These are a collection of course materials that I have created.
Math31 notes - full course with explanation of materials. Most portions have sample exercises.
Math33B notes - explanation of materials with some sample exercises
These are mentioned only as additional resources for your courses. Your primary source of information should be the official textbook and lecture notes. However, it is always useful to have a second source for a different perspective.
Elementary Analysis by Ross : This is the standard textbook used for undergraduates at UCLA.
Real Analysis by Joe Breen : Lectures notes from when Joe Breen taught 131A at UCLA. These notes are good at providing intuition and doing examples.
Principles of Mathematical Analysis by Rudin : Also known as "Baby Rudin" is a classic textbook for undergraduate analysis. Very dry and to-the-point.
Analysis I by Terence Tao : This book provides a more advanced introduction to analysis, perhaps more suitable for 131AH. Regardless, provides additional perspective on the subject. This pdf should be available through Springer.
Linear Algebra Done Wrong : Written in response to Linear Algebra Done Right, this book focuses on application and examples. This is a great complimentary resource, though it takes a slightly different approach and order to the UCLA course.
Linear Algebra and Beyond : This is an in-progress textbook being written by Joe Breen, a former UCLA TA. It is notably unfinished, but has great explanations of proof techniques, intuition behind topics, and exercises. This textbook goes deeper than the 115A course, but appears to be in-line with the 115AH course.
Visual Complex Analysis by Tristan Needham : This textbook offers a unique perspective on complex analysis that focuses on geometry and intuition. It is not particularly useful for Math132 or Math246 at UCLA, but is enjoyable in its own right.
Joe Breen is a legend among the UCLA TAs. He maintains a collection of notes, videos, and exercises on his professional website. These resources range from Math 31B to Math 131A and even into Symplectic Topology and Harmonic Analysis. His main writing can be found here and additional examples or problems can be found here.
Before anything, it needs to be noted that panicking during an exam, freezing during an exam, or experiencing anxiety about an exam is not a reflection of you or your abilities. It does not mean that you know the material any less than anyone else.
I am lucky that for most of my life I did not experience much anxiety over exams. I started to develop some near the end of my undergraduate program, but it didn't really affect my performance until my qualifying exams. In fall 2022, I spent two months studying for my exams only to panic and freeze for a full 90 minutes during one of them. These are the strategies that helped me to study for my exams as well as manage my anxiety.
Most of these strategies may seem obvious. However, if you're freaking out like I was, then it can be difficult to think of them. Through many hours and months of studying and practice exams, these are the strategies that helped me out the most.
While applying for graduate school, I found it very helpful to have references for structure and content. Below I have attached my CV, statement of purpose, diversity statement, and course overview that I used to apply. These are only my UCLA materials and should only be viewed as an example, not a guide.
If you would like to discuss the graduate school application process, then I am happy to talk with you! However, for concrete advice, I will always recommend talking to a professor or someone involved in the process. I can only speak to my own experience which may or may not be typical.
The biggest piece of advice I have is to never, ever visit mathematicsgre.com.
Below are a collection of notes and solutions for UCLA's qualifying exams that I either created or used extensively. Current graduate students should refer to the grad wiki, provided that it still exists and is updated.
I took the analysis qualifying exam in S22, F22, and finally passed in S23. I spent over a year studying and stressing about the exam. If you would like to discuss exam strategies, studying tips, or managing panic, please don't hesitate to reach out. You can find a brief description of what I did to manage exam anxiety and how I studied in the Exam Stress section.
I took the geometry/topology qualifying exam in F22 and passed in S23. Do not mistake my passing the exam for being knowledgeable about the subject.
To prepare for the Algebraic Topology portion of the exam, a few of us held weekly review sessions covering the material. The recordings of these meetings can be found in this YouTube playlist.
I took the basic and passed in F21. Since I did not spend much time studying, I am not a good resource for this exam.
Within Terence Tao's Math 246 course, we were required to write two reports on topics relating to complex analysis. These are the reports that I did. My knowledge and writing has grown immensely since then, so please look with soft eyes.
Schramm Loewner Evolution : Scaling Limit of LERW
Application of Conformal Mappings to Electrostatics
