Today (April 18) is admission decision day for Mathcamp 2024! Decision emails will be sent by this afternoon.

2020 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 2020 Classes

The 2020 Blurbs

An image of the grid displaying 2020 Classes for Weeks 1 through 4

2020 Four-Week Schedule

An image of the grid displaying 2020 Classes for Week 5

2020 Week 5 Schedule

Here is the list of classes by subject:

Algebra

  • A Rubik's cube-based approach to group theory
  • An inquiry-based approach to group theory
  • Classifying complex semisimple Lie algebras
  • Connections to category theory
  • Dominant eigenvalues and directed graphs
  • Don't worry, these cats don't bite! (Basic category theory)
  • Functions you can't integrate
  • Introduction to Coxeter groups
  • Introduction to linear algebra
  • Introduction to ring theory
  • Representation theory of finite groups
  • The matrix exponential and Jordan normal form
  • The Sylow theorems

Analysis

  • Bairely complete
  • Cantor, Fourier, and the first uncountable ordinal
  • Complex analysis
  • Complex dynamics: Julia sets and the Mandelbrot set
  • Continued fraction expansions and e
  • Dirac delta function
  • Fourier analysis
  • Hilbert's space-filling curve
  • How Riemann finally understood the logarithms
  • Infinitesimal calculus
  • Introduction to analysis
  • Stirling's formula
  • The Kakeya needle problem, projective geometry, and fractal dimensions
  • Uncertainty principle
  • Wallis and his product
  • Weierstrass approximation

Applied Math

  • Geometric programming
  • Information theory
  • Let's reverse-engineer photoshop
  • Matrix completion
  • Modeling computation
  • Perceptron
  • Quantum mechanics
  • Random walks and electric networks
  • The redundancy of English
  • Voting theory 101

Combinatorics

  • Block designs
  • Brooks' theorem blues
  • Combinatorial game theory
  • Combinatorics of tableaux
  • Conflict-free graph coloring
  • Counting, involutions, and a theorem of Fermat
  • Crossing numbers
  • Determinantal formulas
  • Exploring the Catalan numbers
  • Extremal graph theory
  • Extremal set theory: intersecting families
  • Extreme extremal graph theory
  • Graphs on surfaces
  • Hyperplane arrangements
  • Introduction to graph theory
  • King chicken theorems
  • Oh the sequences you'll know
  • Posets and the Möbius function
  • Regular expressions and generating functions
  • Spectral graph theory
  • The Plünnecke–Ruzsa inequality
  • Tridiagonal symmetric matrices, the golden ratio, and Pascal's triangle

Computer Science

  • Complexity theory
  • Fourier something something boolean functions
  • Teaching math to computers

Geometry

  • Cubic curves
  • Cut that out!
  • Finding the center
  • Geometry of lattices
  • Gothic windows
  • Integration on manifolds
  • Solving equations with origami

History/Literature

  • Ancient Greek calculus
  • Math and literature

Logic/Set Theory

  • How not to prove the Continuum Hypothesis
  • Mathcamp crash course
  • Skolem's paradox
  • What the continuum cannot be

Number Theory

  • (Relatively) prime complex numbers
  • A tour of Hensel's world
  • Avoiding arithmetic triples
  • Congruences of Bernoulli numbers and zeta values
  • Fair squares (mod p)
  • Introduction to number theory
  • Perfect numbers
  • Ramanujan graphs, quaternions, and number theory
  • The lemma at the heart of my thesis
  • The Riemann zeta function

Probability/Statistics

  • Markov chains and random walks
  • The bell curve

Problem Solving

  • Majorizing-Comparisons Solving of Problems

Topology

  • Cantor's leaky tent
  • Clopen for business: an inquiry-based approach to point-set topology
  • FUNdamental groups and friends: an introduction to topological invariants
  • Homotopy colimits
  • How to glue donuts
  • Introduction to combinatorial topology
  • So you like them triangles?
  • The Hilbert cube
  • Which things are the rationals?

Variety

  • Computing trig functions by hand
  • Grammatical group generation
  • How to ask questions
  • Many Counterexamples, Some Pathology
  • The John Conway hour
  • The puzzle of the superstitious basketball player

2020 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, a set of related classes we call Clusters, and, to help you visualize them in a different way, Cluster Conflicts.

We post schedules and course descriptions ("blurbs") each week throughout camp. Here are the 2020 classes: