a course in which you earned a B or lower may decline to write, or write a letter that does not help your application.

Explore your options. Math majors pursue graduate degrees in many fields, including mathematics, statistics, actuarial science, computer science, data science, operations research, economics, finance, and management science. Talk with your faculty advisor and read about programs early in your junior year.

11. Faculty Advisors

You can get advising in several ways, depending on the question:

Faculty advisor (assigned when you declare the major).
- Every major is assigned a faculty advisor at the time of declaration.
- Meet with your advisor to plan courses, choose electives, and discuss goals (graduate school, careers, etc.).
- You may switch to another faculty advisor later, after you get to know the faculty.

Advising Liaison (especially for pre-majors / lower-division).
- David Biddle (biddle@math.binghamton.edu) is the department's Coordinator of Undergraduate Advising.
- He is the primary contact for students exploring the major (not yet declared) and for majors still completing mostly lower-level coursework.

Director of Undergraduate Studies (DUS) — policies and exceptions.
- The DUS handles department decisions such as transfer-course approvals, prerequisite exceptions, and DegreeWorks exceptions.
- Current DUS: Prof. Vladislav Kargin (vkargin@binghamton.edu).

12. Honors, Awards and Scholarships

We recognize students through graduation with departmental honors and several annual awards/scholarships.

13. Student Organizations and Activities

The students in the Department of Mathematics and Statistics frequently participate in the following organizations and in a wide range of activities.

The Undergraduate Math Club and MAA student chapter
The Association for Women in Mathematics Student Chapter
The Data Science and Analytics Club
The Actuarial Association
The Binghamton Chapter of Pi Mu Epsilon, the National Mathematics Honor Society.

Linear Algebra - Math 304

2022-01-19T10:30:10-04:00

Linear Algebra - Math 304

Fall 2021 - Course Coordinator: Prof. Alex Feingold

Sec	Instructor	Office	Email(*)	Meets	Room
1	Fikreab Admasu	WH-107	Admasu	MWF:8:00-9:30	WH-G002
2	Fikreab Admasu	WH-107	Admasu	MWF:9:40-11:10	WH-G002
3	Alex Feingold	WH-115	Feingold	MWF:11:20-12:50	WH-G002
4	Quincy Loney	WH-332	Loney	MWF:1:10-2:40	WH-G002
5	Matthew Haulmark	WH-202	Haulmark	MWF:2:50-4:20	WH-G002
6	Thomas Zaslavsky	WH-216	Zaslavsky	MWF:4:40-6:10	WH-G002

(*): To send an email to your instructor, click on the link in the Email column of the table.

If a section has its own detailed syllabus webpage, a link to that page will be provided under the Instructor column of the table above.

Below is a partial syllabus with information for all sections that you should know. Your instructor may have a more detailed syllabus about how your section will be run.

Health and Safety Procedures Due to COVID Pandemic

Current rules require everyone to wear a face covering that completely covers both the nose and mouth while indoors (unless they are eating or alone in a private space like an office). A face shield is not an acceptable substitute. Classroom safety requirements will continue to be based on guidance from public health authorities and will be uniformly applied across campus. If these requirements change, a campus-wide announcement will be made to inform the University.

Instructors and students must follow all applicable campus requirements for use of face coverings. The University recommends and supports swift action and clear consequences since a student’s non-compliance risks the safety of others. Instructors will immediately notify students of any in-class instance of inadvertent non-compliance. Any in-class instance of deliberate non-compliance after warning will result in the student being asked to leave the class immediately. Work missed because of ejection from class for non-compliance may only be made up later with the instructor's permission. All students are responsible for bringing a mask to class in order to comply with campus requirements. If you forget your face covering or it does not meet the requirements, you will be asked to leave the room immediately. You may not return until you meet the requirement.

If a student does not comply with the requirements or the instructor’s direction, the instructor will immediately cancel the remainder of the class session and inform the dean’s office, which will work with the Student Records office to issue a failing grade (“F”) for the course regardless of when in the semester the incident occurs. The dean’s office will also inform the Office of Student Conduct. If a student’s refusal to comply is a second offense, the Office of Student Conduct may recommend dismissal from the University. If the rules for health and safety measures change, the campus will be notified and the new requirements will take effect.

Textbook

``Linear Algebra” by Jim Hefferon, Fourth Edition, available as a free download here:

Linear Algebra by Jim Hefferon.

On can buy a cheap printed version and access more free resources at the textbook's official website.

Here are also some additional books that students and instructors may find helpful.

A First Course in Linear Algebra by Robert A. Beezer

Elementary Linear Algebra by K.R. Matthews

Linear Algebra by D. Cherney, T. Denton, R. Thomas, and A. Waldron

Approximate Exam Schedule (Each section instructor will decide when it is appropriate to give Exams 1, 2, 3.)

Exam 1: The week of September 27.

Exam 2: The week of November 1.

Exam 3: The week of December 6.

Final Exam: Monday, December 13, 8:05 - 10:05 PM (a night exam!) in GW-69EX (West Gym).

Grades

The course total will be determined as follows:

Quizzes: 20% (Quizzes should be given approximately once per week except in weeks when an exam is given.)

Exam 1: 15%

Exam 2: 15%

Exam 3: 15%

Final Exam: 30%

WebWork Homework (common for all sections): 5%

Quizzes are important for students to keep up with the progress of the course and to provide timely feedback on how the material is being absorbed. By September 27 (designated as ``Assessment Day” by the Administration), enough quizzes should have been taken to evaluate each student's progress and make a risk assessment for early warning about problems.

A 90%, A- 85%, B+ 80%, B 75%, B- 70%, C+ 65%, C 55%, C- 50%, D 45%

Homework

Online homework will be done using WebWork. The server address is

https://webwork.math.binghamton.edu/webwork2/304Fall2021/

Make sure to change your password as soon as possible to a secure password, and save that choice where it will not be lost.

Expected workload

Expected behavior in class

Academic Code of Honor

Getting Help

Disability Information

Topics	Text	Problems
Introduction, preview, examples; linear combination	Ch. 1, I.1	1:I.1.17,19,21
Gaussian elimination (reduction)	Ch. 1, I.1	1:I.1.22,24,27,32
(Augmented) matrix of a system, solution set	Ch. 1, I.2	1:I.2.15,16,17,18,21,25
Basic logic: statements, connectives, quantifiers	Appendix
Set theory, general functions	Appendix
Homogeneous and non-homogeneous systems (no formal induction in Lemma 3.6)	Ch. 1, I.3	1:I.3.15,17,18,20,21,24
Points, vectors, lines, planes	Ch. 1, II.1	1:II.1.1,2,3,4,7
Distance, dot product, angles, Cauchy-Schwarz and Triangle Inequalities	Ch. 1, II.2	1:II.2.11,12,14,16,17,21,22
Gauss-Jordan reduction, reduced row echelon form	Ch. 1, III.1	1:III.1.8,9,10,12,13,14,15
Linear combination lemma, uniqueness of RREF (no proofs of 2.5, 2.6)	Ch. 1, III.2	1:III.2.11,14,20,21,24
Matrix operations, including the transpose. Linear system as a matrix equation	Matthews 2.1	3:III.1.13,14,15,16
Linear maps (transformations) given by matrices	Matthews 2.2	3:III.1.19; 3:III.2.12,17,30
Vector spaces: definition, examples	Ch. 2, I.1	2:I.1.17,18,19,21,22,29,30
Linear maps between vector spaces	Ch. 3, II.1	3:II.1.18,19,20,22,24,25,26,28
Subspaces. Span	Ch. 2, I.2	2:I.2.20,21,23,25,26,29,44,45
Linear independence	Ch. 2, II.1	2:II.1.21,22,25,28
Properties of linear independence	Ch. 2, II.1	2:II.1.29,30,32,33
Basis of a vector space	Ch. 2, III.1	2:III.1.20,21,22,23,24,25,26,30,31,34
Dimension of a vector space	Ch. 2, III.2	2:III.2.15,16,17,18,19,20,21,24,25,28
Column space, row space, rank	Ch. 2, III.3	2:III.3.17,18,19,20,21,23,29,32,39
Range space and Kernel (Null space)	Ch. 3, II.2	3:II.2.21,23,24,26,31,35
Invertible matrices: definition, equivalent conditions; inverse matrix	Ch.3, IV.4	3:IV.4.13,14,15,16,17,18,19,26,29
Elementary matrices. Row reduction using elementary matrices	Ch. 3, IV.3; CDTW Ch. 2, 2.3	3:IV.3.24,25,32
Determinant of a matrix, properties	Ch. 4, I.1, I.2	4:I.1.1,3,4,6,9; 4:I.2.8,9,12,13,15,18
More on Determinants	Ch. 4, II.1, III.1	4:III.1.11,14,16,17,20,21,22
Matrix of a linear transformation, matrix of the composition, inverse	Ch. 3, III.1, IV.2	3:III.1.13,17,18,19,21,23
Change of basis, similar matrices	Ch. 3, V.1, V.2; Ch. 5, II.1	3:V.1.7,9,10,12; 5:II.1.5,8,11,13,14
Complex numbers	Matthews 5.1–5.6	Matthews 5.8.1,2,5,6,7,9
Eigenvectors, eigenvalues, eigenspaces for matrices and linear operators. Characteristic polynomial	Matthews 6.1, 6.2; Ch. 5, II.3	5:II.3.23,24,25,26,27,28,29,30,31
Diagonalization of matrices	Ch. 5, II.2, II.3	5:II.3.22,33,36,46
Orthogonal and orthonormal bases of $R^n$ and its subspaces; orthogonal matrices	Ch. 3, VI.1, VI.2	3:VI.1.6,7,17,19; 3:VI.2.10
Orthogonal complement of a subspace, orthogonal projection	Ch. 3, VI.3	3:VI.3.11,12,13,14,26,27
Gram-Schmidt process; orthogonal diagonalization of matrices	Ch. 3, VI.2	3:VI.2.13,15,17,18,19,22

Linear Algebra - Math 304

2024-12-14T12:13:52-04:00

Linear Algebra - Math 304

Fall 2024 -- Course Coordinator: Alex Feingold

Sec	Instructor	Office	Email(*)	Meets	Room
1	Quincy Loney	WH-332	Loney	MWF: 8:00-9:30	CW-321
2	Alex Feingold	WH-115	Feingold	MWF: 9:40-11:10	WH-G002
3	James Hyde	WH-112	Hyde	MWF: 11:20-12:50	WH-G002
4	Tae Young Lee	WH-107	Lee	MWF: 1:10-2:40	WH-G002
5	Tae Young Lee	WH-107	Lee	MWF: 2:50-4:20	WH-G002
6	Quaid Iqbal	WH-209	Iqbal	MWF: 4:40-6:10	WH-G002

(*): To send an email to your instructor, click on the link in the Email column of the table.

Below is a partial syllabus with information for all sections that you should know. Your instructor may have a more detailed syllabus about how your section will be run.

Textbook (Required)

Linear Algebra and Its Applications, 6/e, by Lay/McDonald, Pearson+ etext

This course is participating in Binghamton University’s Inclusive Access Program, and your access code will be delivered via the B&N Course Materials link in Brightspace.

The following more detailed instructions have been provided by a Pearson representative. If you want to see images of the webpages for each step, email Prof. Feingold (feingold@binghamton.edu) to request them and he will forward to you an email with those images.

Click Course Tools → Course Materials - B&N First Day

Click Reveal Access Code

Click Copy (under Copy Code)

Navigate back to your MATH 304 course. Scroll to the bottom. Click Course Materials.

Click the Pearson link

Click Access Code

Paste the access code you copied earlier and click Finish

Click Go to My Course

You have successfully enrolled in your course! Please ensure you have access to the eText and Study Plan.

Additional Textbooks and Resources (Supplemental)

Here are a few additional books that students and instructors may find helpful.

Linear Algebra by Jim Hefferon. One can access additional free resources at the textbook's official website.

A First Course in Linear Algebra by Robert A. Beezer

Elementary Linear Algebra by K.R. Matthews

Linear Algebra by D. Cherney, T. Denton, R. Thomas, and A. Waldron

Approximate Exam Schedule (Each section instructor will decide when it is appropriate to give Exams 1, 2, 3.)

Exam 1: The week of September 16, 2024.

Exam 2: The week of October 21, 2024.

Exam 3: The week of November 18, 2024.

Final Exam: Common exam for all sections: Monday, December 9, 2024, 10:25 am - 12:25 pm in LH-001.

Anyone with a final exam conflict must contact their instructor to make an arrangement.

Additional information about the Final Exam procedures:

You should plan to be in the lobby outside of LH-1 by 10:05 AM, 15 to 20 minutes before the exam starts. You will be told when you can enter the room and where to sit. Exams will be placed on the seats spaced apart, and students from each section should be sitting together in the same area. That way you can have questions answered by your familiar instructor.

You need to bring only writing instruments (pencils and erasers are recommended). No cellphones, laptops or electronic devices will be allowed during the exam, and you may be asked to produce a university ID card to prove your identity. Students who come late will not receive any extra time at the end. Students who have accommodations from the SSD will take this exam at the University Testing Center as scheduled starting at 10:25 AM.

This is winter in upstate New York, so snow storms happen. We won't know exactly how much snow will accumulate until it happens, and travel plans may need to be adjusted accordingly. Having a ride that wants to leave before the storm is NOT a reason for missing the final exam, and will not get a make-up exam or an incomplete. The university will not kick students out of the dorms if they need to stay extra time because of a storm.

ONLY A COMPLETE CANCELLATION OF ALL EXAMS BY THE ADMINISTRATION WOULD CHANGE THESE ARRANGEMENTS.

Grades

The course total will be determined as follows:

Quizzes: 15% (Quizzes should be given approximately once per week except in weeks when an exam is given.)

Exam 1: 15%

Exam 2: 15%

Exam 3: 15%

Final Exam: 30%

MyLab Assignments (Common for all sections): 10%

A 90%, A- 85%, B+ 80%, B 75%, B- 70%, C+ 65%, C 60%, C- 55%, D 50%

Here is a link to the Distribution of Final Exam Scores for All Sections and the Letter Grade Interpretation of the scores.

Health and Safety Procedures Due to COVID Pandemic

Expected workload

Expected behavior in class

Academic Code of Honor

Getting Help

Disability Information

Topics for Exam 1	Chapter
Systems of Linear Equations	1.1
Row Reduction and Echelon Forms	1.2
Vector Equations	1.3
Matrix Equations	1.4
Solution Sets of Linear Systems	1.5
Linear Independence	1.7
Linear Transformations	1.8
Standard Matrix for a Linear Transformation	1.9
Matrix Operations	2.1
Invertible Matrices	2.2
Invertible Matrix Theorem	2.3
Topics for Exam 2
Determinants	3.1
Properties of Determinants	3.2
Applications of Determinants (Not responsible for Cramer's Rule or Adjugates)	3.3
Abstract Vector Spaces	4.1
Fundamental Subspaces	4.2
Bases	4.3
Coordinate Systems	4.4
Dimension	4.5
Change of Basis Matrices	4.6
Topics for Exam 3
Eigenvalues and Eigenvectors	5.1
Characteristic Equations	5.2
Diagonalization	5.3
Matrix for a Linear Transformation	5.4
Complex Eigendata	5.5
Inner Products	6.1
Orthogonal Sets	6.2
Orthogonal Projections	6.3
Gram-Schmidt	6.4
Additional Topics
Inner Product Spaces	6.7
Symmetric Matrices	7.1

Syllabi from previous semesters

The syllabus for Math 304 in Spring 2024 is available through this link:

Spring 2024 page

The syllabus for Math 304 in Fall 2023 is available through this link:

Fall 2023 page

The syllabus for Math 304 in Spring 2023 is available through this link:

Spring 2023 page

The syllabus for Math 304 in Fall 2022 is available through this link:

Fall 2022 page

The syllabus for Math 304 in Spring 2022 is available through this link:

Spring 2022 page

The syllabus for Math 304 in Fall 2021 is available through this link:

Fall 2021 page

The syllabus for Math 304 in Spring 2021 is available through this link:

Spring 2021 page

Linear Algebra - Math 304

2024-05-15T09:51:41-04:00

Linear Algebra - Math 304

Spring 2024 -- Course Coordinator: Quincy Loney

Sec	Instructor	Office	Email(*)	Meets	Room
2	Minghao Rostami	WH-127	Rostami	MWF: 8:00-9:30	CW-202
3	Quincy Loney	WH-332	Loney	MWF: 9:40-11:10	WH-G002
4	Quincy Loney	WH-332	Loney	MWF: 11:20-12:50	WH-G002
5	Michael Gottstein	WH-326	Gottstein	MWF: 11:20-12:50	LH-004
6	Sarah Lamoureux	WH-326	Lamoureux	MWF: 1:10-2:40	WH-G002
7	Michael Gottstein	WH-326	Gottstein	MWF: 2:50-4:20	WH-G002
8	Sarah Lamoureux	WH-322	Lamoureux	MWF: 4:00-5:30	LN-2403

(*): To send an email to your instructor, click on the link in the Email column of the table.

Below is a partial syllabus with information for all sections that you should know. Your instructor may have a more detailed syllabus about how your section will be run.

Textbook (Required)

Linear Algebra and Its Applications, 6/e, by Lay/McDonald, Pearson+ etext

Additional Textbooks and Resources (Supplemental)

Here are a few additional books that students and instructors may find helpful.

Linear Algebra by Jim Hefferon. One can access additional free resources at the textbook's official website.

A First Course in Linear Algebra by Robert A. Beezer

Elementary Linear Algebra by K.R. Matthews

Linear Algebra by D. Cherney, T. Denton, R. Thomas, and A. Waldron

Approximate Exam Schedule (Each section instructor will decide when it is appropriate to give Exams 1, 2, 3.)

Exam 1: The week of Feb. 12, 2024

Exam 2: The week of Mar. 18, 2024

Exam 3: The week of Apr. 15, 2024

Final Exam: Common exam for all sections: Monday May 06, 12:50-2:50PM, LH 001

Anyone with a final exam conflict must contact their instructor to make an arrangement.

Grades

The course total will be determined as follows:

Quizzes: 20% (Quizzes should be given approximately once per week except in weeks when an exam is given.)

Exam 1: 15%

Exam 2: 15%

Exam 3: 15%

Final Exam: 30%

MyLab Assignments (Common for all sections): 5%

A 90%, A- 85%, B+ 80%, B 75%, B- 70%, C+ 65%, C 60%, C- 55%, D 50%

Health and Safety Procedures Due to COVID Pandemic

Expected workload

Expected behavior in class

Academic Code of Honor

Getting Help

Disability Information

Topics for Exam 1	Chapter
Systems of Linear Equations	1.1
Row Reduction and Echelon Forms	1.2
Vector Equations	1.3
Matrix Equations	1.4
Solution Sets of Linear Systems	1.5
Linear Independence	1.7
Linear Transformations	1.8
Standard Matrix for a Linear Transformation	1.9
Matrix Operations	2.1
Invertible Matrices	2.2
Invertible Matrix Theorem	2.3
Topics for Exam 2
Determinants	3.1
Properties of Determinants	3.2
Applications of Determinants (Not responsible for Cramer's Rule or Adjugates)	3.3
Abstract Vector Spaces	4.1
Fundamental Subspaces	4.2
Bases	4.3
Coordinate Systems	4.4
Dimension	4.5
Change of Basis Matrices	4.6
Topics for Exam 3
Eigenvalues and Eigenvectors	5.1
Characteristic Equations	5.2
Diagonalization	5.3
Matrix for a Linear Transformation	5.4
Complex Eigendata	5.5
Inner Products	6.1
Orthogonal Sets	6.2
Orthogonal Projections	6.3
Gram-Schmidt	6.4
Additional Topics
Inner Product Spaces	6.7
Symmetric Matrices	7.1

Syllabi from previous semesters

The syllabus for Math 304 in Fall 2023 is available through this link:

Fall 2023 page

The syllabus for Math 304 in Spring 2023 is available through this link:

Spring 2023 page

The syllabus for Math 304 in Fall 2022 is available through this link:

Fall 2022 page

The syllabus for Math 304 in Spring 2022 is available through this link:

Spring 2022 page

The syllabus for Math 304 in Fall 2021 is available through this link:

Fall 2021 page

The syllabus for Math 304 in Spring 2021 is available through this link:

Spring 2021 page

Linear Algebra - Math 304

2022-12-19T23:19:19-04:00

Linear Algebra - Math 304

Fall 2022 - Course Coordinator: Alex Feingold

Sec	Instructor	Office	Email(*)	Meets	Room
1	Luke Elliott	WH-107	Elliott	MWF:8:00-9:30	WH-G002
2	Luke Elliott	WH-107	Elliott	MWF:9:40-11:10	WH-G002
3	Quincy Loney	WH-332	Loney	MWF:11:20-12:50	WH-G002
4	Quincy Loney	WH-332	Loney	MWF:1:10-2:40	WH-G002
5	Alex Feingold	WH-115	Feingold	MWF:2:50-4:20	WH-G002
6	Michael Gottstein	WH-304	Gottstein	MWF:4:40-6:10	WH-G002

(*): To send an email to your instructor, click on the link in the Email column of the table.

If a section has its own detailed syllabus webpage, a link to that page will be provided under the Instructor column of the table above.

Below is a partial syllabus with information for all sections that you should know. Your instructor may have a more detailed syllabus about how your section will be run.

Health and Safety Procedures Due to COVID Pandemic

Textbook

``Linear Algebra” by Jim Hefferon, Fourth Edition, available as a free download here:

Linear Algebra by Jim Hefferon.

One can buy a cheap printed version and access more free resources at the textbook's official website.

Here are also some additional books that students and instructors may find helpful.

A First Course in Linear Algebra by Robert A. Beezer

Elementary Linear Algebra by K.R. Matthews

Linear Algebra by D. Cherney, T. Denton, R. Thomas, and A. Waldron

Approximate Exam Schedule (Each section instructor will decide when it is appropriate to give Exams 1, 2, 3.)

Exam 1: The week of Sept. 26, 2022.

Exam 2: The week of Oct. 31, 2022.

Exam 3: The week of Dec. 5, 2022.

Final Exam: Common exam for all sections, Thursday, Dec. 15, 2022, 3:15 - 5:15 PM, LH-001. Anyone with a final exam conflict must contact their instructor to make an arrangement.

Grades

The course total will be determined as follows:

Quizzes: 20% (Quizzes should be given approximately once per week except in weeks when an exam is given.)

Exam 1: 15%

Exam 2: 15%

Exam 3: 15%

Final Exam: 30%

Homework assignments: WebWork Homework (common for all sections): 5%

A 90%, A- 85%, B+ 80%, B 75%, B- 70%, C+ 65%, C 55%, C- 50%, D 45%

Homework

Online homework will be done using WebWork. The server address is

https://webwork.math.binghamton.edu/webwork2/304Fall2022/

Make sure to change your password as soon as possible to a secure password, and save that choice where it will not be lost.

Important: Besides the WebWork homework sets, you should do problems from the book, either selected by your instructor or as listed below. This part of the homework will not be graded, but it could be important to your success in the course.

Expected workload

Expected behavior in class

Academic Code of Honor

Getting Help

Disability Information

Topics	Text	Problems
Introduction, preview, examples; linear combination	Ch. 1, I.1	1:I.1.17,19,21
Gaussian elimination (reduction)	Ch. 1, I.1	1:I.1.22,24,27,32
(Augmented) matrix of a system, solution set	Ch. 1, I.2	1:I.2.15,16,17,18,21,25
Basic logic: statements, connectives, quantifiers	Appendix
Set theory, general functions	Appendix
Homogeneous and non-homogeneous systems (no formal induction in Lemma 3.6)	Ch. 1, I.3	1:I.3.15,17,18,20,21,24
Points, vectors, lines, planes	Ch. 1, II.1	1:II.1.1,2,3,4,7
Distance, dot product, angles, Cauchy-Schwarz and Triangle Inequalities	Ch. 1, II.2	1:II.2.11,12,14,16,17,21,22
Gauss-Jordan reduction, reduced row echelon form	Ch. 1, III.1	1:III.1.8,9,10,12,13,14,15
Linear combination lemma, uniqueness of RREF (no proofs of 2.5, 2.6)	Ch. 1, III.2	1:III.2.11,14,20,21,24
Matrix operations, including the transpose. Linear system as a matrix equation	Matthews 2.1	3:III.1.13,14,15,16
Linear maps (transformations) given by matrices	Matthews 2.2	3:III.1.19; 3:III.2.12,17,30
Vector spaces: definition, examples	Ch. 2, I.1	2:I.1.17,18,19,21,22,29,30
Linear maps between vector spaces	Ch. 3, II.1	3:II.1.18,19,20,22,24,25,26,28
Subspaces. Span	Ch. 2, I.2	2:I.2.20,21,23,25,26,29,44,45
Linear independence	Ch. 2, II.1	2:II.1.21,22,25,28
Properties of linear independence	Ch. 2, II.1	2:II.1.29,30,32,33
Basis of a vector space	Ch. 2, III.1	2:III.1.20,21,22,23,24,25,26,30,31,34
Dimension of a vector space	Ch. 2, III.2	2:III.2.15,16,17,18,19,20,21,24,25,28
Column space, row space, rank	Ch. 2, III.3	2:III.3.17,18,19,20,21,23,29,32,39
Range space and Kernel (Null space)	Ch. 3, II.2	3:II.2.21,23,24,26,31,35
Invertible matrices: definition, equivalent conditions; inverse matrix	Ch.3, IV.4	3:IV.4.13,14,15,16,17,18,19,26,29
Elementary matrices. Row reduction using elementary matrices	Ch. 3, IV.3; CDTW Ch. 2, 2.3	3:IV.3.24,25,32
Determinant of a matrix, properties	Ch. 4, I.1, I.2	4:I.1.1,3,4,6,9; 4:I.2.8,9,12,13,15,18
More on Determinants	Ch. 4, II.1, III.1	4:III.1.11,14,16,17,20,21,22
Matrix of a linear transformation, matrix of the composition, inverse	Ch. 3, III.1, IV.2	3:III.1.13,17,18,19,21,23
Change of basis, similar matrices	Ch. 3, V.1, V.2; Ch. 5, II.1	3:V.1.7,9,10,12; 5:II.1.5,8,11,13,14
Complex numbers	Matthews 5.1–5.6	Matthews 5.8.1,2,5,6,7,9
Eigenvectors, eigenvalues, eigenspaces for matrices and linear operators. Characteristic polynomial	Matthews 6.1, 6.2; Ch. 5, II.3	5:II.3.23,24,25,26,27,28,29,30,31
Diagonalization of matrices	Ch. 5, II.2, II.3	5:II.3.22,33,36,46
Orthogonal and orthonormal bases of $R^n$ and its subspaces; orthogonal matrices	Ch. 3, VI.1, VI.2	3:VI.1.6,7,17,19; 3:VI.2.10
Orthogonal complement of a subspace, orthogonal projection	Ch. 3, VI.3	3:VI.3.11,12,13,14,26,27
Gram-Schmidt process; orthogonal diagonalization of matrices	Ch. 3, VI.2	3:VI.2.13,15,17,18,19,22

Linear Algebra - Math 304

2022-05-25T09:31:09-04:00

Linear Algebra - Math 304

Spring 2022 - Course Coordinator: Quincy Loney

Sec	Instructor	Office	Email(*)	Meets	Room
1	Michael Dobbins	WH-214	Dobbins	MWF:8:00-9:30	CW-321
3	Eugenia Sapir	WH-213	Sapir	MWF:9:40-11:10	S2-G52
4	Olakunle Abawonse	WH-330	Abawonse	MWF:11:20-12:50	UU-215
5	Quincy Loney	WH-332	Loney	MWF:11:20-12:50	SL-302
6	Quincy Loney	WH-332	Loney	MWF:1:10-2:40	SL-302
7	Thomas Kilcoyne	WH-336	Kilcoyne	MWF:2:50-4:20	LH-012
8	Thomas Kilcoyne	WH-336	Kilcoyne	MWF:4:40-6:10	LN-1120

(*): To send an email to your instructor, click on the link in the Email column of the table.

If a section has its own detailed syllabus webpage, a link to that page will be provided under the Instructor column of the table above.

Below is a partial syllabus with information for all sections that you should know. Your instructor may have a more detailed syllabus about how your section will be run.

Health and Safety Procedures Due to COVID Pandemic

Textbook

``Linear Algebra” by Jim Hefferon, Fourth Edition, available as a free download here:

Linear Algebra by Jim Hefferon.

On can buy a cheap printed version and access more free resources at the textbook's official website.

Here are also some additional books that students and instructors may find helpful.

A First Course in Linear Algebra by Robert A. Beezer

Elementary Linear Algebra by K.R. Matthews

Linear Algebra by D. Cherney, T. Denton, R. Thomas, and A. Waldron

Approximate Exam Schedule (Each section instructor will decide when it is appropriate to give Exams 1, 2, 3.)

Exam 1: The week of February 21

Exam 2: The week of March 28

Exam 3: The week of May 2

Final Exam: Tuesday May 17, 8:05 - 10:05 PM (a night exam!) in GW-69EX (West Gym).

Grades

The course total will be determined as follows:

Quizzes: 20% (Quizzes should be given approximately once per week except in weeks when an exam is given.)

Exam 1: 15%

Exam 2: 15%

Exam 3: 15%

Final Exam: 30%

WebWork Homework (common for all sections): 5%

A 90%, A- 85%, B+ 80%, B 75%, B- 70%, C+ 65%, C 55%, C- 50%, D 45%

Homework

Online homework will be done using WebWork. The server address is

https://webwork.math.binghamton.edu/webwork2/304Spring2022/

Make sure to change your password as soon as possible to a secure password, and save that choice where it will not be lost.

Expected workload

Expected behavior in class

Academic Code of Honor

Getting Help

Disability Information

Topics	Text	Problems
Introduction, preview, examples; linear combination	Ch. 1, I.1	1:I.1.17,19,21
Gaussian elimination (reduction)	Ch. 1, I.1	1:I.1.22,24,27,32
(Augmented) matrix of a system, solution set	Ch. 1, I.2	1:I.2.15,16,17,18,21,25
Basic logic: statements, connectives, quantifiers	Appendix
Set theory, general functions	Appendix
Homogeneous and non-homogeneous systems (no formal induction in Lemma 3.6)	Ch. 1, I.3	1:I.3.15,17,18,20,21,24
Points, vectors, lines, planes	Ch. 1, II.1	1:II.1.1,2,3,4,7
Distance, dot product, angles, Cauchy-Schwarz and Triangle Inequalities	Ch. 1, II.2	1:II.2.11,12,14,16,17,21,22
Gauss-Jordan reduction, reduced row echelon form	Ch. 1, III.1	1:III.1.8,9,10,12,13,14,15
Linear combination lemma, uniqueness of RREF (no proofs of 2.5, 2.6)	Ch. 1, III.2	1:III.2.11,14,20,21,24
Matrix operations, including the transpose. Linear system as a matrix equation	Matthews 2.1	3:III.1.13,14,15,16
Linear maps (transformations) given by matrices	Matthews 2.2	3:III.1.19; 3:III.2.12,17,30
Vector spaces: definition, examples	Ch. 2, I.1	2:I.1.17,18,19,21,22,29,30
Linear maps between vector spaces	Ch. 3, II.1	3:II.1.18,19,20,22,24,25,26,28
Subspaces. Span	Ch. 2, I.2	2:I.2.20,21,23,25,26,29,44,45
Linear independence	Ch. 2, II.1	2:II.1.21,22,25,28
Properties of linear independence	Ch. 2, II.1	2:II.1.29,30,32,33
Basis of a vector space	Ch. 2, III.1	2:III.1.20,21,22,23,24,25,26,30,31,34
Dimension of a vector space	Ch. 2, III.2	2:III.2.15,16,17,18,19,20,21,24,25,28
Column space, row space, rank	Ch. 2, III.3	2:III.3.17,18,19,20,21,23,29,32,39
Range space and Kernel (Null space)	Ch. 3, II.2	3:II.2.21,23,24,26,31,35
Invertible matrices: definition, equivalent conditions; inverse matrix	Ch.3, IV.4	3:IV.4.13,14,15,16,17,18,19,26,29
Elementary matrices. Row reduction using elementary matrices	Ch. 3, IV.3; CDTW Ch. 2, 2.3	3:IV.3.24,25,32
Determinant of a matrix, properties	Ch. 4, I.1, I.2	4:I.1.1,3,4,6,9; 4:I.2.8,9,12,13,15,18
More on Determinants	Ch. 4, II.1, III.1	4:III.1.11,14,16,17,20,21,22
Matrix of a linear transformation, matrix of the composition, inverse	Ch. 3, III.1, IV.2	3:III.1.13,17,18,19,21,23
Change of basis, similar matrices	Ch. 3, V.1, V.2; Ch. 5, II.1	3:V.1.7,9,10,12; 5:II.1.5,8,11,13,14
Complex numbers	Matthews 5.1–5.6	Matthews 5.8.1,2,5,6,7,9
Eigenvectors, eigenvalues, eigenspaces for matrices and linear operators. Characteristic polynomial	Matthews 6.1, 6.2; Ch. 5, II.3	5:II.3.23,24,25,26,27,28,29,30,31
Diagonalization of matrices	Ch. 5, II.2, II.3	5:II.3.22,33,36,46
Orthogonal and orthonormal bases of $R^n$ and its subspaces; orthogonal matrices	Ch. 3, VI.1, VI.2	3:VI.1.6,7,17,19; 3:VI.2.10
Orthogonal complement of a subspace, orthogonal projection	Ch. 3, VI.3	3:VI.3.11,12,13,14,26,27
Gram-Schmidt process; orthogonal diagonalization of matrices	Ch. 3, VI.2	3:VI.2.13,15,17,18,19,22

Linear Algebra - Math 304

2024-01-03T10:59:08-04:00

Linear Algebra - Math 304

Fall 2023 -- Course Coordinator: Quincy Loney

Sec	Instructor	Office	Email(*)	Meets	Room
1	Luke Elliott	WH-107	Elliott	MWF: 8:00-9:30	WH-G002
2	Jia Zhao	WH-126	Zhao	MWF: 9:40-11:10	WH-G002
3	David Biddle	WH-232	Biddle	MWF: 11:20-12:50	WH-G002
4	Eugenia Sapir	WH-213	Sapir	MWF: 1:10-2:40	WH-G002
5	Quincy Loney	WH-332	Loney	MWF: 2:50-4:20	WH-G002
6	Thomas Zaslavsky	WH-216	Zaslavsky	MWF: 4:40-6:10	WH-G002

(*): To send an email to your instructor, click on the link in the Email column of the table.

Below is a partial syllabus with information for all sections that you should know. Your instructor may have a more detailed syllabus about how your section will be run.

Textbook (Required)

Linear Algebra and Its Applications, 6/e, by Lay/McDonald, Pearson+ etext

Additional Textbooks and Resources (Supplemental)

Here are a few additional books that students and instructors may find helpful.

Linear Algebra by Jim Hefferon. One can access additional free resources at the textbook's official website.

A First Course in Linear Algebra by Robert A. Beezer

Elementary Linear Algebra by K.R. Matthews

Linear Algebra by D. Cherney, T. Denton, R. Thomas, and A. Waldron

Three evening exams during the semester, and a Final Exam during final exams week, will be scheduled. Details are as follows:

Exam 1: Wednesday, September 20, LH-1, 8:15-9:45 PM

Exam 2: Wednesday, October 25, LH-1, 8:15-9:45 PM

Exam 3: Wednesday, November 29, LH-1, 8:15-9:45 PM

Final Exam: Tuesday, December 12, LH-1, 8:00-10:00 AM

Anyone with a final exam conflict must contact their instructor to make an arrangement.

Please arrive 10 minutes early for each exam to allow time for seating, and always bring your university ID. No calculators, cellphones, computers, smart watches, or any internet connected devices will be allowed during exams. A student who needs to leave the exam room during an exam must leave their cellphone in the room. Use of a cellphone to get answers to exam questions during an exam is cheating and will be treated as a violation of university honesty rules.

Grades

The course total will be determined as follows:

Quizzes: 15% (Quizzes should be given approximately once per week except in weeks when an exam is given.)

