University of Chicago REU 2012

2012 REU: Announcement and description of the program (pdf)
2012 REU: Application (doc)
2012 REU: Acceptance Form for the Apprentice program (pdf)
2012 REU: Acceptance Form for the Full program (pdf)
2012 REU: Abstracts of the course offerings (pdf)
2012 REU: Schedule for weeks 1 and 2 (pdf)
2012 REU: Schedule for weeks 3 and 4 (pdf)
2012 REU: Schedule for weeks 5 and 6 (pdf)
2012 REU: Schedule for weeks 7 and 8 (pdf)
2012 REU: Mentorship groups (pdf)

Abstracts of the final week talks

Talks Tuesday, August 7 (pdf)
Talks Wednesday, August 8 (pdf)
Talks Thursday, August 9 (pdf)
Talks Friday, August 10 (pdf)

COURSE NOTES (The notes below from past years are also relevant)

APPRENTICE PROGRAM: Linear Algebra and Combinatorics

Laci Babai's 2012 REU web page is now up, go take a look (Go)

NUMBER THEORY

Liang Xiao: Lecture I: Infinitude of Primes and the Riemann Zeta Function (pdf)
Exercise 1 (hints on page 2, but don't peek before giving a try) (pdf)
Eddie Herman: Lecture 2: Dirichlet Characters; Homework Problems p. 7 (pdf)
Liang Xiao: Notes on Lecture 2, Dirichlet Characters (pdf)
Liang Xiao: Lecture 3: Dirichlet L-functions (pdf)
Liang Xiao: Lecture 4: Special values of L-function and number fields (pdf)
Exercise 2: Some L-values and exercises (pdf)
Liang Xiao: Lecture 5: Quadratic characters and quadratic fields (pdf)
Liang Xiao: Lecture 6: Formula for special values of L-functions (pdf)
Liang Xiao: Lecture 7: Computation for Q(square root 2) (pdf)
Matthew Emerton: Special cases of the class number formula (pdf)
Eddie Herman: Notes on the last number theory talk (pdf)

TOPOLOGY: FINITE SPACES and LARGER CONTEXTS

Henry Y. Chan and Zhouli Xu: Finite Spaces Handouts 1 (pdf)
Henry Y. Chan and Zhouli Xu: Finite Spaces Handouts 2 (pdf)
Henry Y. Chan: Notes on Monday, July 16, talk (pdf\ )
Peter May: Updates of a book in progress ($1 for each correction). (Go) The most recent update was posted August 7.
Peter May: New chapters: Properties A, B, and C and subdivision. (Go) Update posted August 7; also incorporated in updated book pdf.

NOTES FROM EARLIER REU's

Matthew Morrow's notes ``Number theory: Reciprocity and polynomials'' (pdf)
Lecture notes on TQFT's (Updated and collated) (TQFT)
Maryanthe Malliaris's pointers to REU paper topics (Logic topics)
Laszlo Babai's summer 2011 REU page (Apprentice web page)
Past notes and reading materials about finite spaces (Finite)

Guides to writing papers (Steve Kleiman and Dan Kleitman, MIT)

Writing a math paper (two formats): READ THIS CAREFULLY (pdf) (pdf)

Another useful guide: READ THIS TOO (pdf)

Tex Help

Template for texing REU papers: USE THIS TEX FILE (tex) (pdf)

An excellent latex web page (web page)

LaTeX -- A document preparation system (web page)

2012 REU: PARTICIPANT PAPERS -- FULL PROGRAM

Joshua Bosshardt: The classification of simple complex Lie algebras (pdf)

Kerisha Burke: Exploring graphs of triangulated $n$-gons (pdf)

Hunter Chase: Fundamental forms of surfaces and the Gauss-Bonnet theorem (pdf)

Chaofan Chen: Rings of integers, Gauss-Jacobi sums, and their applications (pdf)

Daniel Comeaux: An exploration of Minkowski theory and its applications (pdf)

Max Cytrynbaum: $\hat{\text{I}}$to calculus and derivative pricing with risk-neutral measure (pdf)

Genevieve Denoeux: Stability in mathematical game theory (pdf)

Andrew Ding: Plane algebraic curves (pdf)

Alexander J. Dunlap: Topics in percolation (pdf)

Erika Dunn-Weiss: Introduction to geometry (pdf)

Jun Hou Fung: The cohomology of Lie groups (pdf)

Alexander Grant: Preissman's theorem (pdf)

Mitchell Hill: Convergence of random Fourier series (pdf)

Zihao Jiang: Application of manifold theory to Hamiltonian mechanics (pdf)

Matthew Joseph: Markov chain Monte Carlo (pdf)

Young Kun Ko: Probabilistic checking of proofs and hardness of approximation (pdf)

Aaron Krahn: Quantum computation and quantum algorithms (pdf)

Nina Kuklisova: Introduction to Markov chains (pdf)

James Leiner: Brownian motion and the strong Markov property (pdf)

Haoru Liu: Error-correcting codes and finite fields (pdf)

Shankara Pailoor: Meromorphic forms on Riemann surface structures (pdf)

Anirudh Sankar: Monads and algebraic structures (pdf)

Miranda Grace Seitz-McLeese: Classifying the representations of sl_2(C) (pdf)

Abhinav Shrestha: An introduction to the fusion systems of blocks (pdf)

Salman Siddiqi: An introduction to geometric stability theory (pdf)

Yan Shuo Tan: A skeleton in the category: the secret theory of covering spaces (pdf)

Chen Hui George Teo: Brownian motion and Liouville's theorem (pdf)

Kairui Glen Wang: The basic theory of persistent homology. (pdf)

2012 REU: PARTICIPANT PAPERS -- APPRENTICE PROGRAM

Matthew Actipes: A probabilistic view on the economics of gambling (pdf)

Daniele Caratelli: Brouwer fixed point theorem (pdf)

Brian Chen: The heat equation and harmonic functions over graphs (pdf)

Yo Joong Choe: Increasing chromatic number and girth (pdf)

Kevin Cuddy: Convergence of Fourier series (pdf)

Jiaqi Jiang: An introduction to spectral graph theory (pdf)

Daniel Kassler: Nonlinear equations: contractions and chaos (pdf)

Ilyas Khan: Hyperbolic geometry: isometry groups of hyperbolic space (pdf)

Simon Lazarus: Internal set theory and an intuitive development of the calculus (pdf)

Do Q Lee: Numerically efficient methods for solving least squares problems (pdf)

Ang Li: Dirichlet's theorem about primes in arithmetic progressions (pdf)

Lucas Lingle: Lie theory, universal enveloping algebras, and the Poincar\'e-Birkhoff-Witt theorem (pdf)

Ryan Liu: Prime number theorem (pdf)

Conor L. Mahany: Elementary topos theory and intuitionistic logic (pdf)

Christopher Natoli: Fractals as fixed points of iterated function systems (pdf)

Teddy Niemiec: The discrete-time binomial asset-pricing model (pdf)

Daniel Older: Applications of variational principles to dynamics and conservation laws in physics (pdf)

Rick Presman: The generalized Stokes' theorem (pdf)

Kevin Qian: Applications of Fourier analysis to non-analytic fields (pdf)

Turner Smith: Martingales and a basic application (pdf)

Min Jae Song: Euler's formula and the five color theorem (pdf)

Anagha Sundararajan: Shifting and moving: an introduction to dynamical systems (pdf)

George Robert Woodbury: The representation of a number by two or four squares (pdf)

Alejandro Younger: An exploration of Khinchin's constant (pdf)

Thomas Yu: Lagrangian formulation of the electromagnetic field (pdf)