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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.

An image of the blurbs describing 2022 Classes

The 2022 Blurbs

An image of the grid displaying 2022 Classes for Weeks 1 through 4

2022 Four-Week Schedule

An image of the grid displaying 2022 Classes for Week 5

2022 Week 5 Schedule

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 🥶
  • 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
  • 2-adic computer science
  • 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
  • Killing the Cookie Monster
  • 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
  • Quadratic reciprocity
  • 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

  • The answer is χ
  • 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

2022 Academics: The Details

For those who would like to dig into the details of the class archives, these PDFs are for you. Here is the chart of Prerequisites and here is a list of Themes.

We post schedules and course descriptions ("blurbs") each week throughout camp. Here are the 2022 classes: