 Tyler Zhu Blog and Personal Website computer science, mathematics, rationality, and machine learning.
Having done lots of teaching in the past, I've also created many resources which I've collected on this page (with some ones from university as well). If you're looking for classes that I have or are currently TA-ing, they'll be in the list below.

### Handouts and Resources

Throughout high school, I was involved extensively with education, through my school's math club and other teaching efforts, as well as writing a few papers (mostly surveys). This is a collection of those resources.

#### Number Theory

• A Binomial Theorem Trick: In this short article, I discuss a nice trick for evaluating powers of numbers modulo powers of primes. I also give a light elementary introduction to Binomial Coefficients and Fermat's Little Theorem/Euler's Totient Theorem.

#### Combinatorics

• Balls and Boxes: A short, detailed note on the ways to use the Balls and Boxes counting method as well as its different applications.
• Counting: A short exposition of some of my favorite nice combinatorics problems and techniques. None of the problems require any fancy trickery, but just need insightful thinking.
• Graph Theory (pdf): This was the handout I wrote for a lecture at Irvington Math Club on some graph theory basics, from the first theorem of graph theory to Eulerian Trails and Kuratowski's Theorem. The results are motivated by some classic riddles. Slides are included below.
• Graph Theory (slides): Slides for my graph theory lecture.
• Polya's Recurrence Theorem: In this article, I discuss an introduction to the theory of random walks through Polya's Recurrence Theorem, as well as some interesting ways to think about it. This was my research paper during the 2016 Stanford University Mathematics Camp.

#### Algebra

• Polynomials: In this article, I describe a few powerful, lesser-known techniques for dealing with polynomials, including Lagrange's Interpolation Formula.

#### Geometry

• Poles and Polars: One of my favorite handouts. I introduce from scratch the theory of poles and polars, and make mincemeat of a few problems that would be difficult to tackle otherwise.

#### Miscellaneous

• Information Theory: A sketch of interesting ideas relating cryptography, data compression, and entropy. Poorly named title, but fascinating connections.
• Moduli Spaces (Algebraic Geometry): In this paper, we discuss the notion of a moduli space and determine moduli spaces of isomorphism classes of genus 0 and 1 curves with various numbers of marked points. This was my research paper during the 2017 Stanford University Mathematics Camp.
• Nilpotent Groups (Abstract Algebra): My (incomplete) attempt at trying to collect current literature on partial converses to Lagrange's Theorem ended up being an introduction of nilpotent groups with examples. See CLT groups if you're actually interested in converses.
• Inflection Points of Planar Cubic Curves: My final paper for Math 255, Algebraic Curves, discussing the inflexion points of planar cubic curves, their properties, and the underlying Galois group.