Exam 1: 15%

Exam 2: 15%

Exam 3: 15%

Final Exam: 30%

MyLab Assignments (Common for all sections): 10%

A 90%, A- 85%, B+ 80%, B 75%, B- 70%, C+ 65%, C 55%, C- 50%, D 45%

Health and Safety Procedures Due to COVID Pandemic

Expected workload

Expected behavior in class

Academic Code of Honor

Getting Help

Disability Information

Syllabi from previous semesters

The syllabus for Math 304 in Spring 2023 is available through this link:

Spring 2023 page

The syllabus for Math 304 in Fall 2022 is available through this link:

Fall 2022 page

The syllabus for Math 304 in Spring 2022 is available through this link:

Spring 2022 page

The syllabus for Math 304 in Fall 2021 is available through this link:

Fall 2021 page

The syllabus for Math 304 in Spring 2021 is available through this link:

Spring 2021 page

The syllabus for Math 304 in Fall 2020 is available through this link:

Fall 2020 page

Linear Algebra - Math 304

2019-12-17T21:22:16-04:00

Linear Algebra - Math 304

Fall 2019

Sec	Instructor	Office	Phone	Email(*)	Meets	Room
1	Hung Tong-Viet	WH-108	777-2380	tongviet	MWF:8:00-9:30	WH-G002
2	Fikreab Admasu	WH-107	777-4246	admasuf	MW:9:40-11:10, F:9:40-11:10	FA-212, CW-331
3	Vaidehee Thatte	WH-107	777-4246	thatte	MWF:11:20-12:50	OH-G102
4	Alex Feingold	WH-115	777-2465	alex	MWF:1:10-2:40	CW-202
5	Eran Crockett	WH-332		crockett	MWF:2:50-4:20	CW-212
6	Thomas Zaslavsky	WH-216	777-2201	zaslav	MWF:4:40-6:10	CW-321

(*): Each email address in this table is of the form xxx@math.binghamton.edu but that should happen automatically if you just click on the link.

If a section has its own detailed syllabus webpage, a link to that page will be provided under the Instructor column of the table above.

Below is a partial syllabus with information for all sections that you should know. Your instructor may have a more detailed syllabus about how your section will be run.

Textbook

``Linear Algebra and Its Applications, 5th Edition” by David C. Lay, Steven R. Lay, Judi J. McDonald, Pearson Publishers, e-book with MyLab Math. Here is a link to the Pearson webpage for this textbook, including information about MyLab Math homework system: Lay-Lay-McDonald webpage. Here is a link to the specific page for the product which students should buy from Pearson: Required eTextbook and MyLab homework system.

The entire book will be covered if time permits.

Exam Schedule

Only the Final Exam will be common to all sections, but we expect each section will administer other exams on the same day, three times during the semester, as follows:

Exam 1: Wednesday, Sept 25, 2019.

Exam 2: Wednesday, Oct 30, 2019.

Exam 3: Monday, Nov 25, 2019.

Final Exam: Friday, Dec 13, 2019, 12:50 - 2:50 PM, GW-69EX (West Gym), Common for all Sections.

No calculators, cellphones or computers will be allowed during exams. A student who needs to leave the exam room during an exam must leave their cellphone in the room. Use of a cellphone to get answers to exam questions during an exam is cheating and will be treated as a violation of university honesty rules.

Homework

Online homework will be done using MyLab which comes with the textbook. Registration instructions will be posted here before the semester begins.

Expected workload outside of the classroom

Expected behaviour in class

Resources for help with personal problems

The following link to a webpage of the Dean of Students contains important contact information for sources of help if you are having personal problems.

Dean of Students Help Page

Announcements

August 21: First Day of Classes: After meeting your instructor you should have been given this webpage address to check for the syllabus and instructions. Step 1: Read the entire syllabus, including the detailed syllabus for your section. Step 2: Set up your MyLab account for doing homework assignments. Step 3: Attend all classes and keep up with all homework corresponding to your section lectures.

Syllabi from previous semesters

The syllabus for Math 304 in Spring 2019 can be found through the following link:

Math 304 Syllabus for Spring 2019

The syllabus for Math 304 in Fall 2018 is available through this link:

Fall 2018 page

Fall

2015-05-22T12:56:20-04:00

Course syllabi for Fall 2014

MATH 106	Intermediate Algebra Sections: 01, 02
MATH 107	Basic Integrated Mathematics
MATH 108	Algebra and Trigonometry
MATH 130	Mathematics in Action Sections: A 0, A01, A02, A03, A04, A05, A06, A07, A08
MATH 147	Elementary Statistics Sections: A 0, A01, A02, A03, A04, A05, A06, A07, A08, A09, A10, A11, A12, A13, A14
MATH 148	Elementary Statistics for Biologists Sections: A 0, A01, A02, A03, A04, A05, A06, A07
MATH 220	Calculus for Business and Management
MATH 221	Calculus I
MATH 222	Calculus II
MATH 304	Linear Algebra
MATH 314	Discrete Mathematics Sections: 01, 02
MATH 323	Calculus III
MATH 327	Probability with Statistical Methods Sections: A 0, A01, A02
MATH 330	Number systems Sections: 01, 02, 03, 04, 05, 06
MATH 346	Introduction to Financial Mathematics Sections: 01, 02
MATH 371	Ordinary Differential Equations
MATH 372	Dynamical Systems
MATH 386	Combinatorics
MATH 391	Practicum in College Teaching
MATH 401	Modern Algebra I
MATH 447	Introduction to Probability and Statistics I Sections: 01, 02
MATH 448	Introduction to Probability and Statistics II
MATH 450	Actuarial Mathematics I
MATH 461	Topology I
MATH 465	Foundations of Geometry
MATH 478	Real Analysis I Sections: 01, 02
MATH 489	Problem Solving
MATH 497	Independent Work

Spring

2015-11-19T15:13:12-04:00

Course syllabi for Spring 2015

MATH 106	Intermediate Algebra Sections: 01, 02
MATH 107	Basic Integrated Mathematics
MATH 108	Algebra and Trigonometry
MATH 130	Mathematics in Action Sections: A 0, A01, A02, A03, A04, A05, A06, A07, A08
MATH 147	Elementary Statistics Sections: A 0, A01, A02, A03, A04, A05, A06, A07, A08, A09, A10, A11, A12, A13, A14
MATH 148	Elementary Statistics for Biologists Sections: A 0, A01, A02, A03, A04, A05, A06, A07
MATH 220	Calculus for Business and Management
MATH 221	Calculus I
MATH 222	Calculus II
MATH 304	Linear Algebra
MATH 314	Discrete Mathematics Sections: 01, 02
MATH 323	Calculus III
MATH 327	Probability with Statistical Methods Sections: A 0, A01, A02
MATH 330	Number systems Sections: 01, 02, 03, 04, 05, 06
MATH 346	Introduction to Financial Mathematics Sections: 01, 02
MATH 371	Ordinary Differential Equations
MATH 372	Dynamical Systems
MATH 386	Combinatorics
MATH 391	Practicum in College Teaching
MATH 401	Modern Algebra I
MATH 447	Introduction to Probability and Statistics I Sections: 01, 02
MATH 448	Introduction to Probability and Statistics II
MATH 450	Actuarial Mathematics I
MATH 461	Topology I
MATH 465	Foundations of Geometry
MATH 478	Real Analysis I Sections: 01, 02
MATH 489	Problem Solving
MATH 497	Independent Work

Fall

2016-08-24T07:30:24-04:00

Course syllabi for Fall 2016

MATH 106	Intermediate Algebra Sections: 01, 02
MATH 107	Basic Integrated Mathematics
MATH 108	Algebra and Trigonometry
MATH 130	Mathematics in Action
MATH 147	Elementary Statistics
MATH 148	Elementary Statistics for Biologists
MATH 220	Calculus for Business and Management
MATH 221	Calculus I
MATH 222	Calculus II
MATH 304	Linear Algebra
MATH 314	Discrete Mathematics Sections: 01, 02
MATH 323	Calculus III
MATH 327	Probability with Statistical Methods
MATH 330	Number systems Sections: 01, 02, 03, 04, 05, 06
MATH 346	Introduction to Financial Mathematics Sections: 01, 02
MATH 371	Ordinary Differential Equations
MATH 372	Dynamical Systems
MATH 386	Combinatorics
MATH 391	Practicum in College Teaching
MATH 401	Modern Algebra I
MATH 447	Introduction to Probability and Statistics I Sections: 01, 02
MATH 448	Introduction to Probability and Statistics II
MATH 450	Actuarial Mathematics I
MATH 461	Topology I
MATH 465	Foundations of Geometry
MATH 478	Real Analysis I Sections: 01, 02
MATH 489	Problem Solving
MATH 497	Independent Work

Fall

2015-11-30T14:47:23-04:00

Course syllabi for Fall 2015

MATH 106	Intermediate Algebra Sections: 01, 02
MATH 107	Basic Integrated Mathematics
MATH 108	Algebra and Trigonometry
MATH 130	Mathematics in Action Sections: A 0, A01, A02, A03, A04, A05, A06, A07, A08
MATH 147	Elementary Statistics Sections: A 0, A01, A02, A03, A04, A05, A06, A07, A08, A09, A10, A11, A12, A13, A14
MATH 148	Elementary Statistics for Biologists Sections: A 0, A01, A02, A03, A04, A05, A06, A07
MATH 220	Calculus for Business and Management
MATH 221	Calculus I
MATH 222	Calculus II
MATH 304	Linear Algebra
MATH 314	Discrete Mathematics Sections: 01, 02
MATH 323	Calculus III
MATH 327	Probability with Statistical Methods Sections: A 0, A01, A02
MATH 330	Number systems Sections: 01, 02, 03, 04, 05, 06
MATH 346	Introduction to Financial Mathematics Sections: 01, 02
MATH 371	Ordinary Differential Equations
MATH 372	Dynamical Systems
MATH 386	Combinatorics
MATH 391	Practicum in College Teaching
MATH 401	Modern Algebra I
MATH 447	Introduction to Probability and Statistics I Sections: 01, 02
MATH 448	Introduction to Probability and Statistics II
MATH 450	Actuarial Mathematics I
MATH 461	Topology I
MATH 465	Foundations of Geometry
MATH 478	Real Analysis I Sections: 01, 02
MATH 489	Problem Solving
MATH 497	Independent Work

Courses

2022-07-18T13:03:56-04:00

Course Information

Check the University Bulletin for listed courses in the Department of Mathematics and Statistics.

Check the Course Schedules in the Department of Mathematics and Statistics.

Here is a summary of all related courses and their status. When you plan your schedule, pay attention to those courses that are not offered every semester.

Course No.	Course name	Semester	Required/ recommended	Prerequisites
224/225	Calculus I	every	BA and BS	none
226/227	Calculus II	every	BA and BS	225
230	Honors Calculus	every	BA and BS (alternative to 226/227)	225
304	Linear Algebra	every	BA and BS	225
323	Calculus III	every	BA and BS	227 or 230
330	Number Systems	every	BA and BS	227 or 230
346	Intro. to Financial Mathematics	every	BA and BS	227 or 230
404	Advanced Linear Algebra	spring only	elective	304 and 330
447	Probability Theory	every	BA and BS	323
448	Mathematical Statistics	every	BA and BS	330 and 447
450	Long-term Actuarial Math I	fall only	elective	330, 346, and 447
452	Long-term Actuarial Math II	every other spring	elective	304 and 450
454	Financial Mathematics	occasional	elective	346 and 447
455	Intro. to Regression Models	spring only	elective	329 and 448
457	Intro. to Statistical Learning	fall only	elective	329 and 448
458	Time Series	every other spring	elective	448
472	PDE and Mathematical Analysis	spring only	elective	323, 330 and one of 324, 371, or 372
478	Real Analysis I	fall only	elective	304, 323, and 330
479	Real Analysis II	spring only	elective	478
Econ 160	Principles of Microeconomics	every	BA and BS	none
Econ 162	Principles of Macroeconomics	every	BA and BS	none
Econ 360	Microeconomic Theory	every	BS	Econ 160, 220 or 221
Econ 362	Macroeconomic Theory	every	BS	Econ 162
Econ 467	Economic Forecasting	every	elective (alternative to 458)	ECON 362, 366 and 466, MATH 220 or 224/225
Fin 311	Financial Management	every	No required. May be helpful.	Junior Standing and Acct 211, Econ 160 and 162, Math 220 or 224/225
Fin 322	Investments	every	No required. May be helpful.
Fin 324	Corporate Finance	every	No required. May be helpful.

