Honors linear algebra, Fall 2026, NYU Courant
Course Information
Instructor: Zhen Huang (huangzhen at nyu dot edu)
Course number: Math UA 148
Office Hours: Mon 10.45-11.30 am, Wed 8.30-9.30 am, location TBA, or by appointment
Meeting Time and Place: Mon, Wed 9.30-10.45 am, Room 512, Warren Weaver Hall
Course catalog: See here. Also refer to the same page for prerequisites.
TA: Mingxin Li
Textbook: Sergei Treil, Linear algebra done wrong, version dated August 31, 2026. Available here.
Note: This is a different course from Math UA 140 (Linear algebra). We will cover more advanced topics in this course (UA148).
Update
- Sep 21. Homework 2's deadline postponed to Oct 1.
- Sep 12. Homework 1 and Homework 2 have been updated. Homework assignments are normally due on Thursdays, but nothing is due this coming Thursday, September 17. Both Homework 1 and Homework 2 are due on Thursday, September 24. It is advised not to wait for the second week to complete both assignments.
Objectives
The key goal of the course is to learn linear algebra. Furthermore, through this process, we will familiarize ourselves with how to approach problems using modern mathematical thinking (and writing). This will be useful, or even rewarding, in your future studies.
References
There are many linear algebra books, and many of them are very good. We choose the following book as the anchor point of our lectures. We recommend reading a few pages ahead (just a few is fine). We might post additional notes after each lecture. Our presentation might shift things up a little bit.
- Sergei Treil, Linear algebra done wrong, August 31, 2026 version. The PDF is available here.
You are very welcome to check out any other textbooks you can find. A common strategy to learn any math subject is to read two books (preferably from different perspectives) concurrently: whenever you get stuck with one, switch to the other, and vice versa. That being said, in terms of seeking help, you should certainly never hesitate to contact the instructor and TA.
From my perspective, it is easier for students to follow one textbook (i.e. the above one), and the corresponding lecture notes provided by the lecturer. (There is really no need to overcomplicate learning linear algebra by reading many books.) But here is a list of books that you could check out:
- S. Friedberg, A. Insel, L. Spence, Linear algebra. This is the UCLA textbook.
- A. Givental, Linear algebra. These are Givental's notes from a course he taught at UC Berkeley, available at this website.
- K. M. Hoffman, R. Kunze, Linear algebra. This is an old but classic reference.
- P. Lax, Linear algebra and its applications. This is also a classic but quite advanced book. It is a good book to read toward the end of (and after) this course. Lax was a great mathematician here at Courant.
- Sheldon Axler, Linear algebra done right. This is quite popular but we are not following the route taken by this book.
Course Plan
This is a tentative weekly schedule and is likely to change.
[LADW] refers to the textbook. [N] refers to our notes.
| Date | Topic | Sections |
|---|---|---|
| Sep 9 | (Covered by TA). Vector spaces, basis. | [LADW] §§ 1.1, 1,2 selected | Sep 14 | Introduction, subspaces, . | [LADW] §§ 1.1, 1,2, 1.7 |
| Sep 16 | Linear independence, span | [LADW] §§ 1.2, 1.3 |
| Sep 21 | Linear transformations, matvec mul, vector space of linear maps. | [LADW] §§ 1.3, 1.4 |
| Sep 23 | Matmul, compositition, inverse. | [LADW] §§ 1.5, 1.6 |
Homework Plan
Homework assignments are due on Thursdays at 11:59 p.m.| Homework | Assignment | Due Date |
|---|---|---|
| 1 | Sep 24 | |
| 2 | Oct 1 | |
| 3 | Oct 1 |
Course policy
- Grading Policy (tentative): Homework (30%), Midterm 1 (30%), Final (40%).
- Attendance for lectures is not explicitly enforced but is strongly encouraged. Linear algebra could be abstract. And it is helpful to have someone explain these concepts, and have discussions in class. We will also cover things that are not in the textbook (but notes will be given accordingly).
- A few words about AI:
- Millions of people have learned linear algebra without AI.
- It is not possible to ban anyone from discussing things (including homework problems) with AI. But you should not just copy AI's answers. We will not (and are not able to) explicitly check this, but I believe the amount of human thinking you put into homework will be easily reflected in the midterms and finals.
- Math is ultimately about your own understanding and thinking. You can use AI, for example, to help you understand things. But keep in mind, you still have to do the thinking yourself.
- I also think that compared to AI, your classmates might be better for discussing class material and homework, since it is likely that they have been pondering the exact same thing as you.
- Of course, you cannot use AI in exams.
- One thing in particular: I do not recommend learning how to write proofs with AI (at least as of Fall 2026). AI could give you correct and sometimes impressive answers, but in many cases it writes poorly structured proofs (especially if you are new and thus do not know the best way to prompt it). Since this is likely your first rigorous mathematics course, it is important to properly establish early the standards of reasoning and proof that will guide your mathematical development.
- Please make sure to follow the academic integrity policies. Any form of cheating or plagiarism will not be tolerated. See this page.