Mathcamp 2020 will run online: Learn more.

2015 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

  • A (re)Introduction to Polynomials
  • A Dynkin diagram miscellany
  • Abel's Theorem
  • Abelian Groups
  • Abstract Nonsense
  • Advanced Linear Algebra
  • Braid Groups
  • Burnside's Lemma
  • Category Theory in Sets
  • Cyclotomic Polynomials and Extensions
  • Extensions
  • Finite Fields
  • Galois Theory
  • Introduction to Groups
  • Laurent Phenomenon
  • Lie Algebras
  • Linear Algebra
  • Primitive roots
  • Reflection Groups
  • Representation Theory of Finite Groups
  • Ring Theory
  • Sylow Theorems
  • The Banach–Tarski Paradox
  • The tale of summation is in order!
  • Tiling Problems
  • Tropical Curves
  • Colloquium: Putting the Algebra in Algebraic Topology

Analysis

  • Almost All You Want
  • Differentials and higher differentials
  • Differentiation under the Integral Sign
  • Functions of a Complex Variable
  • Fundamental Theorem of Calculus in Dimension n
  • Infinitesimals
  • Lebesgue Measure
  • Metric Spaces
  • Multivariable Calculus
  • Normal Numbers
  • The Ham Sandwich Theorem and Friends
  • What's Up With e?
  • Colloquium: Cauchy's functional equation

Applied Math

  • A Card Trick, and a Set
  • A Mathematician Goes to Vegas
  • Building a machine that learns like a human
  • Cosine Waves on Musical Staves
  • From Geometric Optics to High Speed Underwater Photography
  • Group operations' harmonic implications
  • Mathematical Magic
  • Optimization Problems on Graphs
  • Quantum factoring
  • Special Relativity
  • Statistical Modelling
  • The Cake is a Lie
  • The Fast More Four Do Over
  • The Hidden Dance of Partial Differential Equations
  • The mathematics of polygamy (and bankruptcy)
  • Time-Frequency Analysis
  • Unsolved Problems in Cosmology
  • Voting Theory
  • Colloquium: An Intro to "Data Science"
  • Colloquium: Pad Thai with Electrons
  • Colloquium: Secure Genomic Computation: a Contest

Combinatorics

  • Coloring Maps
  • Combinatorial Game Theory
  • From Counting to a Theorem of Fermat
  • Generating Functions, Catalan Numbers, and Partitions
  • Graphs on Surfaces
  • Induced Matchings from Szemeredi's Regularity Lemma
  • Intro Knot Theory
  • Knight's Tours
  • Latin Squares
  • Posets
  • Qualifying Quiz Problem 6
  • Summing Series
  • The Hoffmann Singleton Theorem
  • The Pruefer Correspondence
  • The Robinson-Schensted Correspondence
  • The Tower of Hanoi
  • Tower of Hanoi
  • Unlikely Maths
  • Wagner's Theorem
  • Colloquium: Triples

Computer Science

  • Algorithms
  • Automated Proofs in Geometry
  • Cryptography
  • Cryptography: What is it and Why Do we Care?
  • Error-Correcting Codes
  • Introduction to Complexity
  • Learn to code!
  • Many Facets of Optimization
  • P vs NP
  • Colloquium: Computers: Friends or foes of the modern mathematician?

Geometry

  • Aperiodic Tiling
  • Apollonian Circle Packings
  • Classifying Symmetry
  • Coloring in Space
  • Counting the Faces of Cut-Up Spaces
  • DIY Hyperbolic Geometry
  • Elliptic Curves Day 1
  • Fractal dimensions
  • Non-classical Constructions
  • Quaternions and rotations
  • Quaternions and rotations
  • Shortest Distance
  • The Projective Plane
  • Colloquium: Can You Hear the Shape of a Drum?
  • Colloquium: Neural Codes
  • Colloquium: Polyhedral Symmetry in the Plane?

History, Literature, and Education

  • Bad History: A Crash Course in Historiography and how not to do the History of Math
  • Development of Probability
  • History of Math
  • The History of Calculus
  • Turing and his Work
  • Colloquium: Are We Special?
  • Colloquium: Finding my Place in {Teacher Educators} ∩ {Mathematicians}: Bringing a Mathematical Eye to Teacher Education

Logic/Set Theory

  • A game you can't play (but would win if you could)
  • Exploring Equality via Homotopy and Proof Assistants
  • Fun with Compactness in Logic
  • LARGE cardinals!
  • Martin's Axiom and Ramsey Ultrafilters
  • Mathcamp Crash Course
  • Measure and Martin's Axiom
  • Ordinal Arithmetic
  • Stupid Games on Uncountable Sets
  • The Löwenheim-Skolem Theorem
  • Ultrafilters
  • Colloquium: Hydras
  • Colloquium: Making Cantor Super Proud

Number Theory

  • Absolute Values: All the Other Ones
  • Algorithms in Number Theory
  • Continued Fractions
  • Multiplicative Functions
  • Quadratic Reciprocity
  • The Factorial Function
  • pNumber Theory
  • Colloquium: My Favorite Prime

Probability/Statistics

  • Markov Chains to Support your Probabilistic Exploits

Problem Solving

  • Problem Solving: Combinatorics
  • Problem Solving: Inequalities
  • Problem Solving: Linear Algebra
  • Problem Solving: Tetrahedra
  • Rapid Fire Problem Solving

Topology

  • Classifying Spaces
  • Combinatorial Topology
  • Fundamental Group
  • Galois Cohomology
  • Homotopy Theory
  • Point-set Topology
  • Colloquium: Reeb Foliation of the 3-Sphere