The course on Linear Algebra and Applications will treat, among others, systems of linear equations, linear independence, bases and dimension, orthogonality, determinants, eigenvalues and eigenvectors, and matrix diagonalization. The prerequisites required for this course are covered in Math 3B, Math 31B, and Math 32A.

The course will have weekly classes on

• Mondays, Wednesdays, and Fridays in MS, room 4000A, from 8:00 to 8:50 am.

The book we will be following is Linear Algebra with Applications (5th edition) by Otto Bretscher. We will be covering material in Chapters 1, 2, 3, 5, 6, 7, and 8. 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 33A Class Notes.

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

• Vocabulary in Linear Algebra.
• Change of coordinates by Jas Singh.
• Diagonalization and the Fibonacci sequence by Jacob Swenberg.
• Essence of linear algebra by 3Blue1Brown.
• Isometries of the plane and linear algebra by Keith Conrad.

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 1, Solutions.
• Practice Midterm 2, Solutions.
• Practice Final, Solutions.

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 open office hours at the Student Math Center can be found here.
• The peer learning facilitator from the Academic Advancement Program is Emma Lu.
• The peer learning facilitator from the UCLA Athletics Academic Excellence is Devyn Chun.
• The Math Success Program from the Community Programs Office can be found here.
• The Frequently Asked Questions of the Undergraduate Math Council can be found here.
• The online calculator Wolfram|Alpha can be found here.

Here are some general materials about the Department of Mathematics, the College of Physical Sciences, and UCLA:

• The Campus Resources document maintained by Britney Robinson can be found here.
• The Frequently Asked Questions of the Undergraduate Math Council 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.