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: