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
- 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:
