Department of Mathematics and Statistics, Binghamton University math304

Dean of Students Help 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.

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:

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:

A First Course in Linear Algebra by Robert A. Beezer

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.

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.

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 paramount 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 major 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, 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

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.

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:

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

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 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:

A First Course in Linear Algebra by Robert A. Beezer

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.

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.

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/webwork2/304Fall2021/

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.

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, 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	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

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

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

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.

Textbook

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

A First Course in Linear Algebra by Robert A. Beezer

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.

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 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%

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 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

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

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%

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.

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:

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

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

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

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

A First Course in Linear Algebra by Robert A. Beezer

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

Fall 2020 page

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.

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. 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.

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:

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

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

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

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

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

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

A First Course in Linear Algebra by Robert A. Beezer

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.

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:

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%

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 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.

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 Spring 2025 is available through this link:

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

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

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

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

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

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

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

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

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

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.

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.

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:

A First Course in Linear Algebra by Robert A. Beezer

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.

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

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:

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:

A First Course in Linear Algebra by Robert A. Beezer

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.

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%

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/

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
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

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:

A First Course in Linear Algebra by Robert A. Beezer

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.

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

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

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.

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

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

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:

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

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

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

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

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

A First Course in Linear Algebra by Robert A. Beezer

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.

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:

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

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

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

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

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

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

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

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

A First Course in Linear Algebra by Robert A. Beezer

Linear Algebra - Math 304

2026-05-13T23:21:35-04:00

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.

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.

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 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:

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

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

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

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:

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

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

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

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

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

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

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

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

A First Course in Linear Algebra by Robert A. Beezer

Linear Algebra - Math 304

2026-06-06T22:37:38-04:00

Linear Algebra - Math 304

Fall 2026 -- Course Coordinator: Hung Tong-Viet

Sections

Sec	Instructor	Office	Email(*)	Meets	Room
1	Pratik Misra	WH-107	Misra	MWF: 8:00-9:30	WH-G002
2	Hung Tong-Viet	WH-108	Tong-Viet	MWF: 9:45-11:15	WH-G002
3	H. Nathan	WH-	Nathan	MWF: 11:45-1:15	WH-G002
4	H. Nathan	WH-	Nathan	MWF: 1:30-3:00
5	Michael Dobbins	WH-214	Dobbins	MWF: 1:30-3:00	WH-G002
6	Thomas Zaslavsky	WH-215	Zaslavsky	MWF: 3:15-4:45	WH-G002
7	Hari Asokan	WH-335	Asokan	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.

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 .

Exam 2: The week of . (Note: The withdraw deadline is .)

Exam 3: The week of .

Final Exam: Common exam for all sections:

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

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

Attendance Policy

VII.B.2. Student Attendance and Classroom Discipline

Reporting Absences

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 2026 is available through this link:

Spring 2026 page

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:

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

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

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

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

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

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

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

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