2023 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 2023 Classes

The 2023 Blurbs

An image of the grid displaying 2023 Classes for Weeks 1 through 4

2023 Four-Week Schedule

An image of the grid displaying 2023 Classes for Week 5

2023 Week 5 Schedule

Here is the list of classes by subject:

Algebra

  • Back to basi(c)s
  • Coxeter groups
  • Finite fields
  • From high school arithmetic to group cohomology
  • Galois theory crash course
  • High-school algebraic geometry
  • Honey, I shrunk the vectors
  • How to count rings
  • Intersections of algebraic plane curves
  • Introduction to group theory
  • Introduction to linear algebra
  • Introduction to ring theory
  • Introduction to Schubert calculus
  • Linear algebra through knots
  • Polygons, friezes, and snakes — oh my!
  • Quiver representations part I
  • Quiver representations part II
  • Representation theory of the symmetric groups
  • Seven trees in one
  • Solving equations with origami
  • The outer life of inner automorphisms
  • The transcendence of a single number (including Liouville's constant)
  • Wedderburn's Theorem
  • What are your numbers worth?

Analysis

  • A couple things Ben kinda knows about measure zero sets
  • A very chill intro to measure theory + dimension
  • aspacefillingcurve (everyone loves analysis, part 2)
  • Calculus of variations
  • Discreet calculus (shh!)
  • Elliptic functions
  • Epsilons and deltas
  • Everything Ben knows about nonmeasurable sets
  • Fourier series
  • Functions of a complex variable
  • Green's Theorem
  • How not to integrate
  • Khinchin's constant and the ergodic theorem
  • Let ε0 > 0 be sufficiently small
  • Mechanics of fluid flow
  • Metric spaces
  • Multivariable calculus crash course
  • Non-standard analysis
  • One-half factorial from scratch
  • Perron trees (everyone loves analysis, part 1)
  • The geometry of fractal sets
  • What actually are the real numbers, anyway?
  • Why do we need measure theory?

Applied Math

  • {Game, graph} theory against the world
  • An introduction to cryptography
  • Guess Who? (Week 1 of 2)
  • Introduction to cryptography
  • Markov chain Monte Carlo
  • Music: the number theory of sound
  • Neural codes
  • Voting theory, Burlington, VT, and the Gibbard–Satterthwaite theorem

Combinatorics

  • Beyond inclusion/exclusion
  • Computer-aided mathematics and satisfiability
  • Dimers and webs
  • Erdős's distinct distance problem
  • Flag algebra marathon
  • Generating functions, Catalan numbers, and partitions
  • Graph colorings
  • Guess Who? (Week 2 of 2)
  • Hlod onto yoru ahts!
  • How to rob your friends
  • How to rob your friends 2: non-transitive dice boogaloo
  • Imperfection
  • Introduction to graph theory
  • Kuratowski's game
  • Latin squares
  • Packing permutation patterns
  • Perfection
  • Polynomial methods in combinatorics
  • Symmetric Functions and their Combinatorics
  • Taming the grouchy Grassmannian
  • The Ra(n)do(m) graph
  • The sum-product conjecture

Computer Science

  • Information theory and the redundancy of English
  • Inspecting gadgets
  • Quantum computing
  • Randomized vs deterministic computation
  • Teaching Math to Computers
  • The evolution of proofs in computer science

Geometry

  • Cubic curves
  • Geometry Gala
  • Geometry, under construction
  • Parabolic curves
  • Polytopes
  • The Kakeya problem
  • The only formula it can be!
  • Unicorns and Poland

Logic/Set Theory

  • Antinomy: meditations on Gödel's undecidable sentences
  • Axiom of choice
  • Consistency of arithmetic by killing hydras
  • Gödel's incompleteness theorems
  • Hacking heads off hydras
  • Infinite arithmetic
  • Infinite Ramsey theory
  • Introduction to model theory
  • Mathcamp crash course
  • Not theory
  • Reverse mathematics
  • The hat-xiom of choice
  • Ultrafilters and voting

Number Theory

  • All aboard the Möbius
  • Bhargava's cube
  • Continued fractions
  • Elliptic curves
  • From the Sato–Tate conjecture to murmurations
  • Introduction to number theory
  • Mediants, circles, and Stern–Brocot patterns
  • Some stories about squares (mod p)
  • Sophie Germain primes
  • The Chevalley–Warning theorem
  • The transcendence of many numbers (including π and e)
  • The Wythoff array
  • Why 0 is the biggest prime
  • Zeroes of recurrence sequences through p-adics

Probability/Statistics

  • First, choose randomly
  • Gaussian magic
  • Is it possible to gamble successfully?
  • Lastly, choose randomly
  • Percolating through percolation theory
  • Predicting the future

Problem Solving

  • Logic puzzles
  • Mathematical Concepts for Solving Puzzles: Parity
  • Mathematical Concepts for Solving Puzzles: Penalty
  • Mathematical Concepts for Solving Puzzles: Planarity
  • Problem solving: geometry galore
  • Problem solving: induction
  • Problem solving: olympiad inequalities
  • Problem solving: triangle geometry

Topology

  • Braid groups
  • Homotopy groups of spheres
  • How to build a donut
  • Knot invariants
  • The Borsuk–Ulam Theorem
  • When will this end???

Variety

  • A magic show
  • Ben teaches Susan's class
  • Calculus without calculus
  • Computing trig functions by hand
  • Fair division using topology
  • How the compactness theorem got its name
  • I'd like some geometry with my topology
  • McKelvey's Chaos Theorem
  • Not the math we need, but the math we deserve
  • Philosophy of math
  • The puzzle of the superstitious basketball player
  • Think different
  • Trail mix

2023 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 Clusters.

We post schedules and course descriptions ("blurbs") each week throughout camp. Here are the 2023 classes: