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2016 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

  • Algebraic Groups
  • Building Groups out of Other Groups
  • Burnside's Lemma
  • Domains and factorization: when everything goes wrong
  • Field Extensions and Galois Theory
  • Finitely-Generated Algebras
  • From Matrices to Representations
  • Geometric Group Theory
  • Group Actions
  • Harmonic Analysis on Abelian Groups
  • Introduction to Group Theory
  • Introduction to Ring Theory
  • Linear Algebra
  • More Group Theory!
  • Multilinear Algebra
  • Ponzi Schemes in Infinite Groups
  • Random Groups
  • Representation Theory of Finite Groups
  • Systems of Polynomial Equations
  • The Banach--Tarski Paradox
  • The Banach--Tarski Paradox
  • The Brauer Group
  • The Cayley-Hamilton Theorem
  • The Democracy of Number Systems
  • The Lonely Torus - A Lie Group Opera
  • The Magic of Determinants
  • The Word Problem for Groups
  • The Yoneda Lemma
  • Twisty Puzzles are Easy
  • Wedderburn's Theorem
  • Colloquium: Intersecting Curves in the Plane

Analysis

  • Asymptotics of Generating Functions
  • Divergent Series
  • Epsilons and Deltas
  • Permuting Conditionally Convergent Series
  • Scandalous Curves
  • Wallis and His Product
  • What Can We Exponentiate?
  • dCalculus
  • Colloquium: The Music of Zeta

Applied Math

  • Benford's Law
  • Computer-Aided Design
  • Factoring With Elliptic Curves
  • IOL 2016
  • Mathcampers Show Presentations
  • Natural Language Understanding
  • Nonzero-Sum Games
  • Period Three Implies Chaos
  • Quantum Mechanics
  • Special Relativity
  • Statistical Modeling
  • The Mathematical ABCs
  • The Mathematics of Board Games
  • The "Free Will" Theorem
  • Colloquium: Elo x Education
  • Colloquium: Should We Vote on How We Vote?
  • Colloquium: Spin!

Combinatorics

  • Almost Planar
  • Calculus on Young's Lattice
  • Card Shuffling
  • Combinatorial Games
  • Extending Inclusion-Exclusion
  • Generating Functions and Partitions
  • Graph Colorings
  • Graph Minors
  • Graph Polynomials
  • Guarding an Art Gallery
  • Harmonic Functions on Graphs
  • Introduction to Graph Theory
  • King Chicken Theorems
  • Latin Squares and Finite Geometries
  • Probably Combinatorics
  • Random Graphs
  • Random Graphs
  • Spectral Graph Theory
  • Spectral Graph Theory
  • The Chip-Firing Game
  • The Hales--Jewett Theorem
  • The stable marriage problem
  • Wythoff's Game
  • de Bruijn Sequences
  • Colloquium: Crossing Numbers of Graphs: Origins and Recent Progress
  • Colloquium: Tree Trotting

Computer Science

  • Advanced Topics in... Sorting?
  • Functional Programming
  • Hard problems that are almost easy
  • Models of Computation Simpler than Programming
  • Neural Networks

Geometry

  • Building Mathematical Structures
  • Building Mathematical Structures
  • Cut That Out!
  • Dynamical Systems
  • Hyper-Dimensional Geometry
  • Hyperbolic Geometry
  • Many Cells Separating Points
  • Projective Geometry
  • Spin: Numbers as Rotations
  • The Hadwiger-Nelson Problem
  • Universal Properties
  • Colloquium: A simple question with a very curious answer
  • Colloquium: Algebraic Proof of Heron's formula
  • Colloquium: There Are Eight Flavors of Three-Dimensional Geometry
  • Colloquium: Tropical Geometry

History/Literature

  • Egyptian Fractions
  • History of Math
  • Math and Literature
  • Turning Points in the History of Mathematics
  • Why Are We Learning This? A seminar on the history of math education in the U.S..

Logic/Set Theory

  • How Not to Prove the Continuum Hypothesis
  • Mathcamp Crash Course
  • Model Theory
  • Stupid Games on Infinite Sets
  • Sum and Product Puzzles
  • Colloquium: Oops! I Ran Out of Axioms
  • Colloquium: The Littlewood-Offord Problem

Number Theory

  • A Very Difficult Definite Integral
  • Algebraic Number Theory
  • Analytic Number Theory
  • Huuuge Primes
  • Multiplicative Functions
  • Pythagorean Triples, Diophantine Equations and Fermat's Last Theorem
  • Quadratic Reciprocity
  • The BSD conjecture
  • Colloquium: Ron Graham's Sequence

Probability/Statistics

  • A Crash Course in Axiomatic Probability
  • Does ESP Exist? or, What's Wrong With Statistics?
  • Paradoxes in Probability
  • Why Aren't We Learning This: Fun Stuff in Statistics

Problem Solving

  • More Problem Solving: Polynomials
  • Problem Solving: Induction
  • Problem Solving: Polynomials
  • Problem Solving: Symmetry, Parity, and Invariants
  • Problem Solving: Tetrahedra
  • Problem Solving: Triangle Geometry

Topology

  • A Tale of Combs and Hedgehogs
  • A Tale of Combs and Hedgehogs
  • Cutting Surfaces into Silly Straws
  • Homotopy (Co)limits
  • K-Theory
  • Knot Theory
  • Point-Set Topology
  • String Theory
  • The Fundamental Group
  • The Hairy and Still Lonely Torus
  • The Topology and Geometry of Surfaces
  • Colloquium: Lattices, Knots and Chaos