Linear Algebra
Fall 2020

Section 001
Tuesdays and Thursdays, 8:40am - 9:55am
Zoom meeting

Section 002
Tuesdays and Thursdays, 10:10am - 11:25am
Zoom meeting

Zoom meeting invitations are posted on the Courseworks page for your section, and require a Columbia University Zoom account.

Dave Bayer
Office Hours

Directory of Classes | Mathematics
Student Services Online

Exam Schedule

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

Makeup exams will only be given under exceptional circumstances.

Exams 1 and 2 will be take home-exams. You will have Friday and Monday to complete each exam. The exams will be open-book, but you are to work alone. All resources on my web site will be available. Other resources such as office hours and teaching assistants will not be available.

After each of these exams is returned to you, I will schedule a 20 minute meeting to ask you to explain your exam answers. 75% of your exam grade will be based on your written work, and 25% of your exam grade will be based on your oral answers. Please write exam answers showing all of your work, with clear presentations so that you can understand your answers.

I have not yet decided on the format for our final exams.


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, 5/E, by Otto Bretscher. Pearson, 2012. ISBN-10: 0321796977, ISBN-13: 9780321796974. Columbia University Bookstore, Amazon, or Addall.

Linear Algebra with Applications, 4/E, by Otto Bretscher. Pearson, 2009. ISBN-10: 0136009263, ISBN-13: 9780136009269. 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 8, 2020 is the last day to drop a class, for Barnard College, Columbia College, Graduate School of Arts & Sciences, School of General Studies, School of 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
7 Sep 8 9 10 11
14 Sep 15 16 17 18
21 Sep 22 23 24 25
28 Sep 29 30 1 Oct 2   Exam 1   
5 Oct   Exam 1    6 7 8 9
12 Oct 13 14 15 16
19 Oct 20 21 22 23
26 Oct 27 28 29 30
2 Nov 3 4 5 6   Exam 2   
9 Nov   Exam 2    10 11 12 13
16 Nov 17 18 19 20
23 Nov 24 25 26 27
30 Nov 1 Dec 2 3 4
7 Dec 8 9 10 11
14 Dec 15 16 17 18

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