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Linear Algebra - Math 304

Spring 2020 - Course Coordinator: Prof. Alexander Borisov

1Alexander BorisovWH-109777-2764borisovMWF:8:00-9:30SL-302
2Casey DonovenWH-202777-2982cdonovenMWF:8:00-9:30WH-G002
3David BiddleWH-126 biddleMWF:9:40-11:10AA-G021
4Charles (Matt) EvansWH-380 evansMWF:11:20-12:50LH-12
5David BiddleWH-126 biddleMWF:11:20-12:50AA-G021
6Alex FeingoldWH-115777-2465alexMWF:1:10-2:40SL-302
7Thomas KilcoyneWH-336 kilcoyneMWF:2:50-4:20LH-12
8Thomas KilcoyneWH-336 kilcoyneMWF:4:40-6:10LH-12

(*): Each email address in this table is of the form 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.


``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

Exam 2: March 18

Exam 3: April 22

Final Exam: TBA Common for all Sections.

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.

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.


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

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

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

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.


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.

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
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 Link to samples will appear here
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.2.15,16,17,19
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
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 Link to samples will appear here
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
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; more problems will be posted here
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
Linear maps (transformations) between general vector spacesCh. 3, II.1 3:II.1.18,19,20,25,26,28
11 Mar 30-Apr 3 Matrix of a linear transformation, matrix of the composition, inverseCh. 3, III.1, IV.2 3:III.1.12,14,15,18,19,20,21,22,26,29; more problems will be posted here
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
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
Eigenvectors, eigenvalues, eigenspaces for matrices and linear operators. Characteristic polynomial Matthews 6.1, 6.2; Ch. 5, II.35:II.3.23,26,27,28,29,30,33
Diagonalizable matrices Ch. 5, II.2, II.3 5:II.3.21,32,35,40,41,44
13 Apr 20-24 Review for Examination 3 Link to samples will appear here
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; more problems will be posted here
14 Apr 27-May 1 Orthogonal complement of a subspace, orthogonal projectionCh. 3, VI.3 3:VI.3.11,12,13,14,26,27
Gram-Schmidt process; orthogonal diagonalization of matricesCh. 3, VI.2 3:VI.2,13,15,17,18,19,22; more problems will be posted here
Review for the Final Examination
15 May 4 Review for the Final Examination Link to samples will appear here
16 Cumulative Final Exam - see schedule


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

math304/start.txt · Last modified: 2020/01/21 08:36 by borisov