Calculus

Calculus is a branch of mathematics that studies continuously changing quantities. A key notion is the passage to the limit: quantities that tend to ultimate values. The basic tools from calculus are differentiation and integration. The methods of calculus are essential to any modern science. Department of Mathematics and Statistics offers the following courses in calculus:

Math 224/225. Calculus I.
Math 226/227. Calculus II.
Math 230. Honors Calculus. Directed at students who already have credit for calculus 1 or even calculus 2 and a strong record of performance in mathematics (like a high score on the calculus AP exam). It is appropriate for strong and mathematically curious students ready to work hard. It can be taken instead of Math 226/227
Math 323. Calculus III.

Probability and Statistics

Many problems which an actuary has to deal with are contingent/uncertain events. Probability theory is the branch of mathematics that studies the assignment of probabilities to random events. Department of Mathematics and Statistics offers the following courses in Probability:

Math 447. Probability Theory: Counting techniques, independence and conditional probability, discrete and continuous random variables, special distributions, expected values and moments, multivariate distributions, conditional distributions, transformations of random variables, limit theorems. 4 credits. Offered both in Fall and Spring.

Another part of mathematics studying randomness is Statistics. Statistics studies the collection and analysis of data. Department of Mathematics and Statistics offers the following courses in Statistics:

Math 448. Mathematical Statistics: Random sampling, point estimation, t, chi-squared, and F distributions, sufficient statistics, minimum variance unbiased estimators, confidence intervals, tests of hypothesis, uniformly most powerful tests, Bayesian methods, linear models. 4 credits. Offered both in Fall and Spring.
Math 455. Introduction to Regression Models. This course covers the mathematical foundation and practical implementations of linear and generalized linear regression models. Topics include estimation and diagnostics of linear models, transformations of variables, model selection, polynomial regression, and logistic regression. The emphasis of the course will be on applications. 4 credits. Offered in Spring only.
Math 457. Intro to Statistical Learning. Statistical learning refers to a set of tools for modeling and understanding complex datasets. This course covers such topics as regression, classification, resampling, model selection, regularization, tree-based methods, support vector machine, principal components analysis, and clustering methods. It concentrates more on the applications of the methods and provides students with valuable hands-on experience. 4 credits. Offered in Fall only.
Math 458. Time Series: The statistical analysis of time series data. Autocorrelation; stationarity, basic time series models; AR, MA, ARMA; trend removal and seasonal adjustment; invertibility; spectral analysis; estimation; forecasting; introduction to financial time series and the ARCH model.

These courses fulfill the Applied Statistics subject and the Mathematical Statistics subject of the VEE requirements. Please see the VEE requirements for more information. These courses also cover partially the syllabi for CAS: Statistics and Probabilistic Models Exam, Construction and Evaluation of Actuarial Models Exam, Statistics for Risk Modeling Exam, and Predictive Analytics.

Financial Mathematics

Department of Mathematics and Statistics offers the following courses in Financial Mathematics:

Math 346. Introduction to Financial Mathematics: Accumulation function, simple and compounded interest, effective and nominal rates of interest and discount, the force of interest, level and nonlevel annuities and perpetuities, amortization, reinvestment, sinking funds, bonds, depreciation methods, short sales of stock, term structure of the interest rates, duration, convexity, derivative markets. The material will focus on the requirements for the Exam FM/2. 4 credits. Offered both in Fall and Spring.
Math 454. Financial Mathematics: Interest rate models, the principle of no-arbitrage, fundamental theorem of asset pricing, evaluation of derivatives, put-call parity, European put and call options, binomial models, Black-Scholes option-pricing model, American options, option Greeks, exotic options, lognormal distribution, diffusion process, Ito's lemma, simulation, and delta-hedging. The material will focus on the requirements for the Exam MFE. 4 credits. Math 346 and Math 447 are prerequisites of this course.

Actuarial Mathematics

Actuaries use sophisticated probability models. Department of Mathematics and Statistics offers the following courses in actuarial stochastic models:

Math 450. Life Contingency Models I: Survival models, life tables, life insurance, life annuities, benefit premiums. 4 credits. Offered each Fall.
Math 452. Life Contingency Models II: Benefit reserves, multiple life functions, multiple decrement models, Markov chains, Poisson processes. 4 credits. Offered in Spring. Availability depends on enrollment.

Economics and Finance

An actuary studies contingent / uncertain events which have financial consequences. Hence he/she must have a good knowledge of Economics and Finance. In addition, VEE requirements include microeconomics, macroeconomics, and corporate finance. The following courses deal with microeconomics and macroeconomics. They fulfill the VEE requirements on the Economics subject:

ECON 160. Principles of Microeconomics.
ECON 162. Principles of Macroeconomics.
ECON 360. Microeconomic Theory.
ECON 362. Macroeconomic Theory.

So far, to fulfill the VEE requirements on the Finance subject, students must take courses from the school of management (SOM):

FIN 311, Financial Management.
FIN 322, Investments.
FIN 324, Corporate Finance.

FIN 311 is open for registration for Harpur students in the Financial Economics major and the Actuarial major. FIN 322 or FIN 324 is not yet open for registration for students out of SOM. Please seek help from your advisor should you want to register for FIN 322 or FIN 324.

Other courses

Other related courses are ECON 466. Introduction to Econometrics; ECON 467. Economic Forecasting; CQS 112. Statistics for Management; ECON 442, Financial Economics.

For computing skills, students can take CS 105, which provides some help on spreadsheets such as Excel, and CS 110, which introduces students to programming using python as the language.

Recommended courses for future math teachers

2025-12-28T12:59:16-04:00

Recommended courses for future math teachers

There is no formal Education track within the math major, but here are some recommendations developed by the Math and Education faculty.

The requirements for the math BA (details available in Academic Guide (2025/2026)) include one course in Algebra, one course in Analysis, and one course in Geometry, as well as a pairing of two related courses. We recommend that within this, future math teachers aim for a broad mathematical background, including Statistics and including several proof-based courses. (Proof-based courses are where you learn to express your mathematical ideas clearly, so they're particularly important for teachers.)

For the pairing, we recommend Probability and Statistics (MATH 447 and 448).

For the Analysis course, we recommend future teachers choose from Differential Equations (MATH 371), Dynamical Systems (MATH 372), Complex Analysis (MATH 375), and (for those interested in a rigorous examination of Calculus) Real Analysis (MATH 478).

For the Algebra course, we recommend future teachers take Number Theory (MATH 407).

For the Geometry course, we recommend future teachers choose Foundations of Geometry (MATH 465). In the event that this course is not available, future teachers should choose Topics: History in Mathematics (MATH 488H).

For additional breadth, we highly recommend future teachers take a combinatorics course: either Combinatorics (MATH 386) or Graph Theory (MATH 381)

Students are strongly advised to take Calculus courses as early as possible, since these are prerequisites for many later courses, and to take MATH 330 in the sophomore year, since MATH 330 is a prerequisite to all other proof-based courses. Beyond that, there are many good ways to fit these recommended courses into four years: here is a sample schedule.

Year	Fall	Spring
1	Calculus 1 (MATH 224 and 225)	Calculus 2 (MATH 226 and 227)
2	Calculus 3 (MATH 323), MATH 330	Linear Algebra (MATH 304)
3	Probability (MATH 447), Number Theory (MATH 407)	Statistics (MATH 448), Analysis course
4	Geometry course or Combinatorics (MATH 386)	Geometry course or Graph Theory (MATH 381)

Information about Math 227 Place-Out Exam

2025-07-24T15:47:41-04:00

Information about Math 227 Place-Out Exam

This page contains information about the MATH 227 place-out examination. This examination is for those who got 5 in AP Calculus BC and entered the university on or after Fall 2020. Currently, students with 5 in AP Calculus BC who entered Fall 2020 or later will receive MATH 224 (2 credits), MATH 225 (2 credits), MATH 226 (2 credits) & MSCI XXX (2 credits). Upon successfully passing the place-out exam, students will receive credit for MATH 227 instead of MSCI XXX.

Not to be confused with the placement exam, which is for students who want to take Calculus I or Business Calculus.

This year's exam will take place on Monday, August 18th, 7:00-9:00 pm, in LH 001. It will be a 2-hour written examination, similar in coverage to the Math 227 final examination. You must register to take the exam, using the link at the bottom of this page. Note: you can only attempt the place-out once, and only if you did not take MATH 227.

Since you have credit for MATH 226, you should not sign up for the regular MATH 226/227 pair of courses. Since you are signing up for courses before you take the place-out examination, and it is easier to drop courses rather than add, you may want to sign up for a section of MATH 227 in the first half of the semester. You can also sign up to take a stand-alone MATH 227 in the second half of the semester, although this is less ideal; for this you should use the second form on the Forms page: https://www2.math.binghamton.edu/p/forms/start

You may also want to register for Linear Algebra (MATH 304), Honors Calculus (MATH 230), and/or Number Systems (MATH 330). In truly exceptional circumstances, for students with serious exposure to higher mathematics, other options may be available. For any questions, email Prof. Alexander Borisov at borisov@math.binghamton.edu

For a more detailed description of the MATH 227 place-out examination coverage, see this page:

https://www2.math.binghamton.edu/p/calculus/math_226_227/start

In particular, three sample Math 227 final examinations are available here:

https://www2.math.binghamton.edu/lib/exe/fetch.php/calculus/math_226_227/227_sample_finals.pdf

with solutions at

https://www2.math.binghamton.edu/lib/exe/fetch.php/calculus/math_226_227/math227samplefinal_1-2-3_solutions_updated2.pdf

You only get one try at placing out of Math 227. So make sure to prepare as well as you can.

Register for the place-out exam at this link: https://docs.google.com/forms/d/e/1FAIpQLSdbzGVu_Tc0rf1M4hHxrbz7mxxJWvYlE4KTad-HM37F5W2oJw/viewform

For any questions, email Prof. Alexander Borisov at borisov@math.binghamton.edu

Course Planning by Track

2026-03-06T20:52:27-04:00

Course Planning by Track

This page offers track-specific guidance on course sequencing. See also:

Prerequisite Dependency Infographic
Sample 4-Year Plans (Google Drive, one spreadsheet per catalog year, with tabs for each track and 4+1 option)

All Tracks

Complete Math 330 (Number Systems) as soon as possible — no later than your fourth semester, preferably your third.
Finish Math 304 (Linear Algebra), Math 323 (Calculus III), and Math 330 before advancing to upper-level courses (MATH courses above 330).
A grade of C or better is required for a course to count toward the major and to satisfy prerequisites. If you do not earn C or better in a required course twice, you will be automatically dropped from the major.
Prerequisite requirements are strictly enforced — you will be automatically dropped from a course if you did not earn C or better in its prerequisite.
Meet with your assigned faculty advisor regularly.
Plan to take two math courses per semester on average.
Make a contingency plan — what will you do if you need to retake a course?
Get involved. The Math Club, Actuarial Association, Association for Women in Mathematics, and Pi Mu Epsilon honor society chapter are good ways to connect with peers and learn about opportunities.

BA Mathematics Track

Finish the five lower-level courses (Calculus series, 304, 330).
Take one course from each of analysis, algebra, and geometry/topology.
Take two more upper-level courses, as long as they are not both from the same group.
Within the five upper-level courses, ensure there is a qualifying pair as specified in the Academic Guide.

BS Mathematics Track

The BS requires more upper-level and proof-oriented courses including Real Analysis I & II (Math 478/479), Modern Algebra (Math 401), and Topology (Math 461). If you are aiming at graduate school in mathematics, this is the recommended track. Consult the Academic Guide for the full requirements.

Actuarial Science Track

Take Math 346 (Intro Financial Math), Math 447 (Probability Theory), and Math 448 (Mathematical Statistics) as soon as possible — they are prerequisites for many electives.
It is too late to take Math 448 in your senior year.
The Actuarial track also requires Econ 160 and Econ 162; the BS additionally requires Econ 360 and Econ 362. Plan these into your first two years.
Consider taking School of Management VEE courses if you can — they are not required but useful for actuarial exam preparation.

