2013 Classes

Here is an overview of our courses from this summer. You can also see a grid version of the 2013 global schedule.

Algebra

• Commutative Algebra
• From Linear Algebra and Group Theory to the Hydrogen Atom
• Group Theory
• Linear Algebra
• Matrix Groups
• Multilinear Algebra
• Polynomial Method
• Representation Theory of Finite Groups
• Representations of the Symmetric Group
• Ring Theory
• Symmetric Polynomials and Schubert Calculus
• Trail Mix day 3: Intersection madness

Analysis

• Epsilon the Enemy
• Functions of a Complex Variable
• Harmonic Analysis
• Hyperreal Analysis
• Metric Spaces
• Multivariable Calculus Crash Course
• On the Controversy Between Messrs. Leibniz and Bernoulli Concerning Logarithms of Negative and Imaginary Numbers
• The Bear Catch-A-Berry Theorem
• Trail Mix day 2: Integration by parts and the Wallis product

Applied Math

• A Taste of Chaos
• Auction Theory
• Communication Complexity
• Elections: Influence and Stability
• Google Advertising
• Learning as Program Synthesis
• Permutation Groups, Coxeter Algebras & SUSY
• Spacetime Supersymmetries
• Spread in Networks: Containing the Harmful, Encouraging the Virtuous.
• Using Linear Algebra
• Voting Theory

Combinatorics

• (Th)ink Again
• 4.99 Color Theorem
• A Tale of 3 Knot Invariants
• Chip Firing, Sandpiles, and all that Jazz!
• Chip-firing and Riemann-Roch
• Combinatorial Game Theory
• Combinatorics of Partitions
• Counting
• Finding the Perfect Match
• Flows
• Introduction to Graph Theory
• Partially Ordered Sets
• Partizan Game Theory
• Permutations and Bruhat orders
• The Graph Minor Theorem
• The John Conway Hour
• The Probabilistic Method
• Vanning Trees

Computer Science

• (Th)ink Machine
• Cryptography
• Finding the Center
• Machine Learning
• Many Campers Sort Piles
• PRIMES in P
• Extreme Probability!
• Programming in Haskell
• Quantum Computing
• Root-Finding Algorithms
• Simple Models of Computation
• The Forehead Game: Multiparty Communication Complexity
• The Traveling Salesman and Friends

Geometry and Topology

• Curvature of Polyhedra
• Cut That Out!
• Euler's Greatest Hits
• Flag Varieties
• Fractal Geometry
• Geometry is Awesome, Dude!
• Hilbert's Geometries
• Inside Convexity
• Mathematical Origami
• Mathematical Sculpture
• Not Just Scratching the Surface: Cohomology and Topology of Surfaces
• Surfaces and Symmetries
• The Cross-ratio

Logic/Set Theory

• Category Theory
• Crash Course on Mathematical Abstraction
• How not to prove the continuum hypothesis
• Reverse Mathematics
• Set Theory
• The Category of Sets
• The Littlewood-Offord Problem
• Ultrafilters and Hindman's Theorem

Number Theory

• Algebraic Number Theory
• Continued Fractions
• Introduction to Number Theory
• Trail Mix day 1: Perfect Numbers
• Trail Mix day 4: Hensel's Brave New World

Problem Solving

• Problem Solving: Polynomials
• Proofs and Problem Solving