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
- 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:
