Professor Ian Tice has a well-designed, 337-page set of notes covering advanced integration tools, Fourier series and Hilbert spaces, the Fourier transform, distributions, and Sobolev spaces. Contact him if you are interested. 

Here are my own assignments and final project.

Here is my handwritten note for basic differential equations. The first part is a basic review of nonlinear ODEs, and the second part contains my personal notes taken while studying the famous textbook "Partial Differential Equations" by Lawrence Craig Evans. 

Here is a set of typed exercises with solutions. I collected them from different sources.

Here is my typed note for functional analysis. These notes contain a brief review of Hilbert spaces, Banach spaces, and locally convex spaces. I skipped Chapter 4 Weak Topologies and Chapter 5 Linear Operators since I became lazy in the second half of that semester. Also, lots of valuable details and examples are omitted, which means this note is actually incomplete.

Here is my handwritten note for measure theory. These notes contain a brief review of the derivation from outer measures to measures, regularity, measurable functions, integration, convergences, basic Lp space, signed measures, and product spaces.

Here is my handwritten note for probability theory. These notes contain a brief review of necessary measure theory, law of large numbers, central limit theorem, and martingale theory (my focus). Several exercises are attached. 

Here is a set of typed exercises with my own but incomplete solutions, and questions are from my homework. Here is another set of typed exercises with my own solutions, and questions are from previous basic exams.

The reference textbook I used is the famous "Probability: Theory and Examples. 5th Edition" by Richard Timothy Durrett. My mom helped me extract exercises in the form of screenshots to urge me prepare for an exam. Thank you mom :)

Here is the note my student, Rex Liu, shared with me. I think it is well prepared and will help everyone review. Here are some resources: 

Midterm & Solution 1; Homework & Solutions 1, 2, 3, 4, 5, 6; and Recitation 1, 2, 3, 4, 5, 6.

Here is my handwritten note for point-set topology. These notes contain a brief review of open sets, topological spaces, close sets, Hausdorff, basis, homeomorphism, connectedness, path connectedness, Cauchy, completeness, completion, compactness, sequentially compactness, neighborhood, nets, cluster points, ultranet, and filters. The reference textbook I used is the famous "Topology. 2nd Edition" by James Raymond Munkres.