The course on Linear Algebra will treat, among others, proof techniques, abstract vector spaces, linear transformations between them, matrices, and inner product spaces. The prerequisites required for this course are covered in Math 33A.

The course will have weekly classes on

• Mondays, Wednesdays, and Fridays in GEOLOGY, room 6704, from 11:00 to 11:50 am.

The book we will be following is Linear Algebra (4th edition) by Stephen H. Friedberg, Arnold J. Insel, and Lawrence E. Spence. We will be covering material in Chapters 1, 2, 4, 5, and 6. The recommended reference books are Linear Algebra by Paul Balmer and How To Prove It by Daniel J. Velleman. Supplemental refereces are Linear Algebra Done Right by Sheldon J. Axler, Linear Algebra Done Wrong by Sergei R. Treil, and An Infinite Descent into Pure Mathematics by Clive Newstead. You may find all the information you will need on the Syllabus.

The following notes are a formal outline of the material we will be covering. These notes are not comprehensive nor are intended to be a substitute for the textbook or the lectures. If you find mistakes (typographical or other) in these notes, or have comments, please let me know.

• MATH 115A Class Notes.

The following are additional materials closely related to the class notes.

• Proof techniques.
• Fields.
• Examples of linear transformations.
• Change of coordinates by Jas Singh.
• Essence of linear algebra by 3Blue1Brown.
• The dimension of a vector space by Keith Conrad.
• The minimal polynomial and some applications by Keith Conrad.
• Isometries of the plane and linear algebra by Keith Conrad.
• Bases for infinite dimensional vector spaces by Karen E. Smith.

There will be typically weekly homework. The assignments will be posted before Mondays at 9:00 am. The assignments will be due on Gradescope the following week, on Friday at 11:59 pm. The assignments and deadlines will be posted here. You are encouraged to work in groups.

There will be typically weekly discussion sessions. These are thematic worksheets around a subject, intending to provide a deep dive into a challenging topic while having readily available feedback. The starred problem(s) will be due on Gradescope on Thursday at 11:59 pm. The worksheets and deadlines will be posted here. You are encouraged to work in groups.

Here the exams and their solutions will be posted. You can find the official UCLA schedule for the final exams here.

The following are practice exams that you may use to prepare:

• Practice Midterm.
• Practice Final.

There are many resources available for a student at UCLA, I encourage you to use them and make the most out of them. Here are some materials specific to this course:

• The Canvas forum can be found here. I encourage you to use this to post questions (anonymously if you wish), answers, and discuss the material presented in the lectures.
• The peer learning facilitator from the Academic Advancement Program is Dinc Ozeren.
• The open office hours at the Student Math Center can be found here.
• The online calculator Wolfram|Alpha can be found here.

I also encourage you to form study groups with your classmates. However, please keep in mind that you will only learn how to do the exercises if you try them on your own: without trying, looking up the solutions or copying others' work is absolutely useless.