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Projects from Fall 2023

Project Title Mentor Mentee Resources Used
Matrix Lie Groups and Their Lie Algebras Yangyang Li Finn Braaten
  • Lie Groups, Lie Algebras, and Representations
    		•
    High dimensional probability Minjae Park Colin Yao
  • High Dimensional Probability
    		•
    Mathematical models in finance math Minjae Park Jiahong Cai
  • Stochastic Calculus for Finance II
    		•
    Elements of Computability Theory Duarte Maia Kelly Mao
  • Recursively Enumerable Sets and Degrees
    		•
    Dynamics and Ergodic theory Daniel Mitsutani Dino Zavattini
  • Ergodic Theory and Differentiable Dynamics
    		•
    Differential Topology and Morse Theory Junhao Fan Derek Zhu
  • Topology from a Differential Viewpoint
    		•
    Representation of Finite Groups Jinyue Luo Tracy Wu
  • Linear Representation of Finite Groups
    		•
    Algebraic topology with a view towards topological phases of condensed matter Nicholas Wawrykow Kabir Dubey
  • Algebraic Topology
    • , Hatcher
    Viscosity solutions of first order Hamilton-Jacobi equations and their connection to optimal control. Joe Jackson Shreya Mukherjee
  • Lecture Notes by H.V. Tran
    		•
    Introduction to Category Theory Colin Aitken Romain Amzallag
  • Category theory in context
    		•
    The zeta function and a proof of the Prime Number Theorem via complex analysis Alicia Lima Michael Lee
  • Complex Analysis by Stein
    		•
    The Four-Color Theorem Livia Xu Hazal Kara
  • Graph theory with appilcations
    		•

    Projects from Fall 2017

    Project Title Mentor Mentee Resources Used
    Extensive Games with Perfect Information and Kuhn's Theorem Jia Kong Younggeun Yoo
    Chaotic Dynamics Kiho Park Myles Kornfeld
  • An Introduction to Chaotic Dynamical Systems
    		•
    Elementary Number Theory Tung Nguyen Benjamin Andrew
  • Elementary Theory of Numbers by William J. Leveque
    		•
    An introduction to mathematical logic Jonathan DeWitt Yuezhen Li
  • Mathematical Logic by Chiswell and Hodges
    		•
    An introduction to Teichmuller theory and mapping class groups. Paul Apisa Meg Doucette
  • A Primer on Mapping Class Groups by Farb and Margalit
    		•
    Fourier transform and applications Francisc Bozgan Ran Tao
  • Fourier Analysis by Stein and Shakarchi
    		•
    Fourier theory and applications to music Nazerke Bakytzhan L.M.
  • Music: a mathematical offering, by Dave Benson
    		•
    Scheme Theory Drew Moore Jiaqi (Jimmy) Leng
  • Algebraic Geometry and Arithmetic Curves by Liu
    		•
    Axiomatic geometry Benjamin O'Connor Rebeka Pushkar
  • Euclid's Elements
  • Hilbert's Foundations of Geometry
    		•
    Galois theory and elliptic curves Karl Schaefer David Lin
  • Arithmetic of Elliptic Curves by Silverman
  • Rational Points on Elliptic Curves by Silverman and Tate
    		•

    Projects from Spring 2017

    Project Title Mentor Mentee Resources Used
    Category Theory Isabel Leal Rafael Wingester Ribeiro De Oliveira
  • Category Theory by Mac Lane
    		•
    Algebraic Geometry Yordanka Kovacheva Sameer Kailasa
    Geometry/Topology Nick Salter Larsen Linov
    Machine Learning Zana Tran Ted Kim
    Number Theory Mathilde Gerbelli-Gauthier Karolina Simcic
    Number Theory Karl Schaefer Karen Butt
    Nonstandard Analysis Nir Gadish Diego Bejarano
    Number Theory Eric Stubley Ashen Wiseth
    Representation Theory Sean Howe John Holiday
    Geometry/Topology Kevin Casto Matthew Correia
    Topology Jia Kong Younggeun Yoo
    Combinatorics Francisc Bozgan Giorgio Young
    Analysis Gong Chen Fernando Al Assal
    Dynamics Kiho Park Bryce Gollobit

    Projects from Winter 2017

    Project Title Mentor Mentee Resources Used
    Analysis Jonathan DeWitt Giorgio Young
    Analysis Foling Zou Paolo Degiorgi
    Category Theory Henry Chan Trevor Moore
    Combinatorics Tim Black Zhenying Tian
    Number theory Eric Stubley Leon Zhang
    Analysis Alan Chang Ariel Goldszmidt
    Algebra Yordanka Kovacheva Zijian Wang
    Topology Jia Kong Younggeun Yoo
    Number theory Drew Moore Hung Ho
    Algebra Mathilde Gerbelli-Gauthier Karolina Simcic
    Differential Equations Gong Chen Xingyu Wang
    Logic Nir Gadish Diego Bejarano
    Complex analysis Li Yu Edward Zamborsky
    Galois theory Karl Schaefer Adele Padgett
    Ergodic Theory Kiho Park Bryce Gollobit
    Differential Equations Daniel Campos Zhichen Sha
    Number Theory Nazerke Bakytzhan Paul Lee

    Projects from Fall 2016

    Project Title Mentor Mentee Resources Used
    Number Theory Drew Moore Frimpong Baidoo
    • Marcus "Number Fields"
    • Neukirch "Algebraic Number Theory"
    • Greenberg "An Elementary Proof of the Kronecker Weber Theorem"
    Algebraic Topology Foling Zou Paolo Degiorgi
    • Characteristic classes, Milnor and Stasheff
    • A concise course to algebraic topology, May
    Twists of Elliptic Curves Karl Schaefer Karen Butt
    Combinatorics Santiago Chaves Alexander Bai
    Introduction to Dynamical Systems Georgios Sakellaris Jacob Mazor
    • Brin, Stuck. Introduction to Dynamical Systems.
    Analysis Gong Chen Samir Khan
    Algebraic Geometry Ping Ngai Chung Eric Silva
    • Fulton, William. Algebraic Curves
    Topology Tori Akin Anand Abraham
    • Introduction to Lattices and Order by Davey and Priestley
    Representation Theory Jeff Manning Arieh Zimmerman
    Analysis Stephen Cameron Jack Zhou
    Complex Analysis Li Yu Willard Kwak
    Measure Theory Alan Chang Alex Manchester
    Topology Jia Kong Younggeun Yoo
    Dynamical System Carlos di Fiore Bryce Gollobit
    Topology Nick Salter John Halliday
    Burnside's Lemma Nazerke Bakytzhan Xingyu Wang
    Hartshorne Yordanka Kovacheva Danny Stoll
    • Hartshorne
    • Vakil's notes
    Geometry/Topology Ronno Das Erik Hupp
    • "Differential Forms in Algebraic Topology" - Raoul Bott and Loring W. Tu

    Projects from Spring 2016

    Project Title Mentor Mentee Resources Used
    Analysis Max Engelstein Nitin Krishna
    Number Theory Yun Cheng Jason Liang
    Algebra Minh-Tam Trinh Brian Burns
    Factoriaztion Homology Quoc Ho Alberto San Miguel Malaney
    Analysis Gong Chen Jan Ertl
    Category Theory Drew Moore Benjamin McKenna
    Analysis Claudio Gonzales Giorgio Young
    Geometric Langlands Sean Howe Jack Sempliner
    Number Theory Tung Nguyen Michael Cronin
    • Number Theory by George E. Andrews.
    Algebraic Number Theory via Solving $x^2 + k = y^3$ Zana Tran Kushal Haran
    Functional Analysis Daniel Campos Adel Ashraf Rahman
    Algebraic Geometry Olivier Martin Victor Zhang
    Analysis Casey Rodriguez Ryan Hopkins
    Topology MurphyKate Montee Jordan Hisel
    Analysis Li Yu Daniel Mitsutani
    Analysis Ben Seeger Adam Sudit
    Topology Yi-Wei Henry Chan Eric Silva
    Complex Analysis Alan Chang Theo Gibbs
    Topology Yordanka Kovacheva Diego Bejarano
    • Topology by Munkres
    Differential Geometry Reid Harris Dae Heun Koh
    Topology Carlos di Fiore Edward Zamborsky
    Ratner's Theorem Clark Butler Rachel McEnroe
    Logic Nir Gadish Arieh Zimmerman

    Projects from Winter 2016

    Project Title Mentor Mentee Resources Used
    Algebraic Topology Quoc Ho Alberto San Miguel Malaney
    Algebraic groups over fields Minh-Tam Trinh Peter Xu
    • Borel, Linear Algebraic Groups
    • Milne, Algebraic Groups
    • Silverman, The Arithmetic of Elliptic Curves.
    Analysis Alan Chang Isaac Friend
    • Stein & Shakarchi, Real Analysis
    Algebra Tianqi Fan Yi Wang
    Class Field Theory Mathilde Gerbelli-Gauthier Jack Sempliner
    • Cassels and Frohlich - Algebraic Number theory
    • Serre - Local Fields
    Analysis Reid Harris Nathanial Holderman
    Analysis Max Engelstein Ryan Hopkins
    Discrete Gauss Bonnet Tori Akin Zhenying Tian
    Logic Nir Gadish Arieh Zimmerman
    • Warner - Differentiable manifolds
    Complexity Theory Timothy Black Bowen Wang
    Geometry MurphyKate Montee Eric Silva
    • Geometry of Curves and Surfaces, by doCarmo.
    Algebra Daniel Johnstone Shi-Ning Sun
    Analysis Daniel Campos Elia Portnoy
    • Lax - Linear algebra
    • Yaglom, Boltyanskii - Convex figures.
    • Lax - Functional analysis.
    Topology Subhadip Chowdhury Dan Su
    Algebraic Topology Yi-Wei Henry Chan Kevin Dong
    Algebraic Geometry Yiwen Zhou Rachel McEnroe
    • Matsumura, Hideyuki, and Miles Reid. Commutative ring theory.
    • Matsumura, Hideyuki. "Commutative Algebra”
    Number Theory Joel Specter Sanjit Shashi
    Local fields Isabel Leal Frank Wang
    Dirichlet's unit theorem Yun Cheng Matthew Morgado
    Distribution of prime numbers Weiyan Chen Vincent Dzik
    • Introduction to Analytic Number Theory by Apostol.
    Ordinary Differential Equations Li Yu Shayon Sengupta
    Analysis Gong Chen Adel Ashraf Rahman
    Analysis Georgios Sakellaris Nitin Krishna
    Algebraic Combinatorics Angela Wu Robert Green
    • Godsil - Algebraic Combinatorics
    Dynamics Clark Butler Redmond McNamara

    Projects from Fall 2015

    Project Title Mentor Mentee Resources Used
    Differential Geometry Ian Frankel Joey Zou
    • "Differential Geometry of Curves and Surfaces" by Manfredo P. doCarmo
    • "Differential Forms and Applications" by Manfredo P. doCarmo
    Algebraic Geometry Yiwen Zhou Rachel McEnroe
    Harmonic Analysis Daniel Campos Redmond McNamara
    • E. Stein "Singular integrals and differentiability properties of functions"
    • R. Bass "Real analysis for graduate students"
    • W. Littman "Studies in Partial Differential Equations".
    Topology MurphyKate Montee Jake Koenig
    • A Primer on Mapping Class Groups by Dan Margalit and Benson Farb
    • Course notes from a 2013 course by Jake Rasmussen.
    Algebra Quoc Ho Alberto San Miguel Malaney
    Pure Mathematics Nir Gadish Arieh Zimmerman
    Algebraic Topology Chen Lei Zachary Kirsche
    Algebraic Topology Foling Zou Zhengqu Wan
    • Algebraic Topology, Allen Hatcher
    Number Theory Yun Cheng Frank Wang
    • Serre - Course in Arithmetic
    Semisimple and reductive Lie algebras Minh-Tam Trinh Peter Xu
    • Sepanski, Compact Lie Groups
    • Borcherds, Haiman, Reshetikhin, Serganova, Berkeley Lectures on Lie Groups and Quantum Groups.
    Combinatorics Timothy Black Stefan Lance
    Analysis Alan Chang Ryan Hopkins
    • Stein and Shakarchi, Fourier Analysis
    Algebraic Geometry Anthony Wang John Halliday
    • Hartshorne Algebraic Geometry
    • Atiyah MacDonald Commutative Algebra
    • Shafarevich Algebraic Geometry I
    • Mumford Red Book of Schemes
    The Dynamics of Circle Homeomorphisms Subhadip Chowdhury Wenyu Chen
    Geometry Yan Mary He Nianyi Chen
    • Elementary Differential Geometry by Pressley.
    • Geometric methods in Mathematical Physics by Schutz.
    Class Field Theory Sean Howe Jack Sempliner
    Analysis Gong Chen Yixuan Li
    • Evans, partial differential equations
    Representation Theory Li Yu Ryan Teehan
    Complexity Theory Angela Wu Edward Zamborsky
    • Hopcroft and Ullman - Introduction to Automata Theory, Languages and Computation, 2nd ed.
    Dynamics Clark Butler Ben Lowe
    Measure Theory Max Engelstein Nitin Krishna
    Lie groups Margaret Nichols Gabriel Lynch
    Galois Theory Joel Specter Sanjit Shashi
    $SL_2(\mathbb{R})$ David Aulicino Stephanie Sinnappan

    Projects from Spring 2015

    Project Title Mentor Mentee Resources Used
    Theory of computation John Wilmes John Lekberg
    • Introduction to the Theory of Computation by Michael Sipser
    Functional analysis Daniel Campos Milo Marsden
    • A. Kolmogorov, S. Fomin, Elements of the Theory of Functions and Functional Analysis
    • J. Dieudonne, Foundations of Modern Analysis Volume 1
    • Yu. Shashkin, Fixed Points
    • R. Agarwal, et.al., Fixed Point Theory and Applications
    Working toward Gauss Bonnet Tori Akin Robert Green
    • Guilleman and Pollack
    Linear Algebra Yun Cheng Ryan Hopkins
    Linear Algebra Valia Gazaki Yi Wang
    • "Advanced Linear Algebra" by Steven Roman.
    Linear Algebra Isabel Leal Rafael Wingester Ribeiro de Oliveira
    • Steven Roman's "Advanced Linear Algebra"
    Representation theory Jonathan Wang Sean Colin-Ellerin
    Algebraic topology Carlos di Fiore Zachary Kirsche
    Topology Yiwen Zhou Keshav Prasad
    • Munkres, James. "Topology."
    • Armstrong, Mark Anthony. "Basic topology."
    • Milnor, John Willard. “Topology from the differentiable viewpoint”
    Analysis of Boolean Functions Timothy Black Leo Gladkov
    • Ryan O'Donnell - Analysis of Boolean Functions.
    Riemannian geometry Sean Howe Sohini Upadhyay
    Combinatorics Vaidehee Madhav Thatte Songyuan Ding
    Galois theory Quoc Ho Alberto San Miguel Malaney
    • Galois Groups and Fundamental Groups by Tamás Szamuely
    • Algebra (GTM) by Serge Lang
    Algebraic topology Yi-Wei Henry Chan Redmond McNamara
    Infinite games Jacob Perlman Victor Zhang
    • An introduction to Conway's Games and Numbers - Schleicher & Stoll
    • Winning Ways - Berlekamp, Conway, & Guy
    • On Numbers and Games - Conway
    Applications of class field theory Sean Howe Jack Sempliner
    Dynamical systems Carlos di Fiore Trevor Pearce
    Differential equations Gong Chen Elvin Bora
    Algebra Raluca Havarneanu Kevin Dong
    Dynamics Paul Apisa Rachel McEnroe
    • "Zeta Functions and the Periodic Orbit Structure of Hyperbolic Dynamics" - Parry and Pollicott
    Dynamical systems Clark Butler Daniel Older
    Model theoretic proofs in algebraic geometry Nir Gadish Kyle Gannon
    • The topology of O-minimal structures
    Analysis Daniel Johnstone Angela Lam
    Lie groups Bena Tshishiku Jonathan Sorce
    • Baker, Matrix groups
    • Fulton-Harris, Representation theory
    Complexity and Approximation Algorithms Angela Wu Liyu Xia
    • Computers and Intractability, Garey and Johnson.
    • Approximation Algorithms, Vazirani.