Data Science and Statistics Track

Take Math 447 (Probability Theory), Math 448 (Mathematical Statistics), and Math 445 (Principles of Data Science) or Math 446 (Scientific Computing in Python) as soon as possible. It is too late to take these in your senior year.
Math 455 (Regression Models) and Math 457 (Intro to Statistical Learning) are core to this track — plan to take them in your third year.

Overview of the Major Tracks

2025-12-07T02:49:24-04:00

Overview of the Major Tracks

(For forms, transfer policies, and advising details, see the Undergraduate Program main page.)

Mathematics belongs both to liberal arts and to sciences. It is not only the language of science (including social science), but also studied for its own beauty. It is therefore one of the most vital and lively subjects in the University curriculum.

The Undergraduate Program of the Department of Mathematics and Statistics include six major degree options in three major tracks.

The common preliminary lower-level courses required for all math major options are calculus I–III (Math 224/225, Math 226/227 or Math 230, and Math 323), linear algebra (Math 304), and number systems (Math 330). Read the Academic Guide for a very comprehensive and detailed official description about the coursework requirements for each of the six major degree options.

Mathematics Tracks (BA/BS)

The BA in Mathematical Sciences allows students to flexibly design a course of study that fits their individual interests, with options to emphasize either breadth or depth. Students are encouraged to gain experience in several areas of mathematics. Core areas include Analysis, Algebra, and Geometry/Topology. Additional areas include Actuarial Science, Statistics, Combinatorics, Computer Science, and related fields. Students must complete one upper-level course from each of the three core areas, plus two additional upper-level courses. To obtain a BA degree in mathematical sciences with the mathematics track, a student must complete a minimum of 40 credits of coursework.

The BS degree program is more intensive and provides excellent preparation for graduate study in mathematics and related disciplines. Students considering a BS degree should consult with their academic advisors as early as possible and plan their schedules carefully to meet the demanding requirements. To obtain a BS degree in mathematical sciences with the mathematics track, a student must complete a minimum of 64 credits of coursework

Data Science & Statistics Track (BA)

Data science and statistics focus on turning raw data into reliable insight and decisions in the presence of uncertainty. This field combines statistical modeling, computing, and domain knowledge, with applications across the natural and social sciences, business, engineering, and the humanities.

The BA track in Data Science & Statistics is designed to provide a strong mathematical and statistical foundation together with modern data-science tools, while leaving room for a second major or minor. Students complete core coursework in calculus, linear algebra, probability, mathematical statistics, regression, and statistical learning, together with a computing-intensive course and a practical experience in data analysis (for example, an internship, research project, or consulting course).

This track works especially well in combination with majors such as computer science, biology, psychology, economics, finance, accounting, management, or other social and natural sciences. To obtain a BA degree in mathematical sciences with the Data Science & Statistics track, students must complete the required core and elective courses described in the University Bulletin and on the departmental planning sheets. Approximate number of credits is 52–56.

Data Science & Statistics Track (BS)

The BS track in Data Science & Statistics is a more intensive program aimed at students who want a deeper mathematical and computational background for graduate study or technically demanding careers in data science, statistics, or related fields.

In addition to the core courses shared with the BA track (calculus, linear algebra, probability, mathematical statistics, regression, statistical learning, and computing), BS students take further upper-level mathematics and statistics, such as real analysis, advanced linear algebra, optimization, stochastic processes, or related topics. They also complete additional advanced electives and a practical experience in data analysis.

Students considering the BS track are strongly encouraged to consult with their academic advisors early and to plan their schedules carefully to meet the more demanding requirements. To obtain a BS degree in mathematical sciences with the Data Science & Statistics track, students must complete all required core and elective coursework specified in the University Bulletin and departmental degree-planning materials. Approximate number of credits is 64–68.

Actuarial Tracks (BA/BS)

The Actuarial Science track is designed to prepare students for an actuarial career. Actuaries use probability models to quantify uncertainty and risk in business problems. They assemble and analyze data related to risks in order to answer questions such as how much to charge policyholders for auto, life, or health insurance, how to design retirement plans, and how to formulate investment strategies in light of future risks. They provide crucial evaluations of risk that inform their companies’ strategic decisions.

Because of their central role in decision making, actuaries are well compensated; salaries offered to actuaries are substantial, and there is ample opportunity for advancement in the actuarial profession. Moreover, actuarial careers often lead to upper management and executive positions.

Refer to the Math department section on actuarial sciences for more detailed information.

Professional advancement results from passing a series of examinations administered by the actuarial societies and by completing specific courses approved by these societies.

To obtain a BA degree in mathematical sciences with an actuarial science track, a student must complete 52 credits of coursework, including 11 courses in Mathematical Sciences and 2 courses in Economics. The BS degree with an actuarial science track requires 76 credits of coursework, including 15 courses in Mathematical Sciences and 4 courses in Economics.

Future Career Paths

In the technology-oriented climate of today, mathematicians and statisticians have excellent employment opportunities. Our graduates are employed not only in mathematics teaching and research, and in the traditional fields of physics, chemistry, computer science, and engineering, but also, and increasingly, in business, economics, environmental sciences, geology, biology and the health sciences among others.

The following websites below provide some resources on the career perspective for math and stats graduates.

Mathematics Teachers

For students who are interested in becoming math teachers, Binghamton offers:

An undergraduate minor in Education
A Master of Arts in Teaching (MAT) in Mathematics Adolescent Education; Either the BA (Mathematics Track) or BS (Mathematics Track) is suitable for preparing this MAT program.
Here is a list of recommended courses for future math teachers.

Math 304 Linear Algebra - Section 4 - Fall 2014

2017-01-05T18:20:20-04:00

Math 304 Linear Algebra - Section 4 - Fall 2014

Meeting Times: MWF 3:30-5:00 PM in LN 1120
The class does not meet on the following days:
M 9/1, W 9/24, F 9/26, F 10/3, W 11/26, F 11/28

Instructor: Luise-Charlotte Kappe
Office: OW 126
e-mail: menger@math.binghamton.edu
Office hours: M 2-3 PM, W 1:30-2:30 PM, F 2-3 PM, and by appointment
NOTE: The office hours of the other Math 304 instructors are open to all Math 304 students. See the course website for further details.

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TEXTS

“Linear Algebra”, A Text for Math 304, Fall 2014, at Binghamton University, by Matt Brin and Gerald Marchesi, 13th edition, published by the Department of Mathematical Sciences, Binghamton University, available through the University Bookstore.
“Beginning Linear Algebra” by Seymour Lipschutz, Schaum's Outlines, McGraw-Hill.(This is a workbook and supplements the main text, gives practice problems, examples and additional problem assignments.)

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COURSE CONTENT: Chapters 1-5 of “Linear Algebra”, parts of Chapter 6.

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EVALUATION: Your grade will be based on the final, two midterms, weekly quizzes, as well as attendance and class participation. The weight distribution is as follows:


Final	30 %
Two Midterms (20% each)	40 %
Quizzes	25 %
Class Participation and Attendance	5 %
Total	100 %

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The two midterms (10/2 and 11/6) and the final (12/18) are common to all sections. For further details see the website.

There will be weekly quizzes that will be announced in advance. The material covered will have a strong correlation to the homework covered in class. Be aware that there will be no make-ups for missed quizzes, but at least two quizzes, missed or with the lowest grade, will be dropped. The first quiz will be W 9/10, covering Sections 1.1-1.3.

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Quiz Announcements

Thirtienth Quiz, W 12/10, Topic: 6.2.1-6.2.4. Due to weather reasons, Quiz 13 will be postponed to Friday, 12/12. A key will be handed out right after the quiz is handed it. The graded quiz can be picked up either in the review on Sunday or at the final.
Twelfth Quiz, F 12/5, Topic: 6.1.
Eleventh Quiz, M 11/24, Topic 5.3.
Tenth Quiz, W 11/19, Topic 5.1-5.2.
Ninth Quiz, F 11/14, Topic: 4.8.
Eighth Quiz, M 11/3, Topic: 4.3-4.6.
Seventh Quiz, W 10/29, Topic: 4.1-4.2.
Sixth Quiz, F 10/24, Topic: 3.6.1-3.6.3.
Fifth Quiz, F 10/17, Topic: 3.5.
Fourth Quiz, F 10/10, Topic: 3.3 and 3.4.
Third Quiz, M 9/22, Topic: 2.1-2.3.
Second Quiz, W 9/17, Topic Sec. 1.4 and 1.5.
First Quiz, W 9/12, Topic Sec. 1.1-1.3.

Homework Announcements

Week 15
- For M 12/8: 6.2 (68),(69); 6.3 S6-10, S6-11.
- For W 12/10: 6.3 S6-13, S6-14; Review Problems: # 40.
- For F 12/12: Review Problems # 32-39; #7-11.

Week 14
- For M 12/1: 6.1 (64).
- For W 12/3: 6.1 (65) # 1,3,4,5; 6.3 S6-1.
- For F 12/5: 6.2 (66) # 1,2; 6.3 S6-6, S6-8.

Week 13
- For M 11/24: 5.5 S5-7, S5-9.

Week 12
- For M 11/17: 5.2 (56).
- For W 11/19: 5.2 (58); 5.3 (59).
- For F 11/21: 5.3 (60),(61),(62).

Week 11
- For M 11/10: 4.8 (52) # 2-5, (53) # 2, (54) # 1,3,5.
- For W 11/12: 4.8 (52) # 2,3; 4.9 S4-10.
- For F 11/14: 4.9 S4-20; 5.1 (55).

Week 10
- For M 11/3: 4.6 (49); 4.9 S4-10 (a).
- For W 11/5: Practice Test 2, # 3,7,8,11.
- For F 11/7: 4.8 (51), (52) # 1.

Week 9
- For M 10/27: 4.3 (46), # 1,2; 4.9 S4-1, S4-2.
- For W 10/29: 4.4 (47); 4.9 S4-3, S4-4, S4-6.
- For F 10/31: 4.5 (48) # 2,3; 4.9 S4-5, S4-7.

Week 8
- For M 10/20: 3.6 (41); 3.8 S3-15.
- For W 10/22: 3.6 (42); 3.8 S3-20 thru S3-28.
- For F 10/24: 4.1 (44); 4.2 (45) # 1,2,3.

Week 7
- Due M 10/13: 3.5 (39) # 1-4; 3.8 S3-9, S3-12.
- For W 10/15: 3.5 (39) # 2 and 5; 3.8 S3-11, S3-12.
- For F 10/17: 3.6 (40); 3.8 S3-13, S3-18.

Week 6
- Due M 10/6: 3.3 (34), (35); 3.6 S3-1, S3-2.
- Due W 10/8: 3.3 (36) # 1,3,4; 3.4 (38); 3.8 S3-3, S3-4.
- Due F 10/10: 3.4 (37); 3.8 S3-6, S3-7, S3-8.

Week 5
- Due M 9/29: 2.7 (24),(25), (26).
- Due W 10/1: Practice Problems for Test 1,# 9, 10 and 11
  (Hint for 10 and 11: find the associated matrices for F and G).

Week 4
- Due M 9/22: 2.6 (21) # 1, 2.11 S2-4, S2-5a).

Week 3
- Due M 9/15: Sec.1.7 S1-15, S1-16, Sec.2.1 (14) #1-4.
- Due W 9/17: 2.2 (15) 1a), 1b), 2d), 2i), 2m) and 4).
- Due F 9/19: 2.4 (17), 2.5 (18), (20).

Week 2
- Due M 9/8: Section 1.2 (4) #1; Section 1.7 S1-9, S1-10, S1-11.
- Due W 9/10: Sec.1.3 (7), Sec.1.4 (8), Sec.1.7, S1-1, S1-2.
- Due F 9/12: Sec.1.5 (9), Sec. 1.6 (10), Sec.1.7 S1-4, S1-14.

Week 1
- Due F 9/5: Section 1.1 (1) #1; Section 1.2 (2) #1; (3) #1.

Math 530: Linear Algebra for Statisticians

2022-09-15T20:00:11-04:00

Math 530: Linear Algebra for Statisticians

Basic Info

Meeting times/Place: MWF 10:50am -11:50am at LN2403

Office hours: MWF 9:45 - 10:30 AM, Monday 1 - 2 PM (in person, office WH136, or by Zoom), or by appointment

Prerequisites: Math 304 (Linear Algebra), 329, 330 or equivalent.

