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.

Read the 2019 Blurbs

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