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 BUNCHE, room 1209B, from 11:00 to 11:50 am. The online classroom is Zoom Meeting 945 8336 4011.

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.
• Midterm 1 Review on 23 January 2022.
• Midterm 1 Review on 27 January 2022.
• Midterm 2 Review on 12 February 2022.
• Midterm 2 Review on 16 February 2022.
• 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 Tuesdays at 9:00 am. The assignments will be due on Gradescope the following week, on Wednesday at 11:59 pm. The assignments, deadlines, and solutions will be posted here.

There will be typically weekly discussion sessions. These are thematic problems around a subject, intending to provide a deep dive into a challenging topic. The worksheets will be posted before Tuesdays at 9:00 am. The worksheets and solutions 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 Katia Dahmani.
• The Math Success Program from the Community Programs Office can be found here. You can go to their drop-in hours (no appointment necessary). You can also set up an appointment 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.