Texts

We will use Strang “Linear Algebra with Applications”, and “Numerical Linear Algebra” by Lloyd Trefethen and David Bau.

The electronic versions of these books are available at the Piazza course webpage.

Learning outcomes

We will cover several types of matrices, various matrix decompositions including SVD, QR and Cholesky, their application to linear regression, and Multivariate Gaussian distribution.

Computing

I will ask students to subscribe to Datacamp.com for 1 or 2 months (do not pay annual subscription!) and take 3 Datacamp courses in “Python”. Specifically, “Introduction to Python”, “Intermediate Python”, “Python Data Science Toolbox 1”. Every datacamp course will be expected to be finished in 1 or 2 weeks and at the end of each one, the student will send me a proof that he or she has passed the course. There will be additional Python based exercises.

Communication

I will mostly use Piazza Forum (https://piazza.com). In particular, I will post all announcements and lecture notes on this website. So make sure that you are enrolled at Piazza. You can either sign up at “https://piazza.com/binghamton/fall2022/math488math530” or send me an email. Since this is a forum, questions and answers by students are encouraged. I will use MyCourses/Brightspace only minimally if at all.

Homework Policy

The homework on linear algebra will be assigned using Gradescope.

There will be a deduction of 25% of the grade for homework assignments that are not typeset using LaTeX. (For users with no experience with LaTex, I suggest trying “https://www.overleaf.com/”.)

There will be a deduction of 15% of the grade for each day homeworks are late (the final grade for a late homework that is N days late will be 0.85^N times the real grade). Homeworks may be discussed with classmates but must be written and submitted individually.

There will also be some Python homework which will have to be submitted both on Gradescope (pdf file) and through a Google form (source file).

Exams

The will be two midterms and one final exam.

Grading

The grading scale will be different for undergraduate and graduate students.

Linear Algebra Homework 25%
Python Courses + Python Homework 25%
Midterms 20% (10% each)
Final Exam 30%

Tentative Schedule

Midterm Exam I	September 30
Midterm Exam II	October 28

Alex Feingold

2026-04-06T05:10:41-04:00

Alex Feingold

Professor
Ph.D., 1977, Yale University
At Binghamton since 1979
Areas of Interest: Algebra, Lie algebras and their representations, conformal field theory, piecewise isometry groups
Summary of research interests

Math Reviews list of published papers .
(Institutional subscription to MathSciNet is needed for viewing.)

E-mail:	feingold@binghamton.edu, alex@math.binghamton.edu
Office:	WH 115
Fax:	(607) 777-2450

Courses:
- Spring 2026
  
  Math 304 Section 06 : Linear Algebra
  
  MWF 1:30 - 3:00 CW-206
  
  Math 304 Section Coor : Linear Algebra
  
  - -
Ph. D. Students:
- Joshua Carey, Spring, 2022
  Thesis: Branching rule decomposition of the level-1 $E_8^{(1)}$-module with respect to the irregular subalgebra $F_4^{(1)} \oplus G_2^{(1)}$
- Diego Penta, Spring, 2016
  Thesis: Decomposition of the Rank 3 Kac-Moody Lie Algebra F with Respect to the Rank 2 Hyperbolic Subalgebra Fib
- Christopher Mauriello, Spring, 2013
  Thesis: Branching Rule Decomposition of Irreducible Level-1 E₆⁽¹⁾-modules with respect to F₄⁽¹⁾
- Quincy Loney, Summer, 2012
  Thesis: Decomposition of Level-1 Representations of D₄⁽¹⁾ With Respect to its Subalgebra G₂⁽¹⁾ in the Spinor Construction
- Omar Saldarriaga, Summer, 2004
  Thesis: Fusion Algebras, Symmetric Polynomials, Orbits of Elementary N-Groups, and Rank-Level Duality
- Mike Weiner, Spring, 1994
  Thesis: Bosonic Construction of Vertex Operator Para-Algebras from Symplectic Affine Kac-Moody Algebras

Here's a link to my personal web page where you can find links to syllabi of my current and recent courses, links to pictures of my mathematical sculptures, links to the webpages I maintain for the Phi Beta Kappa liberal arts honor society, and for the Pi Mu Epsilon math honor society, as well as many other interesting links.

Math 304 Linear Algebra Summer 2020

2020-05-14T15:24:08-04:00

Math 304 Linear Algebra Summer 2020

(This page is under construction)

Syllabus

comimg soon

Code of Academic Honesty

Lectures

Videos will be uploaded with names of the form

(C)xyz : C for concept, I will talk about concepts, there will be examples, but I will not do any computation, for example I will just tell you that the roots of x^2+5x+6 is -3,-2 without show you the steps (this is a bad example, I expect you to know how to solve x^2+5x+6 if you are taking this class).

(P)xyz : P for problem, I will work out simple problems, and give details (or just enough details).

(R)xyz : R for request, I will respond to some of your request, for example more example, more steps in demonstration or additional topics.

I will upload videos for system of linear equations by the end of May, to give you an idea of what to expect.

other videos will be upload according to the class schedule.

Exams (and possibly presentation)

Exams will be administered through ProctorU, if privacy is an issue for you, then you may need to consider other course options.

I'm planning on giving a poll at the start of the semester to decide between:

1. 2 Midterm 1 Final

2. 1 Midterm 1 Presentation 1 Final

Presentation

Presentation topics will be decided by me taking into consideration of your preferences, you will either be explaining:

1. a new concept in Linear Algebra that is not in the course,

2. an application of Linear Algebra in other fields Economics, Chemistry, statistics, probability, computer science etc. (the list is endless).

Sarah Lamoureux

2026-04-06T05:10:41-04:00

Sarah Lamoureux

Lecturer
Ph.D., 2023, Binghamton University
At Binghamton since 2024
Summary of research interests

E-mail:	alamour1@binghamton.edu, lamoureux@math.binghamton.edu
Office:	WH 330
Fax:	(607) 777-2450

Office hours:
- MW 4:00 - 5:30

Courses:

Spring 2026

Math 220	Section 03 :	Calculus for Business and Management
	MWF 11:45 - 1:15	CW-305
Math 304	Section 02 :	Linear Algebra
	MWF 8:00 - 9:30	CW-209
Math 304	Section 03 :	Linear Algebra
	MWF 9:45 - 11:15	CW-209

Actuarial Majors

2022-07-18T13:05:00-04:00

Declare Actuarial Majors

Binghamton University offers two degrees in this field: BA in Actuarial Science and BS in Actuarial Science. Before you declare a major in actuarial science, you may want to think about the following questions very carefully:

Have you shown strong aptitude in mathematics or quantitative skills in general? An example would be grades of your calculus courses. Usually, if you did not get a grade greater than B in calculus, it is early indicator that you will have some difficulties in the actuarial program. In extreme cases, you may suffer from studying something that you are not very good at, fail several attempts to an exam and may not even find a job related to actuarial career after graduation.
Are you a self-motivated person? Can you work on yourself to study the materials without an instructor? Do you study because you want to become an actuary or your parents want you to do? Remember there are many advanced exams to pass even after you graduate from college.

If your answers to either questions are YES, then you may be on the right track to become an actuary.

To declare an actuarial major, click here.

On the other hand, be aware that you can become an actuary without a degree in actuarial science. A really self-motivated person can buy a book off the bookstore and study without the class.

Major Requirements

The major requirements for each student may differ and they depend on the time that the student first entered the university. See the university bulletin for the requirements for a particular year. In case of ambiguity, the student should consult the Degree Work, the designated advisor in the math department, the director of undergraduate studies in the math department, or the Harpur advising office.

Effective for students entering the university in or after Fall 2017

The following courses are required for the BA and BS degrees.

Common requirements for both BA and BS
- Calculus and Linear Algebra: 224 and 225, either both 226 and 227 or 230, 323, 304;
- Number Systems: 330 (it is strongly advised that this course is taken as soon as 227 or 230 is completed);
- Computing: 329;
- Actuarial foundation courses: 346, 447, 448;
- Actuarial elective courses: two courses from 450, 452, 454, 455, 457, and either 458 or ECON 467;
- Economics courses: ECON 160 and 162.
Additional requirements for BS only
- Advanced math courses: two courses from 404, 472, 478 and 479;
- Actuarial elective courses: two additional courses from 450, 452, 454, 455, 457, and either 458 or ECON 467;
- Advanced Economics courses: ECON 360 and 362.

For a course to count for the degree, a grade 'C' or better must be obtained. See the Grade Requirements and Prerequisites section below.

There are 12.5 required 4-credit courses for the BA degree (10.5 from the Department of Mathematics and Statistics and 2 from the Department of Economics).

There are 18.5 required 4-credit courses for the BS degree (14.5 from the Department of Mathematics and Statistics and 4 from the Department of Economics).

Sample Course Lineup

The table below shows a sample schedule for a typical BS actuarial major. For BA students, fewer courses are required. Many of our majors come in with AP credits for Calculus I (224/225) and Econ 160/162. In this case, shift the schedule up by one or two semesters.

Semester	Math courses	Other courses	Notes
1	224/225	Econ 160 (vee)
2	226/227 (or 230), 304	Econ 162 (vee)
3	323, 346	Acct 211 (vee)	Prep for FM
4	330, 447,	Fin 311 (vee)	Take FM & Prep for P
summer			Take P/1
5	329, 448 (vee), 450	Econ 360	Look for internship
6	452, 455	Econ 362	MLC
7	457, 478
8	454 or 458, 479		MFE, Statistics Exam, Predictive Analytics

Courses that fulfill a VEE requirement are labeled (vee). Not all the courses above are required. Those which are not part of the major requirements are recommended but not required.

Grade Requirements and Prerequisites

Effective for students entering the university in or after Fall 2020

Any math course in which a student earns a grade of C- or less is not acceptable as a prerequisite for any other course offered by the Department of Mathematics and Statistics unless stated otherwise in the course description.
Any math course in which a student earns a grade of C- or less cannot be used to fulfill the requirements of the major or minor.
Math courses may only be repeated once to meet the above minimum grade requirements for the major. No course for the major may be taken more than twice. Students who fail to receive a grade of C or better after two attempts in a required major course will be dropped from the major. Withdrawals do not count towards the attempt limit. Students who are seniors may petition for an exception to this policy.
A pass grade (P) does not count toward the major or minor unless the only grade available is Pass/Fail; in this case, consent of the Department is required.
A student who has received credit for a course may not take one of its prerequisites for credit at a later time.

Courses

2025-03-27T12:00:21-04:00

Courses

Department course schedules: for internal planning purposes only. Please refer to the class schedule on BU Brain for the official and most up-to-date information.
Final exam schedules
Help room schedules
Office hours

An overview of undergraduate courses in the math department, excluding some non-major courses, shows the prerequisite dependency between courses. Please refer to the University Bulletin for the exact requirements for the degree.

Linear Algebra Summer 2016

2016-08-11T11:37:14-04:00

Linear Algebra Summer 2016

Links

Syllabus

WeBWorK

Your WeBWorK username is the part of your Binghamton University email address that comes before the @ symbol. Your default password is the same as your username.

Spring 2016 Linear Algebra Home Page

The Spring 2016 page contains links to exams, quizzes, and notes from previous semesters.

Tests

	Maximum score	1st quartile	Median	3rd quartile
Test 1	70	59	64	69	Solutions
Test 2	150	134.75	121.5	109	Solutions
Test 3	150	119.5	100	85	Solutions
Test 4	150	111	99	89.5	Solutions
Final	300

Quizzes

Week 1		Quiz 1	Quiz 2	Quiz 3
Week 2	Quiz 4	Quiz 5	Quiz 6	Quiz 7
Week 3	Quiz 8	Quiz 9	Quiz 10	Quiz 11
Week 4	Quiz 12	Quiz 13	Quiz 14	Quiz 15
Week 5	Quiz 16	Quiz 17	Quiz 18	Quiz 19

Humor

Linear Algebra - Math 304

2017-11-28T11:09:12-04:00

Linear Algebra - Math 304

Fall 2017

Old Announcements

Test 2 Room

The location for Test 2 depends on your section number:

Section 1: LH-014

Section 2: LH-014

Section 3: LH-002

Section 4: LH-014

Section 5: LH-002

Section 6: LH-002

Test 2 Second Review Session

Casey Kapklein will be holding a second review session for the second exam for MATH 304. The review session will be 8:00 pm to 10:00 pm, Tuesday, November 7th in Science Library 206.

