2014 Classes

Here is an overview of our courses from this summer. You can also see a grid version of the 2014 global schedule.

Algebra

• Algebra in Higher Dimensions
• Counting Conics
• Cubic curves
• Elliptic functions
• Galois theory
• Group Theory
• Introduction to Ring Theory
• Linear Algebra
• Quaternion Algebras
• Sylow Theorems
• The Banach–Tarski Paradox
• Tilings, Groups, and Orbifolds
• Universal algebra

Analysis

• Complex Analysis
• Discrete Derivatives
• Irrationalia
• Real Analysis
• Scandalous Curves
• The Intermediate Value Theorem and Chaos

Applied Math

• Bayesian Statistics
• Compressed Sensing
• Linear and nonlinear systems of differential equations
• Probability and the Mind
• Quantum Mechanics in Pictures
• Reasoning about knowledge and uncertainty, with a bit of game theory
• The Bell Curve
• The Laws of Thought
• The Math of Magic
• Voting theory

Combinatorics

• A Tale of Knots and Games
• Combinatorial Game Theory
• Electrical Networks and Graphs
• Generating Functions, Partitions, and Catalan Numbers
• Graph Coloring
• Intro to Graph Theory
• Knot Theory
• Latin Squares
• NP-Completeness and Latin Squares
• Partitioning
• Random Graphs
• See-Saw Swap Solitaire and Other Games on Permutations
• The Hales–Jewett Theorem
• The Internet
• The John Conway Hour
• Colloquium: John Conwaay
• The story of ranks and cranks of partitions

Computer Science

• (Th)ink Machine
• Error-Correcting Codes
• Evasiveness
• Grading Proofs Made Easy: Probabilistically Checkable Proofs of Proximity
• How Fast Can We Multiply?
• Knowledge and common knowledge in multi-agent systems
• Models of Computation Simpler than Programming

Geometry

• Finite Geometries
• Fractal Zoo
• Geometry of Groups
• Geometry of Numbers
• Möbius Transformations and The Night Sky (or, an Ape Pointing At The Stars)
• The Geometry of Spacetime

Logic/Set Theory

• A Hat Problem
• Category Theory
• Goedel's incompleteness theorem
• Hydras
• Infinite Trees
• Mathcamp Crash Course
• On beyond i
• The Continuum Hypothesis

Number Theory

• A quick introduction to number theory
• Analytic Number Theory
• Bernoulli Numbers
• Congruent numbers and elliptic curves
• Polynomial Fermat's Last Theorem
• Pythagorean Triples and Unsolvable Equations
• Sieves!
• The Chebyshev Prime Number Theorem
• Through the eyes of a prime: An introduction to p-adic numbers
• When Factoring Goes Wrong

Problem Solving

• Problem Solving: Geometry
• Problem Solving: Number Theory
• Problem Solving: Polynomials
• Problem Solving: The Probabilistic Method

Topology

• Combinatorial Topology
• Dance of the astonished topologist
• How to cut a Sandwich
• Point-set topology
• Sperner's Lemma