## What's in here?

These are the lecture notes I took, and if you're interested in the $\LaTeX$ code, have a look on GitHub. If you're interested in my setup, look at this GitHub repo or just here.

All notes are written in modern style $\LaTeX$ with explicit definition/theorem references and hyperlinks. Also, the drawing is done professionally and cleanly.

Due to the privacy policy, notes from classes I am/was teaching, the source code is unavailable.

## Junior @University of Michigan

### Fall 2021

#### Linear Programming (MATH561/IOE510/TO518)

This is the first course in the series of graduate-level, large-scale and rigorous mathematical programming courses taught by Jon Lee. Topics include **Duality Theorems**, the mathematical rigorous **Simplex Algorithm**, **Complementary Slackness**, **Large-Scale Linear Programming**, **Sensitivity Analysis**, and **Integer Programming** with their applications.

This course is not intended to teach you how to

hand-solve small-scalelinear programming problems, rather, it's intended to give a rigorous foundation of solvinglarge-scalelinear programming problems in an algorithmic way. We rely on`python`

and`Gurobi`

for examples to solve various problems in the assignments.

#### Analysis of Social Networks (EECS544/EECS444)

This is a graduate-level course about social network analysis taught by Vijay G Subramanian, aiming at a rigorous mathematical understanding of various social network algorithms and theories. Topics include **Graph Partitioning Algorithms**, **Stochastic Processes**, **Random Graph Theory**, and **Algorithmic Game Theory**, including **Auctions** and **Matching Market Algorithms**.

The course title makes this course's intended audiences rather narrow, but actually one can get a lot out of this course, especially some classical graph algorithms with theoretical analysis.

### Winter 2022

#### Algebraic Topology (MATH592)

This is a graduate-level course taught by Jennifer Wilson about Introduction to Algebraic Topology. Topics include **CW-Complex**, **Fundamental Group**, **Van-Kampen Theorem**, **Homology**, and also their applications like Lefschetz fixed-point theorem.

Some topology and abstract algebra background is required, especially group theory. But other than that, the course is self-contained enough.

#### Real Analysis (MATH597)

This is the graduate-level real analysis course taught by Jinho Baik. Topics include **Measure Theory**, **Hilbert Spaces**, **Banach Spaces**, **$L^p$ Spaces**, and some **Fourier Analyses**. While focusing on real measures, we did discuss signed and complex measures for completeness.

This course is pretty rigorous and well-structured and acts as a pre-requests for functional analysis (MATH 602). It's self-contained enough, and only need some previous exposure of mathematical analysis.

## Senior @University of Michigan

^{1}

Fall 2022#### EECS572, TA)

Randomness and Computation (This is the advanced graduate-level theory course focused on randomized complexity and related topics taught by Mahdi Cheraghchi. Topics include various **randomized algorithms**, **Randomized Complexity**, **Markov Chains**, **Random Walks**, **Expander Graphs**, **Pseudo-random Generators**, and **Hardness v.s. Randomness**.

Overall a rigorous course covering all background knowledge one might need to do research in the related fields. I'm grateful to be a teaching assistant for this course together with Neophytos Charalambides as an undergrad.

#### Approximation Algorithms and Hardness of Approximation (EECS598-001)

This is the graduate-level algorithm course taught by Euiwoong Lee, which focuses on methods of designing and analyzing approximation algorithms, together with the theoretical background on showing the hardness of approximation. Topics include **Covering**, **Clustering**, **Network Design**, and **CSP**. We also discussed **Lasserre (SoS) Hierarchy**, **Unique Game Conjecture**, and **Probabilistic Checkable Proofs**.

This is one of the most exciting courses I have taken: algorithmic design, hardness of approximation and fancy topics such as

SoS hierarchy,PCP,UGCare all fun to learn, especially the approximated complexity theory part.

#### Functional Analysis (MATH602)

This is the graduate-level functional analysis course taught by Joseph Conlon. The focus of this course is rather standard, including **Banach and Hilbert Spaces Theory**, **Bounded Linear, Compact, and Self-Adjoint Operators Theorem**, **Representation, Hahn-Banach, Open Mapping Theorem**, and **Spectral Theory**. We also covered some point-set topology along the way.

A rigorous course giving you the needed tools for analyzing function spaces. It'll give you a solid understanding on infinite dimensional vector spaces and how to deal with operators over these spaces.

### Winter 2023

#### EECS475, TA)

Introduction to Cryptography (This is the upper-level theory course on formal cryptography and related topics taught by Mahdi Cheraghchi. Topics include various **Historic Ciphers**, **Perfect Secrecy**, **Symmetric Encryption** (including pseudo-random generators, stream ciphers, pseudo-random functions and permutations), **Message Authentication**, **Cryptographic Hash Functions**, and **Public Key Encryption**.

An interesting foray to theoretical cryptography. I'm grateful to be a teaching assistant for this course together with Nikhil Shagrithaya as an undergrad.

#### Mathematical Logic (MATH681)

This is the graduate-level mathematical logic course taught by Matthew Harrison-Trainor, aiming to obtain insights into all other branches of mathematics, such as algebraic geometry, analysis, etc. Specifically, we will cover **Model Theory** beyond the basic foundational **Ideas of Logic**.

"Learn some fundamental stuffs and show-off to your friends" is basically my mind-set when taking this course ðĪŠ But seriously, learning something fundamental at this level is a new experience and challenge for me, but hey, it's the last semester, so might just relax and see how it goes!

#### Riemannian Geometry (MATH635)

This is the advanced graduate-level differential geometry course focused on Riemannian geometry taught by Lydia Bieri. Topics include local and global aspects of differential geometry and the relation with the underlying topology.

I always want to have a solid understanding on differential geometry since the recent advances in machine learning theory relying on related concepts quite heavily in some particular branches such as optimization and the well-known manifold hypothesis, or even more practical, manifold learning.

## First Year Ph.D. @University of Illinois Urbana-Champaign

### Fall 2023

#### Empirical Process Theory (STAT576)

This is the advanced graduate-level statistics course focused on empirical process theory taught by Sabyasachi Chatterjee. Topics include the **Uniform Law of Large Numbers** and the **Uniform Central Limit Theorem** with their applications, and **Weak Convergence**.

No comment right now. If I need to give one, the only thing I will say is this course is HARD.

- I also took Nonlinear Programming (MATH663/IOE611), but the professor provided excellent lecture slides, so I won't bother scribing it myself.âĐ