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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.

An image of the blurbs describing 2021 Classes

The 2021 Blurbs

An image of the grid displaying 2021 Classes for Weeks 1 through 4

2021 Four-Week Schedule

An image of the grid displaying 2021 Classes for Week 5

2021 Week 5 Schedule

Here is the list of classes by subject:

Algebra

  • Archers at the ready!
  • 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

  • Algorithms on your phone
  • 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
  • Quadratic forms
  • 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

Variety

  • How to ask questions
  • Party parrot workshop
  • Trail mix

2021 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 2021 classes: