## 2022 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

• Cluster algebras from surfaces
• Introduction to group theory
• Introduction to linear algebra
• Ring theory
• On beyond i
• Bonus group theory part 2
• Grammatical group generation
• Eigenstuff!
• Exploring extreme x in e^x
• Fruit math memes
• Schubert calculus
• Representation theory of finite groups
• Commutative algebra and algebraic geometry
• In-fun-ite groups
• The abc's of polynomialand
• Finite fields
• Algebraic solutions to Painlevè VI
• Introduction to Galois theory
• The word problem for groups
• Universal algebra
• Multiplicative functions
• Partially Ordered Galois Group Equivalence RelationS

### Analysis

• Overly convoluted plans
• Introduction to real analysis: epsilons and deltas
• The residue theorem
• Equidistribution
• My two favourite type of sets: Cantor sets and Kakeya sets
• Everyone hates analysis
• A curious connection between p-adic distances and triangulations of a square
• Cantor before set theory
• Chaotic dynamics and elephant drawing
• Metric spaces
• Overly convoluted drawings

### Applied Math

• Applied game theory
• Computer-aided design
• Measuring fairness
• Special relativity
• Pure mathematics as applied physics
• Electric circuits and random walks
• Thermodynamics and statistical mechanics
• Gibbard--Satterthwaite's impossibility theorem
• The uncertainty principle
• Elo ratings

### Combinatorics

• Introduction to graph theory
• Generating functions, Catalan numbers, and partitions
• The mathematics of forbidden words
• 1,2,5,14... FRIEZE ðŸ¥¶
• Three-term arithmetic progressions
• Extremal graph theory
• The Hales--Jewett theorem
• The Ra(n)do(m) graph
• Counter? I hardly know 'er!
• Hyperplane arrangements
• Map coloring tourism
• Szemerèdi's {theorem, regularity lemma}
• Conway's soldiers
• Electric charge on matchsticks
• Graph on, graph off
• Counting with polynomials
• The Littlewood–Richardson rule
• Sets that can tile lattices
• Greed
• Combinatorial reciprocity: counting through the looking-glass
• Extreme extremal graph theory
• How to avoid taking APs: the blame game
• Graph algorithms
• Lattices and invariant theory
• Counting with linear algebra
• How to juggle
• Why June Huh won the Fields medal
• Block designs
• The combinatorial Nullstellensatz
• Superpatterns

### Computer Science

• Complexity theory
• Formal proof verification in Lean
• Zero knowledge proofs
• Machine learning (NOT neural networks)
• The satisfiability problem
• The Golay code
• Evil floating point bit level hacking
• Sorry, it turns out SAT is hard after all
• The square root of a NOT gate

### Geometry

• How to avoid being eaten by bears... in space!
• Machine geometry
• Fractal geometry
• Teichmüller theory of the torus
• On beyond on beyond i
• The 17 wallpaper patterns
• Curves that classify geometry problems
• Hyperbolic geometry
• Hyperspheres
• Heisenberg geometry
• High-dimensional potatoes
• Mathematical billiards
• Spherical trigonometry with applications

### Logic/Set Theory

• Computability theory
• Crash course
• The continuum hypothesis
• The category of sets
• Nonstandard analysis
• Ultrafilters and combinatorics
• The axiom of choice

### Number Theory

• Introduction to number theory
• Jacobi sums
• Algorithms for large primes
• Lehmer factor stencils
• Integer right triangles
• Diophantine approximation
• High-dimensional oranges
• The distribution of prime numbers
• The Riemann zeta function
• The multiplication table problem
• Primes in the Eisenstein integers

### Probability/Statistics

• Martingales
• Information theory
• The probabilistic method
• Buffon's needle
• Frequentist statistics
• Bayesian statistics

### Problem Solving

• Problem solving: graph theory
• Problem solving: cheating in geometry
• Problem solving: quick and quirky questions

### Topology

• Degree theory
• Learn topology with PALs!
• Maximally colorful mathematics
• Common continuity
• Baire necessities for Banach--Tarski
• Algebraic topology: homology
• Knot theory
• Game theory, traffic, and the price of anarchy
• Tracking pants

### Variety

• Ancient Greek mathematics
• The geometry of music
• Counting things with bad maps
• Arrow's impossibility theorem
• Getting your money's worth from a 4-function calculator
• Reading Leibniz's notes in Latin
• The sound of proof