2019 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.

An image of the blurbs describing 2019 Classes

Read the 2019 Blurbs

An image of the grid displaying 2019 Classes

View the 2019 Schedule

Here is the list of classes by subject:

Algebra

  • Bhargava's Cube
  • Conway–Coxeter Frieze Patterns
  • Counting Points over Finite Fields
  • Eigenstuff and Beyond
  • Everything You Ever Wanted to Know About Finite Fields
  • Factoring in the Chicken McNugget Monoid
  • Farey Tales
  • From High School Arithmetic to Group Cohomology
  • Galois Theory Crash Course
  • Group Theory & Rubik's Cubes
  • Harmonic Analysis on Finite Abelian Groups
  • Introduction to Group Theory
  • Introduction to Ring Theory
  • Linear Algebra
  • Long Live Determinants!
  • Markov Triples and Continued Fractions
  • Packing Permutation Patterns
  • Perspectives on Cohomology
  • Quiver Representations
  • Representation Theory of Associative Algebras
  • Riemann Surfaces
  • Sporadic Groups and Where to Find Them
  • The Centuries-Old English Tradition of Publicly Performing Hamiltonian Cycles in Cayley Graphs of Symmetric Groups (Change Ringing)
  • The Class Number
  • The Polish Attack on the Enigma
  • Unique and Nonunique Factorization
  • Wedderburn's Theorem
  • You Can't Solve the Quintic
  • Young Tableaux and Representation Theory

Analysis

  • (Dys)functional Analysis
  • A Convoluted Process
  • A Very Difficult Definite Integral
  • Calculus on Young's Lattice
  • Calculus without Calculus
  • Discrete Derivatives
  • Functions of a Complex Variable
  • Infinitely Many Proofs of Infinitely Many Primes
  • Multivariable Calculus Crash Course
  • PARTIAL DIFFERENTIAL EQUATIONS
  • Real Analysis: Limits
  • Real Analysis: Measures
  • Rescuing Divergent Series
  • Take it to the Limit
  • The Riemann Zeta Function

Applied Math

  • Chaos in Voting
  • Magic
  • Mathcamplandia
  • Musical Lattices
  • Not Your Grandparents' Algorithms Class
  • Procrastination
  • Quantum Mechanics
  • Systems of Differential Equations
  • The Good and Bad Mathematics of Pennsylvania's Gerrymandering Lawsuit
  • The Mathematics of Fairness
  • Thinking of Images as Mathematical Objects
  • Colloquium: Should We Vote on How We Vote?
  • Colloquium: The Most Depressing Theorem I Know
  • Colloquium: Your Clock on Your Phone: Tracking Your Body's Internal Time with Math

Combinatorics

  • A Proof of the Sensitivity Conjecture
  • Beyond Inclusion/Exclusion
  • Cap Sets, SET, and ProSet
  • Cauchy–Davenport with Combinatorial Nullstellensatz
  • Cluster Algebras
  • Counting, Involutions, and a Theorem of Fermat
  • Crossing Numbers, from 1954 to 2012
  • Electrifying Random Trees
  • Elegant Applications of Linear Algebra to Combinatorics
  • Game Theory
  • Generating-Function Magic
  • Going in Cycles
  • Hedetniemi's Conjecture
  • Matching Bears With Campers
  • Matroids and Greed
  • Permutation Combinatorics
  • Polytopes (Higher Dimensional Polygons)
  • Randomized Algorithms
  • Root Systems
  • Sperner, Monsky, and Brouwer
  • Studying Betting Games with Other Betting Games
  • The Combinatorics of Boarding an Airplane
  • The Hoffman–Singleton Theorem
  • The Monotone Sequence Game
  • The Probabilistic Method
  • Two Games and a Code
  • Young Tableaux and Combinatorics
  • Young Tableaux and Probability
  • Colloquium: Superpermutations, Traveling Salesmen, and The Melancholy of Haruhi Suzumiya
  • Colloquium: Tournaments Having the Most Cycles
  • Colloquium: When Bare Hands Fail

Computer Science

  • Algorithms in Number Theory
  • Breaking Bad: RSA Encryption
  • Graph Coloring and Containment
  • Introduction to Gerrymandering
  • Probabilistic Models and (a little bit of) Machine Learning
  • Super Mario Bros. is NP-hard

Geometry

  • Building Mathematical Sculptures
  • Homological Algebra: The Art of Gluing
  • Non-Euclidean Geometries
  • THE Intuitive Proof of the Hairy Ball Theorem
  • The Hopf–Poincaré Index Formula
  • Why We Like Complex Projective Space
  • Young Tableaux and Enumerative Geometry
  • Colloquium: Dictionary Shapes
  • Colloquium: Stably Surrounding Spheres with Smallest String Size

History/Literature

  • The Mathematical ABC's
  • The Sound of Proof
  • Why the Millennium Problems?
  • Colloquium: Exceptional Mathematics: from Egyptian Fractions to Heterotic Strings
  • Colloquium: Good Practice: Teaching, Learning & Beauty in Math and Beyond
  • Colloquium: Women and Gender Minorities in Math

Logic/Set Theory

  • Finite-ness
  • Infinite Graphs
  • Infinite Trees
  • Infinite-Ness
  • Logic and Arithmetic
  • Martin's Axiom
  • Mathcamp Crash Course
  • Traffic
  • Colloquium: Degrees of Unsolvability
  • Colloquium: Why Should We Care About Category Theory?

Number Theory

  • All About Quaternions
  • Analysis with Prime Numbers
  • Introduction to Algebraic Number Theory
  • Introduction to Number Theory
  • Not-Proofs of Fermat's Last Theorem
  • Perfect Numbers
  • Reciprocity Laws in Algebraic Number Theory
  • Units in Algebraic Number Theory
  • Zeta Functions

Problem Solving

  • Multi-Coefficient Solving of Problems
  • Problem Solving: Induction
  • Problem-Solving Cornucopia
  • Colloquium: Knowledge Puzzles

Topology

  • All Things Manifoldy
  • Fundamental Groups
  • Galois Correspondence of Covering Spaces
  • Knot Theory
  • Morse Theory
  • Perspectives on Cohomology
  • Point-Set Topology
  • The Weierstrass ℘ Function
  • Tychonoff's Theorem