    Projects from Winter 2015

    Project Title Mentor Mentee Resources Used
    Graph Property Testing Timothy Black Ridwan Syed
    Linear algebra Oishee Banerjee Nitin Krishna
    • Algebra by Michael Artin Abstract Algebra by Dummit and Foote.
    Numerical analysis Tori Akin Noah Baskes
    Classification of representations of the symmetric group Jonathan Wang Peter Gao
    • Dummit-Foote
    Measure theory Yiwen Zhou Kushal Haran
    • Segal, Irving Ezra. Kunze, Ray Alden: "Integrals and Operators"
    • Brezis, "Functional Analysis, Sobolev Spaces and Partial Differential Equations (Universitext)"
    Measure theory, probability Paul Apisa Wenyu Chen
    • "Real Analysis: Modern Techniques and Their Applications" by Gerald Folland.
    Functional analysis Tianqi Fan Liyu Xia
    • A short course on spectral theory William Arveson
    Logic Nir Gadish Kyle Gannon
    • Proof of the Mordell-Lang conjecture for function fields
    Topology Carlos di Fiore Sohini Upadhyay

    Projects from Fall 2014

    Project Title Mentor Mentee Resources Used
    Algebraic geometry Sean Howe Jack Sempliner
    Analysis/PDE Gong Chen Mark Perlman
    • Fourier Series and Integrals by Dym, H./ McKean, Henry P.
    • Classical and Multilinear Harmonic Analysis Vol 1 by Schlag, W.
    • Fourier Analysis by Duoandikoetxea, J.
    Algebra Raluca Havarneanu Ricardo Veloz
    Set theory - Iterated forcing Nir Gadish Kyle Gannon
    • Set theory, by Kenneth Kunen
    Representation Theory on $S_n$ Angela Wu Liyu Xia
    • Spectral Analysis of the Supreme Court- Lawson, Orrison, Uminsky.
    • Group Representations in Probability and Statistics - Diaconis.
    Differential geometry Yan Mary He Kunal Goyal
    • J. Lee, Introduction to Smooth Manifolds.
    • J. Milnor, Topology from the Differentiable Viewpoint.
    • Spivak, Calculus on Manifolds
    Elementary number theory Valia Gazaki Rafael Wingester Ribeiro de Oliveira
    • Elementary Number Theory in Nine Chapters, Second Edition by James J.Tattersall
    Morse theory Clark Butler Ben Lowe
    • Milnor - Morse Theory
    Probability Jacob Perlman Justin Guo
    Fundamental group and dynamics Carlos di Fiore Sameer Kailasa
    • Hatcher- Algebraic Topology
    • Lang- Real analysis
    • Katok- Introduction to modern dynamical systems
    • Spivak- A comprehensive introduction to differential geometry.
    • Milnor- Topology from a differentiable viewpoint.
    • Bott, Tu-Differential Forms in algebraic topology
    Number theory Yiwen Zhou Owen Cummings
    • "Number Theory 1: Fermat's Dream"
    • "Number Theory 2: Introduction to Class Field Theory" by Kazuya Kato, Nobushige Kurokawa, Takeshi Saito

    Projects from Spring 2014

    Project Title Mentor Mentee Resources Used
    Discrete Group actions on Topological Spaces Subhadip Chowdhury Weston Ungemach
    • "Classical Tessellations and Three-Manifolds" by Montesinos
    • "Fuchsian Groups" by Katok
    • "Three-Dimensional Geometry and Topology, Vol. 1" by Thurston
    • "A Primer on Mapping Class Groups" by Farb and Margalit
    Logic Jonathan Stephenson Kyle Gannon
    • Marker's Model Theory
    • Hodges' A shorter Model Theory
    Number theory Yun Cheng Adam Freymiller
    Nonstandard Probability Jacob Perlman Alexander McDonough
    • Nelson, Edward (1987). Radically Elementary Probability Theory.
    • Williams, David (1991). Probability with Martingales
    Property Testing and Machine Learning Angela Wu Min Jae Song
    • Fischer, E. The art of uninformed decisions: A Primer to Property Testing
    • Goldreich, O., Goldwasser, S., Ron, D. Property testing and its connection to learning and approximation
    • Alon, N., Dar, S., Parnas, M., Ron, D. Testing of clustering
    Stochastic differential equations Laurence Field Wayne Yang
    • Lawler, Random Walk and the Heat Equation (intro to BM and applications)
    • Oksendal, Stochastic Differential Equations (also covers BM)
    Mathematical physics Isabel Leal Redmond McNamara
    • The N-Vortex Problem: Analytical Techniques (By Paul Newton)
    Analysis/topology Georgios Sakellaris Kunal Goyal
    • Munkres - Topology, Carothers - Real Analysis
    Representation theory Asilata Bapat Zihao Jiang
    • Group Theory in Physics by John Cornwell
    • Lie Groups, Physics, and Geometry: An introduction for Physicists, Engineers and Chemists by Robert Gilmore
    Lie theory Jenny Wilson Fernando Al Assal
    • Stillwell, Naive Lie Theory
    • Curtis, Matrix groups
    • Tapp, Matrix Groups for Undergraduates
    Number theory Sean Howe Ang Li
    • Qing Liu - Algebraic Geometry and Arithmetic Curves
    • Miles Reid - Undergraduate Algebraic Geometry
    Number theory Preston Wake Jesse Silliman
    • Scholze - The Langlands-Kottwitz method for the modular curve
    • Deligne - Weil II
    • Freitag, Kiehl - Etale cohomology and the Weil conjecture
    Combinatorial Designs Vaidehee Madhav Thatte Joey Zou
    • Applied Combinatorics, Roberts
    Probability/differential equations Hyomin Choi Jing Miao
    • Intro to Stochastic Calculus with Applications by G.Lawler
    Hodge theory on Riemann surfaces Nick Salter Rick Presman
    • W. Schlag, "A course in complex analysis and Riemann surfaces"
    Representations of symmetric groups Sergei Sagatov Jason Liang
    • Sagan, B. The Symmetric Group.
    Differential geometry Rachel Vishnepolsky Rachel McEnroe
    Differential geometry Rachel Vishnepolsky Thomas Yu
    Algebra Raluca Havarneanu Amber Yuan
    • Linear Representations of Finite Groups, JP Serre
    Applied algebraic topology Katharine Turner Brandon Rayhaun
    Dynamics Paul Apisa Jonas Actor
    • Katok and Hasselblatt - Introduction to the Modern Theory of Dynamical Systems
    • Milnor - Dynamics in One Complex Variable
    Intro to the theory of computing John Wilmes Liyu Xia
    • Introduction to the Theory of Computation by Michael Sipser

    Projects from Winter 2014

    Project Title Mentor Mentee Resources Used
    Symplectic topology Bena Tshishiku Weston Ungemach
    • Lectures on Symplectic Geometry, Cannas da Silva's J-holomorphic curves
    • Symplectic Topology, McDuff-Salamon
    Applied algebraic topology Katharine Turner Brandon Rayhaun
    Differential geometry Rachel Vishnepolsky Rachel McEnroe
    • Guillemin and Pollack: Differential topology
    • Morita: Geometry of differential forms
    Game theory Simion Filip Vrushank Vora
    Applied mathematics Hyomin Choi Peter Hein
    • Fourier Analysis by Stein
    Algebraic topology Jenny Wilson Haonan Zhou
    Elliptic Curve Cryptography and Number Theory Sean Howe Alexander Dunlap
    • Washington - Elliptic Curves: Number Theory and Cryptography (2nd edition).
    Hodge theory Kathryn Mann Rick Presman
    • Claire Voisin "Hodge Theory and Complex Algebraic Geometry", vol 1.
    Number theory Isabel Leal Jordan Hisel
    • Milne's notes on group theory, fields and Galois theory, and algebraic number theory.
    • "Number Theory 2: Introduction to Class Field Theory" , by K. Kato
    Lie groups Subhadip Chowdhury Michael Oliver
    Partial differential equations Georgios Sakellaris Mark Perlman
    • Evans - Partial Differential Equations
    Logic Jacob Perlman Alexander McDonough
    • Chapter 1 from Ed Nelson's unfinished book on nonstandard analysis (available at https://web.math.princeton.edu/~nelson/books.html) \\ Internal set theory: a new approach to nonstandard analysis, Bulletin of the American Mathematical Society, 83 (1977
    Representation theory of finite groups Sergei Sagatov Ang Li
    • Serre, J.P. Linear Representations of Finite Groups.
    Combinatorics/Number theory Valia Gazaki Charles Argue
    Complex analysis Yi-Wei Henry Chan Skylar DeTure
    Logic Jonathan Stephenson Kyle Gannon
    • Set Theory, Kunen Set Theory and the Continuum hypothesis — Cohen
    • Set Theory: Boolean-Valued Models and Independence Proofs (Oxford Logic Guides) — Bell

