The format of Mathcamp 2022 is still TBD, but we hope to run a residential program! Learn more.

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.

Here is the list of classes by subject:

Algebra

  • Banach-Tarski
  • Classification of Subgroups of GL2(Fq)
  • 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: An and the "other" An
  • 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