Mathcamp 2019 Classes

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.

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