Linear Algebra
Fall 2021

Section 001
Tuesdays and Thursdays, 8:40am - 9:55am
328 Milbank Hall (Barnard)

Section 002
Tuesdays and Thursdays, 10:10am - 11:25am
328 Milbank Hall (Barnard)

Dave Bayer
Office Hours

Directory of Classes | Mathematics
Student Services Online

Final Exam update

Our final exam is now an open-book take-home exam due Wednesday, December 22. It appears as an “assignment” on our CourseWorks page. Full details are given there, including options for students who have already completed this exam in-person on Thursday, December 16.

Zoom Problem Session for Final Exam

I held a problem session during Study Days, as preparation for our Final:

The session was recorded for later viewing on Courseworks.

Zoom Meetings

Our classes will normally be held in person, in 328 Milbank Hall (Barnard). We will use Zoom meetings for problem sessions.

The Zoom Class Sessions tab on CourseWorks gives a link for joining our Zoom meetings. Our two sections have been combined on Courseworks, so this link is the same for both sections. All meetings will be recorded for later viewing.

I will make an email announcement if it becomes necessary to use Zoom meetings for our classes.


By university and college policy, students are expected to attend class as their circumstances allow.

Should you be unable or unwilling to attend class, our course is particularly well-suited to being taken asynchronously. There are a complete set of videos of my lectures from Fall 2016:

I also post several decades of practice materials based on previous exams:

Separate from my in-person office hours, I will offer Zoom problem sessions before each exam.

Exam Schedule

Including our final, there will be a total of three exams. Course grades will be determined by these exams and graded homework:

Exams 1 and 2 will be in-class. Makeup exams will be given under exceptional circumstances.

Our final exam is now an open-book take-home exam due Wednesday, December 22. It appears as an “assignment” on our CourseWorks page. Full details are given there, including options for students who have already submitted this exam in-person on Thursday, December 16.



Each homework set consists of ten practice exam problems, and will be due before each exam.

Homework completed on paper may either be handed in using the homework box for your section, across from 410 Mathematics.

Homework completed digitally (such as on a tablet) may be uploaded via the Assignments tab on CourseWorks. You may also scan and upload your homework, using a scanner or a scanner app, or print out your homework and hand in the paper.

We will not accept camera photos.


I receive emails at both and

In general, one should use a work email address for work communications. In college, you should write professors using your university email address. Otherwise your message could be classified as spam, and go unread. If your university email address is not your uni, then please include your uni in your message.

In my case, I use Sanebox to prioritize my email, and I’ve whitelisted Barnard and Columbia email addresses to give them top priority.

Help Room, and Teaching Assistants

Assistance with linear algebra is available from the Columbia Help Room. Here is its current schedule.

I will include information here about our teaching assistants and preceptors once they are assigned.

Course Materials

This page hosts PDF files from this semester and previous semesters:

In Fall 2016, Columbia Disability Services videotaped my linear algebra course:

Here are some resources others have found helpful:


Linear Algebra with Applications (Classic Version), 5th Edition, by Otto Bretscher. Pearson, 2019. ISBN-13: 9780135162972 (Print), 9780321916914 (eText). Columbia University Bookstore, Amazon, or Addall.

The most recent edition of Bretscher is the text required by our department for Linear Algebra.

Homework assignments will be distributed as PDF files. They will serve as exam preparation, and will not taken from Bretscher. Therefore, I will have no direct way of knowing which edition, if any, of Bretscher that you obtain. I will recommend chapters to read from Bretscher, but students have found many alternative resources online that serve their needs, supplementing or replacing this text.

I nevertheless urge you to read as much linear algebra as possible. To have confidence in your understanding, you need to be able to decipher references to linear algebra in more advanced textbooks, after our course. My examinations test your computational abilities; I aim to provide an intuitive grasp of theory that makes sense of these computations. To be able to easily read linear algebra later, one needs to practice reading linear algebra now. I have no practical way to test that you have been reading linear algebra; this is your responsibility.


October 12, 2021 is the last day to drop a class, for Barnard, Columbia College, General Studies, Arts, GSAS, and Professional Studies. Check with your school’s academic calendar to confirm the dates that apply to you.

University Academic Calendar
Barnard Academic Calendar

This calendar gives our schedule of classes and exams:

Monday Tuesday Wednesday Thursday Friday
6 Sep 7 8 9 10
13 Sep 14 15 16 17
20 Sep 21 22 23 24
27 Sep 28 29 30 1 Oct
4 Oct 5   Exam 1    6 7 8
11 Oct 12 13 14 15
18 Oct 19 20 21 22
25 Oct 26 27 28 29
1 Nov 2 3 4   Exam 2    5
8 Nov 9 10 11 12
15 Nov 16 17 18 19
22 Nov 23 24 25 26
29 Nov 30 1 Dec 2 3
6 Dec 7 8 9 10
13 Dec 14 15 16   Final    17   Final   

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