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.

The 2023 Blurbs

2023 Four-Week Schedule

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:

• Week 1 Schedule and Blurbs
• Week 2 Schedule and Blurbs
• Week 3 Schedule and Blurbs
• Week 4 Schedule and Blurbs
• Week 5 Schedule and Blurbs