2017 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.

Read the 2017 Blurbs

View the 2017 Schedule

Here is the list of classes by subject:

Algebra

• Banach-Tarski
• Classification of Subgroups of GL₂(F_q)
• Crash course on Representation theory
• Division Rings
• Finite Fields
• Finite "Sets"
• Galois Theory Crash Course
• Group Theory
• How Not To Prove That a Group Isn't Sofic
• Linear Algebra
• Many Clubs Share People
• Planar Algebras
• Pseudo-Telepathy via Representation Theory of Finite Groups
• Quadratic Field Extensions
• Quandles
• Ring Theory
• Simplicity itself: A_n and the "other" A_n
• Solving cubic and quartic equations without the mess
• Topological groups
• Unique Factorization Domains
• Colloquium: Algebra and the Internal GPS
• Colloquium: Twenty-Seven Lines

Analysis

• Advanced Complex Analysis
• Calculus without Calculus
• Discrete Derivatives
• Elliptic Functions
• Functions of a Complex Variable
• How Not to Solve Tricky Integrals
• How to Define the Square Root
• Multivariable Calculus Crash Course
• Real Analysis
• Riemann Surfaces
• Systems of Differential Equations
• Trig Functions by Hand
• What's The Deal With e?

Applied Math

• Algorithms to Generate Randomish Numbers
• Choosing Random Numbers
• Computer Aided Design
• Fast Matrix Multiplication
• From the Intermediate Value Theorem to Chaos
• How To Get Rich Quick By Playing The Lottery
• How to Build a Calculator
• Math Writing Workshop
• Math and Brains
• Mathematica Workshop
• My Favorite Magic Trick
• Not Your Grandparents' Algorithms Class
• Special Relativity
• The Bell Curve
• The Logistics of Zombies: Cobwebs and Chaos
• The Mathematics of Voting
• The Traveling Salesman Problem: Recent Breakthroughs
• Urban Planning
• Voting Systems
• Colloquium: Using Math to Protect Democracy

Combinatorics

• Cap-Set Problem: Recent Progress
• Coloring Graphs on Surfaces
• Combinatorial Gems
• Decomposing and Factoring
• Exclusion-Inclusion
• Generating Functions and Regular Expressions
• How to Pronounce "Lucas"
• Hyperplane Arrangements
• Intro to Graph Theory
• Permutation Statistics
• Quivers
• Ramsey Theory
• The Combinatorial Nullstellensatz
• The Stable Marriage Problem
• The Szemerédi Regularity Lemma
• Weak Separation
• Welzl's theorem on graph homomorphisms
• Young Tableaux
• Colloquium: The Icosian Game
• Colloquium: The Party Problem and Ramsey

Computer Science

• Cryptography, and How to Attack It
• Evasiveness
• Machine Learning (NO neural networks)
• Shannon Capacity of Graphs

Geometry

• Coloring the Hyperbolic Plane
• Cubic Curves
• Finite Geometries
• Fractals and Dimension
• Geometry in Motion
• Intersecting polynomials
• Penrose Tilings
• Symmetries of Spaces
• The Kakeya Conjecture
• The Kakeya Maximal Conjecture
• Using quaternions to describe symmetries of Platonic solids
• Vertex-Transitive Polytopes
• Wallpaper Patterns
• What's It Like to Live in a Hyperbolic World?
• Colloquium: Farey Fractions and Plane Geometry
• Colloquium: Many Campers Split Pizza
• Colloquium: Squaring the Circle

History/Literature

• Ancient Greek Mathematics
• Turing and His Work

Logic/Set Theory

• Cloudy with a Chance of the Continuum Hypothesis
• Constructive Logic
• Godel's Incompleteness Theorem
• How to "Divide"
• Hyperreal Numbers
• Logic Puzzles
• Mathcamp Crash Course
• Metric Space of Metric Spaces
• Non-Classical Logic
• Set Theory
• Surreal Numbers
• The Pseudoarc
• Colloquium: Down the Rabbit Hole
• Colloquium: Games People (Don't) Play
• Colloquium: Hydras

Number Theory

• Analytic Number Theory
• Bernoulli Numbers
• Every natural is "Fibonacci": Games, Miles and Kilometres
• Prime Numbers
• Quadratic Reciprocity
• Riemann and Series
• Smol Results on the Mobius Function
• Colloquium: Opinionated Primes
• Colloquium: Why are drums shaped by number theory sometimes louder than others?

Probability/Statistics

• A Crash Course in Axiomatic Probability
• And That Is Why Birds Shouldn't Drink Alcohol
• Laws of large numbers
• Mathematics in Crisis: The St. Petersburg Paradox
• Problem Solving: Probabilistic Method
• Queueing Theory
• Underhanded Tricks with Markov Chains

Problem Solving

• Problem Solving Discussion
• Problem Solving: Convexity
• Problem Solving: Diophantine Equations
• Problem Solving: Geometric Transformations
• Problem Solving: Linear Algebra
• Problem Solving: the "Just Do It" method

Topology

• All Things Manifoldy
• Euler Characteristic
• How to Count Using Topology
• Impossible Cohomology
• The Baire Category Theorem
• The Fundamental Group
• Topological Tic Tac Toe
• What is Homology?
• Colloquium: Covering Spaces and Square Dancing
• Colloquium: Rational Tangles