Test 2 Review Session

Casey Kapklein will be holding a review session for the second exam for MATH 304. The review session will be 4:30 pm to 6:30 pm Friday, November 3rd in Lecture Hall 8.

Test 1 Room

The location for Test 1 depends on your section number:

Section 1: LH-014

Section 2: LH-002

Section 3: LH-002

Section 4: LH-014

Section 5: LH-002

Section 6: LH-014

Test 1 Review Session

I will be holding a review session for the first exam for MATH 304. The review session will be 8 pm to 10 pm Tuesday, October 3rd in Lecture Hall 8. –Casey

Tara Koskulitz

2026-04-06T05:10:40-04:00

Tara Koskulitz

E-mail:

tkoskul1@binghamton.edu

Office: WH 326
Office hours:

MW 11:00 - 12:30
Courses:
- Spring 2026
  
  Math 304 Section 07 : Linear Algebra
  
  MWF 1:30 - 3:00 WH-G002
  
  Math 304 Section 08 : Linear Algebra
  
  MWF 3:15 - 4:45 WH-G002

Stefan Viola

2026-04-06T05:10:39-04:00

Stefan Viola

E-mail:

sviola2@binghamton.edu

Office: WH 326
Office hours:

MW 1:30 - 3:00
Courses:
- Spring 2026
  
  Math 304 Section 04 : Linear Algebra
  
  MWF 9:45 - 11:15 LN-2403
  
  Math 304 Section 05 : Linear Algebra
  
  MWF 11:45 - 1:15 LN-2403

Wei Yang

2026-04-06T05:10:39-04:00

Wei Yang

E-mail: wyang@math.binghamton.edu
Office: WH 326 / WH 335
Personal Website : weiyang2048.com
Spring 2023 Schedule:
- Math 304 Linear Algebra, MWF 11:20-12:50, AA G07
  Notes
- Math 323 Calculus III, MWF 1:10 - 2:40, WH G01
  Notes
- Office Hours : MWF 10:00-11:00, WH 335

Math 304 Linear Algebra: Summer 2017

2017-07-02T12:46:46-04:00

Math 304 Linear Algebra: Summer 2017

Links:

Syllabus

WeBWorK

Your WeBWorK username and password are the segment of your Binghamton University e-mail address that comes before the @ symbol. For example, if your email address is abcxyz1@binghamton.edu, both your username and password are abcxyz1. Please change your password upon logging in for the first time.

Emmanuel Adara

2026-04-06T05:10:41-04:00

Emmanuel Adara

Robert Riley Visiting Assistant Professor
Ph.D., 2025, the University of Alabama
At Binghamton since 2025
Summary of research interests

E-mail:	eadara@binghamton.edu, eadara@math.binghamton.edu
Office:	WH 322
Fax:	(607) 777-2450

Office hours:
- M 11:00 - 12:00
Courses:
- Spring 2026
  
  Math 304 Section 01 : Linear Algebra
  
  MWF 8:00 - 9:30 CW-109

Linear Algebra

2017-01-19T11:36:07-04:00

Linear Algebra

Home

Syllabus

SYLLABUS FOR MATH 304-FALL 2015

2017-08-25T16:01:31-04:00

SYLLABUS FOR MATH 304-FALL 2015

The course covers basics of elementary linear algebra. It is not just computation but the intent is that some concepts and understanding give and gain significance from the computation. It is meant to be at the level of a Second year mathematically competent student.

The text is book written by Matthew Brin and Gerald Marchesi ;Linear Algebra 16-th edition. We will cover the first 6 chapters fairly thoroughly and if time provides delve into Chapter 7. A weekly schedule plan is laid out below.

WEEK 1	Aug 31-Sept4	Chapter 1	Sections 1.1-1.3.1
WEEK 2	Sept 8-Sept 11	..	.. 1.3.2-1.5
WEEK 3	Sept 16-Sept 18	..	.. 1.6.1-1.6.9
WEEK 4	Sept 21;Sept 24-25	Chapter 2	Sections 2.1-2.3
WEEK 5	Sept 28-Oct 2	..	.. 2.4-2.7
WEEK 6	Oct 5-Oct 9	..	.. 2.8-2.10; Test 1
WEEK 6	Oct 5-Oct 9	Chapter 3	.. 3.1-3.2
WEEK 7	Oct 12-Oct 16	..	.. 3.3-3.6
WEEK 8	Oct 19-Oct 23	..	.. 3.7-3.8
WEEK 8	Oct 19-Oct 23	Chapter 4	.. 4.1-4.2
MIDTERM EXAM	WED. OCT 21, 7:00 PM- 9:00 PM	Location To Be Announced
WEEK 9	Oct 26-Oct 30	..	.. 4.2-4.7
WEEK 10	Nov 2- Nov 6	..	.. 4.8- 4.9
WEEK 11	Nov 9- Nov 13	Chapter 5	.. 5.1-5.3.2
WEEK 12	Nov 16-Nov 20	..	.. 5.3.3-5.5
WEEK 13	Nov 23-Nov 24	..	.. Review Test 2; THANKSGIVING
WEEK 14	Nov 30-Dec 4	Chapter 6	.. 6.1-6.2.3
WEEK 15	Dec 7- Dec 11	..	.. 6.2.4; 6.2.6 OR 7.1 ; QUIZ
WEEK 16	Dec 14-15		REVIEW

Final exam date and location to be announced.

Exams

Tests 1 and 2, and the Quiz at the end will be prepared for the individual sections and graded by the instructor(some sharing of writing and grading may occur). The Midterm is scheduled Oct. 21 in the evening. Please plan accordingly for class conflicts and extreme hardship we will schedule a make-up date. The time and location of the Final exam will be determined by the University during the scheduled times for final exams.

The exams will be pretty detailed and will require your mastery of the material to do well. Typically the percentage score expectation for the various grades are: A 85-100 ; B 70-85 ; C 50-70 ; D 40-50 with + and - at the extremes.

Weighting of the contributions to final grade

There will be 1000 possible for the course comprised as follows;

Final exam	400 pts.
Midterm	250 pts.
Hourly Exams	200 pts. (100 each)
End Quiz	50 pts.

Additionally, there will be 100pts. contributed by the instructor to be based on work in the class. Each instructor will choose how to use attendance, in class quizzes, homework or special assignments to determine this contribution.

Linear Algebra Summer 2015

2016-07-13T13:33:00-04:00

Linear Algebra Summer 2015

Important links

Syllabus

WeBWorK

Math Help Rooms

Exams

	Maximum score	Average score	1st quartile	Median	3rd quartile
Exam 1	70	66.69	68	70	70
Exam 2	150	124.50	121.25	129	138
Exam 3	150	83.13	67.25	92.5	101.75
Exam 4	150	108.06	89.75	106.5	134.5

Linear Algebra - Math 304 - 01

2026-04-06T05:10:41-04:00

Linear Algebra - Math 304 - 01

Fall 2017

Syllabus

Instructor:	Fernando Guzmán	WH-116	x-72876	fer@math.binghamton.edu

Classroom:	S2-144	MWF 8:00 - 9:30

Office Hours:	Tuesday	12:00 - 1:00
(subject to change)	Wednesday	3:00 - 4:00
(subject to change)	Friday	12:00 - 1:00

Homework

Linear Algebra - Math 304 central web site for all sections.

Announcements

Office hours for finals week:
- Monday 12/11, 3:00-4:00
- Wednesday 12/13, 3:00-4:00
- Thursday 12/14, 11:00-12:00

Tuesday office hour changes to 12:00-1:00 for the rest of the semester
Office hour for Tuesday, Nov. 7 is moved to 12:00-1:00pm
Office hour for Wednesday, Oct. 11 is moved to 2:00-3:00 pm
Test 1 is Wednesday, Oct 4th at 7:00 pm in LH-014
Starting Friday 08/25/17, classes will be held in S2-144

Linear Algebra - Math 304

2026-04-06T05:10:41-04:00

Linear Algebra - Math 304

Fall 2017

Math 304	Section 06 :	Linear Algebra
	MWF 1:30 - 3:00	CW-206
Math 304	Section Coor :	Linear Algebra
	-	-

Math 304	Section 07 :	Linear Algebra
	MWF 1:30 - 3:00	WH-G002
Math 304	Section 08 :	Linear Algebra
	MWF 3:15 - 4:45	WH-G002

Math 304	Section 04 :	Linear Algebra
	MWF 9:45 - 11:15	LN-2403
Math 304	Section 05 :	Linear Algebra
	MWF 11:45 - 1:15	LN-2403

Department of Mathematics and Statistics, Binghamton University

Course Description

Course Description

MATH 105, BEGINNING ALGEBRA

MATH 106, INTERMEDIATE ALGEBRA

MATH 107, BASIC INTEGRATED MATHEMATICS

MATH 108, ALGEBRA AND TRIGONOMETRY

MATH 130, MATHEMATICS IN ACTION

MATH 147, ELEMENTARY STATISTICS

MATH 148, ELEMENTARY STATISTICS FOR BIOLOGISTS

MATH 220, CALCULUS FOR BUSINESS AND MANAGEMENT

MATH 221, CALCULUS I

MATH 222, CALCULUS II

MATH 304, LINEAR ALGEBRA

MATH 314, DISCRETE MATHEMATICS

MATH 323, CALCULUS III

MATH 327, PROBABILITY WITH STATISTICAL METHODS

MATH 330, NUMBER SYSTEMS

MATH 346, INTRODUCTION TO FINANCIAL MATHEMATICS

MATH 356, MATHEMATICAL MODELING

MATH 371, ORDINARY DIFFERENTIAL EQUATIONS

MATH 372, DYNAMICAL SYSTEMS

MATH 375, COMPLEX VARIABLES

MATH 381, GRAPH THEORY

MATH 386, COMBINATORICS

MATH 391, PRACTICUM IN COLLEGE TEACHING

MATH 401, MODERN ALGEBRA I

MATH 402, MODERN ALGEBRA II

MATH 404, ADVANCED LINEAR ALGEBRA

MATH 407, INTRODUCTION TO THE THEORY OF NUMBERS

MATH 447, INTRODUCTION TO PROBABILITY AND STATISTICS I

MATH 448, INTRODUCTION TO PROBABILITY AND STATISTICS II

MATH 449, PROBLEM SOLVING IN ACTUARIAL SCIENCE

MATH 450, ACTUARIAL MATHEMATICS I

MATH 452, ACTUARIAL MATHEMATICS II

MATH 454, FINANCIAL MATHEMATICS

MATH 461, TOPOLOGY

MATH 465, FOUNDATIONS OF GEOMETRY

MATH 471, PARTIAL DIFFERENTIAL EQUATIONS

MATH 472, PDE AND MATHEMATICAL ANALYSIS

MATH 478, REAL ANALYSIS I

MATH 479, REAL ANALYSIS II

MATH 480, SEMINAR IN ALGEBRA

MATH 488, TOPICS IN HIGHER MATHEMATICS

MATH 489, PROBLEM SOLVING

MATH 497, INDEPENDENT WORK

MATH 498, HONORS STUDY IN MATHEMATICS

Linear Algebra - Math 304

Linear Algebra - Math 304

Spring 2021 - Course Coordinator: Prof. Alex Feingold

Textbook

Approximate Exam Schedule (Each section instructor will decide when it is appropriate to give Exams 1, 2, 3.)

Grades

Homework

Expected workload

Expected behavior in class

Academic Code of Honor

Getting Help

Disability Information

Suggested problems from our textbooks

Sample Exams and Other Study Materials

Syllabi from previous semesters

Linear Algebra - Math 304

Linear Algebra - Math 304

Fall 2020 - Course Coordinator: Prof. Alexander Borisov

Textbook

Exam Schedule

Grades

Homework

Expected workload

Expected behavior in class

Academic Code of Honor

Getting Help

Disability Information

Tentative Schedule

Sample Exams and Other Study Materials

Syllabi from previous semesters

Linear Algebra - Math 304

Linear Algebra - Math 304

Spring 2020 - Course Coordinator: Prof. Alexander Borisov