## 2021 Classes

Here is an overview of our courses from this summer. You can read the class descriptions ("blurbs"), view the global schedule in a grid, or see all the classes sorted by category.

Here is the list of classes by subject:

### Algebra

• Conjugation in the symmetric group
• Dirichlet's class number formula
• Finite fields and how to find them
• Finite fields: the power of Frobenius
• Galois theory crash course
• Introduction to group theory
• Introduction to linear algebra
• Introduction to ring theory
• Kleinian groups and fractals
• Lights, camera, group actions!
• Noncommutative ring theory (1 of 2)
• Noncommutative ring theory (2 of 2)
• Representations of symmetric groups
• Symmetries of a (hyper)cube
• The fundamental theorem of algebra and its many proofs
• The word problem for groups
• What are your numbers worth? or, the part of algebraic number theory we can actually do

### Analysis

• A pair of fractal curves
• Completeness of the real numbers
• Finite Fourier analysis
• Functions of a complex variable (1 of 2)
• Functions of a complex variable (2 of 2)
• Introduction to analysis
• Kakeya sets over finite fields
• Multivariable calculus crash course
• Nowhere differentiable but continuous functions are everywhere!
• PDEs part 1: Laplace's equation
• The calculus of variations
• The derivative as a linear transformation
• The inverse and implicit function theorems
• Vitali's curse

### Applied Math

• Axiomatic music theory
• Better sheep through modeling
• Better sleep through modeling
• Cryptography and how to break it
• Introduction to auction theory
• Introduction to quantum computing
• Lattices that make up the world
• Supervised machine learning: the essentials
• The mathematics of voting
• The pirate game
• The quantum factorization algorithm
• The Schwarzschild solution
• The special theory of relativity
• Traffic and the price of anarchy

### Combinatorics

• A combinatorial proof of ``the'' quintic formula
• A Combinatorial Proof of the Jacobi Triple Product Identity
• A property of \$a^n\$
• Ben's favorite game theory result
• Combinatorial species
• Compactness in combinatorics of coloring
• Evolution of random graphs
• Graph colorings
• Incidence combinatorics
• Introduction to graph theory
• Nonunique factorization in the Chicken McNugget monoid
• Perfection
• Sperner's lemma and Brouwer's fixed point theorem
• The probabilistic method
• There are less than \$10^{39}\$ Sudoku puzzles

### Computer Science

• Computability theory and finite injury
• Learning online learning online
• Mechanical computers
• Sit down and (don't) solve SAT?
• Sparsest cut

### Geometry

• Curvature lies within
• Euclidean geometry beyond Euclid
• Insert geometry joke here
• Myth of the 13 Archimedean Solids
• Non-Euclidean geometries
• Taxicab geometry
• The 17 worlds of planar ants

### History/Literature

• Is math real?

### Logic/Set Theory

• Hilbert's 3rd problem
• Martin's axiom
• Mathcamp crash course
• Model theory
• Surreal numbers
• Ultra-fantastic ultra filters

### Number Theory

• Arithmetic progressions and primes and parrots
• Arithmetic progressions and primes and parrots
• Continued fractions
• Counting, involutions, and a theorem of Fermat
• Factoring large prime numbers
• Fractal projections and a number theory question
• How to count primes
• Topics in number theory

### Probability/Statistics

• Causal inference: how can we tell if \$X\$ causes \$Y\$?

### Problem Solving

• Problem solving: geometric transformations
• Problem solving: lecture theory
• Problem solving: linear algebra
• Problem solving: tetrahedra

### Topology

• Classifying infinite-type surfaces
• Draw every curve at once
• Knot theory
• Topology through Morse theory