## 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.

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
• 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