Linear Algebra (Math UN2010) Fall 2026

Instructor: Semon Rezchikov
Time: Monday/Wednesday 2:40-3:55pm EST
Location: Ll002 Milstein Center
Email: srezchik at barnard dot edu (Please put "[UN2010]" in your email subject thread if emailing me)
Webpage: here! Homework will be posted here as well as on Courseworks
Office: Barnard Davis 301D

Instructor Office hours: 4-5pm on Mondays EST and 1-2pm on Tuesdays EST in my office.

Textbook: Linear Algebra with Applications (5th Edition) by Otto Bretscher. Problems will be assigned out of Bretscher (though I may supplement with my own problems). Math majors may also wish to refer to "Linear Algebra Done Wrong" by Sergei Treil; his textbook is more proof-based. (The title is a reference to a popular proof-based linear algebra textbook; Treil takes a different approach to the material than that author does.)

You can find a copy of essentially every textbook you ever need in PDF form online. Feel free to get in touch to ask if you do not know where to look. 

Topics: Narrowly speaking, linear algebra is the study of linear systems of equations, their properties, and their solutions. Broadly speaking, linear algebra is the study of linear functions, the simplest kind of functions. Linear algebra shows up everywhere because of a simple philosophy: "If you have something complicated, start by understanding the simplest piece (the linearization)". We will see that we can get a lot of control over this "simplest piece". (The second reason it shows up is that, once you know linear algebra, you see that it's so powerful you'd like to use it everywhere you can think to.) 

Some material in the class will not be covered in the textbook. There will be notes posted for this material on this website and on courseworks.

How much you get out of this class will be proportional to how much you put in. Linear algebra is perhaps the single most commonly used math topic past high school algebra, both in and outside math itself. There are more ways to talk about linear algebra than I can count, and certainly more than I can cover in a semester's worth of lectures. To help you explore, I will post completely optional supplemental material guiding your study on some of these different approaches. I plan to have materials both for proof-minded students (math majors, mostly) and for algorithmically motivated students (computer scientists and engineers, mostly), both of which will cover material not usually found in a first linear algebra course.

Prerequisites: Calculus III (UN1201) or equivalent. You should have experience and practice with vectors, dot products, and cross products, as well as determinants of 2x2 and 3x3 matrices.  

Homework: There will be a total of approximately 10 homework assignments. Most homework will be assigned on Wednesday and due by the following Wednesday. Homework is to be submitted in Gradescope before the start of class on Wednesdays.

You can work together with other students on the assignments (I encourage it - explaining math helps you understand and remember math), but answers must be written up in your own words, and you must write down who you collaborated with. You may use AI to learn but you cannot use AI to write up the answers to your homework; doing so will likely cause you to do badly on the exams, which are the vast majority of your grade.

Late homework will not be accepted. I will not accept emailed homework without a very good excuse (absense due to sports meet etc).

Tests: There will be two midterm exams and one final exam. The exams will be administered in class.

The tests are open-note (in the sense that you can refer to some notes of your own that you bring in), but nothing else; you may not collaborate with classmates or use any digital tools.

The midterms only cover the material between the tests; the final is cumulative.

(tentative)

Midterm 1: October 7 in class
Midterm 2: November 11 in class

Final: Projected to be on Dec 23 at 12-3pm

If you need a make-up exam, you must contact me several weeks ahead of time to arrange for it. Make-up exams will only be given under unavoidable circumstances (sports meets, etc.)

Grading: The final course grade is weighted as:

Homework: 10%
Midterm 1: 27.25%
Midterm 2: 27.25%
Final: 35%

Your bottom homework score will automatically be dropped.

Students with disabilities: To receive accomodations for exams (or otherwise), you must register with the Disability Services office and present an accomodation letter.
More information is available here.

Getting help: Math, and college, can be hard; anybody who's done a lot of math will tell you that they've struggled. If you're finding that you're struggling with the course, you should get help immediately.
If you're finding yourself overwhelmed but don't get help, then the tide may very well sweep you away and leave you completely lost!
You can come to my office hours (listed on my main page and this syllabus), or to the help room, where there is always a TA - your specific TA's help room hours will be posted as well. And as mentioned above, I recommend working with your friends! Lastly, please do not hesitate to reach out to me. 
There is information here about tutoring services. I will warn that private tutoring, especially in NYC, can be extremely expensive.

Homework

Homework is due in Gradescope on Courseworks before class starts.

You must show your work and your reasoning: just writing down the final answer to the question will not receive full marks (and will certainly not recieve full marks on the exams, which are the majority of your grade). Please also make it clear in your write-up which question is being answered, ideally by putting your name and the question number on every page of your write-up.

Notation: (Chapter #).(Section #).(Exercise #), so 1.2.5 denotes Exercise in section 2 of Chapter 1, which can be found in the part of the textbook titled `Exercises 1.2` which begins on page 18 of the textbook.

• HW1: 1.1.6, 1.1.32 (Hint: the conditions define a system of 3 linear equations), 1.2.5, 1.2.20. (This homework can exceptionally submitted in person in class.)
• HW2: 1.3.4, 1.3.8, 1.3.14, 1.3.29, 1.3.30, 1.3.61, 2.1.24-30 (i.e. 2.1.24, 2.1.25, ..., 2.1.30; these are all the same kind of problem). This homework looks long, but the problems are substantially easier than in HW1. Please submit answers in Gradescope, in class submissions will no longer be accepted.

Class Schedule

Mtg #	Date	Status	Topic	Reading / HW	Notes
1	Wed Sep 9	Class	Intro + 1.1		First class
2	Mon Sep 14	Class	1.2
3	Wed Sep 16	Class	1.2, 1.3, multiplication rules in 2.1 and 2.3, start Ch 2.	HW1 due
	Fri Sep 18	Deadline			Last day to add a class (Barnard and Columbia). End of Change of Program.
4	Mon Sep 21	Class	2.1, 2.2, 2.3
5	Wed Sep 23	Class	2.4, 3.1, 3.2, 3.3	HW2 due
6	Mon Sep 28	Class	3.3, 3.4 + outline of 4
7	Wed Sep 30	Class	Ch 4	HW3 due
8	Mon Oct 5	Class	Ch 4 + examples
9	Wed Oct 7	MIDTERM 1	Ch 1-4	study sheet	Midterm 1
10	Mon Oct 12	Class
	Tue Oct 13	Deadline			Last day to drop a Fall course (Barnard and Columbia).
11	Wed Oct 14	Class		HW4 due
12	Mon Oct 19	Class
13	Wed Oct 21	Class		HW5 due
14	Mon Oct 26	Class
15	Wed Oct 28	Class		HW6 due
	Mon Nov 2	Cancelled			Academic holiday — no classes (offices open)
16	Wed Nov 4	Class		HW7 due
17	Mon Nov 9	Class
18	Wed Nov 11	MIDTERM 2		study sheet	Midterm 2
19	Mon Nov 16	Class
20	Wed Nov 18	Class		HW8 due
	Thu Nov 19	Deadline			Last day to withdraw from a Fall class — Barnard students only.
21	Mon Nov 23	Class
	Wed Nov 25	Cancelled			Academic holiday — no classes (Thanksgiving eve)
22	Mon Nov 30	Class
23	Wed Dec 2	Class		HW9 due
24	Mon Dec 7	Class
	Mon Dec 7	Deadline			Last day to withdraw with a “W” — Columbia students only.
25	Wed Dec 9	Class		HW10 due
26	Mon Dec 14	Class			Last day of classes
	Mon Dec 14	Deadline			Deadline to request or revoke a P/D/F grade (Barnard and Columbia).
	Tue Dec 15	Study day			No classes. Study day.
	Wed Dec 16	Study day			No classes. Study day.
	Wed Dec 16	Deadline			Deadline to request an Incomplete (Barnard).

Final exam: Wed Dec 23, 12:00–3:00pm (exam period Dec 17–23).