2011 Classes

Here is an overview of our courses from this summer. You can also see a grid version of the 2011 global schedule.

Algebra

• Adventures in Group Theory
• Algebraic Geometry
• Commutative Algebra
• Counting Algebra with Generating Series
• Doubly Infinite Laurent Series
• Freedom
• Group Theory
• Groups in Action: Finite Rotational Symmetries
• Introduction to Ring Theory
• Linear Algebra
• Partially-Ordered Sets and Möobius Inversion
• Planar Algebras
• Topics in Group Theory

Analysis

• Analysis on the Hyperreals
• Complex Analysis
• Discrete Calculus
• Do-It-Yourself Real Numbers
• Metric Spaces and Real Analysis
• Multivariable Calculus Crash Course (MC³)
• Transcendental Numbers

Applied Math

• Collective Rationality
• Complex Dynamics
• Mathematics of Manipulation: Democracy, Power, and Marriage Proposals
• Special Relativity
• Tensor Products
• The n-body Problem
• Colloquium: Matings of Polynomials

Combinatorics

• Combinatorial Game Theory
• Counting with Generating Series
• Flows on Graphs
• Hyperplane Arrangements
• Introduction to Graph Theory
• Matroids
• Matroids II
• Perfect Graph Theory
• Spectral Graph Theory
• The Conway Hour
• Colloquium: John Conway
• Colloquium: Möbius Inversion and Colorings of Graphs
• Colloquium: The magic of expanders

Computer Science

• Calendrical Calculations
• Mathematical Formulas and the P vs. NP Problem
• Probabilistic Programs: A Foundation for Artificial Intelligence
• Proofs are Programs
• Quantum Computation
• Colloquium: Topological Quantum Computation

Geometry

• Isom(Hⁿ)
• Combing the Sphere and Vector Fields
• Conformal Geometry of the Sphere
• Convex Polytopes
• Cubic Curves
• Ehrhart
• Paper folding construction
• Tangent Spaces and Metrics on the Sphere
• The Gauss Circle Problem
• The Geometry of Metric Spaces
• Thirteen Ways of Looking at a Projective Plane
• Colloquium: Isoperimetric Inequalities

Logic/Set Theory

• Gödel's Incompleteness Theorems
• Infinite Trees
• Infinity and Beyond
• Set Theory as a Foundation for Mathematics
• The Category of Sets
• Colloquium: How do we know that 2+2=4?

Number Theory

• p-adics
• Diophantine Equations
• Introduction to Number Theory
• The Riemann Zeta Function
• Colloquium: The curious case of x_n+1 = kx_n(1-x_n)

Problem Solving

• Basic Problem Solving
• Intro to Problem Solving
• Olympiad Problem Solving
• Problem Solving

Topology

• Covering Spaces and the Fundamental Group
• Knotty Groups
• Point Set Topology (in Four Weeks)