    Projects from Fall 2013

    Project Title Mentor Mentee Resources Used
    Number Theory Daniel Le Ang Li
    • Stopple, A Primer of Analytic Number Theory: From Pythagoras to Riemann
    Semiriemannian geometry Wouter van Limbeek Thomas Yu
    • "Semiriemannian Geometry" by O'Neill.
    Applied Algebraic Topology Katharine Turner Brandon Rayhaun
    Differential Geometry Rachel Vishnepolsky Rachel McEnroe
    Combinatorics Vaidehee Madhav Thatte Charles Argue
    • On Numbers and Games,by Conway.
    • Winning ways for your mathematical plays Volumes 1,2 by Berlekamp, Conway, Guy
    Geometry Subhadip Chowdhury Jordan Hisel
    Number Theory and Cryptography Isabel Leal Ridwan Syed
    • "A Classical Introduction to Modern Number Theory", by Ireland and Rosen
    • "A Course in Number Theory and Cryptography", by Koblitz
    Algebraic Geometry Asilata Bapat Hyung Kyu Jun
    • Ravi Vakil's "Foundations of Algebraic Geometry"
    • Robin Hartshorne's "Algebraic Geometry"
    Markov Chains Laurence Field Lokesh Anand
    • Lawler, Introduction to Stochastic Processes (second edition).
    Applied Mathematics Hyomin Choi Peter Hein

    Projects from Spring 2013

    Project Title Mentor Mentee Resources Used
    Linear algebra Ana Balibanu Christopher Geoga
    • Calculus, Vol. 2: Multi-Variable Calculus and Linear Algebra by Tom M. Apostol
    Complex analysis Daniel Johnstone Jiaqi Jiang
    Partial differential equations Hyomin Choi Rachel McEnroe
    An Introduction to Knot Theory Jenny Wilson Wesley Howden
    • Adams - The Knot Book
    • Lickorish - An Introduction to Knot Theory
    Number theory Valia Gazaki Matthew Actipes
    • "Elementary Number Theory" by David M. Burton
    Logic Matthew Wright Orest Xherija
    Fourier Analysis Tianqi Fan Sofigjing Jovanovska
    • Fourier Analysis: An Introduction Elias M. Stein, Rami Shakarchi
    Chromatic homotopy theory Mona Merling Elden Elmanto
    Bezout's Theorem Sean Howe Nathaniel Sauder
    • Guillemin and Pollack - Diff. Top.
    • Stein and Shakarchi - Complex Analysis
    Discrete mathematics John Wilmes Hyung Kyu Jun
    • Algebraic Graph Theory by Chris Godsil and Gordon Royle.
    • Expander Graphs an their Applications by Shlomo Hoory, Nathan Linial, and Avi Wigderson.
    Lie groups, Lie algebras, representation theory Sergei Sagatov Siddharth Narayanan
    • Hall, B. Lie Groups, Lie Algebras and Representations.
    • Lee, J. M. Introduction to Smooth Manifolds.
    Introduction to Fourier Analysis Georgios Sakellaris George Hyun
    • Stein, Shakarchi - Fourier Analysis: an Introduction
    Algebraic topology Yi-Wei Henry Chan Rick Presman
    The problem of Hopf invariant one Zhouli Xu Jing Miao
    • Hatcher Algebraic Topology
    • Pollack Differential Topology
    • May Concise
    Differential Topology / Riemannian geometry Wouter van Limbeek Daniel Older
    • Guillemin, Pollack - Differential Topology.
    • Do Carmo - Riemannian Geometry.
    Homotopy theory Emily Smith Izaak Meckler
    Applied topology Katharine Turner Brandon Rayhaun

    Projects from Winter 2013

    Project Title Mentor Mentee Resources Used
    Logic Matthew Wright Abhinav Shrestha
    K-theory Mona Merling Elden Elmanto
    An introduction to schemes and varieties Valia Gazaki Conor Mahany
    • Hartshorne: "Algebraic Geometry"
    • Ravi Vakil: "Foundations of Alg. Geometry"
    Three-Dimensional Geometry and Topology Nick Salter Bruno Cabral
    • Thurston: Three-dimensional Geometry and Topology.
    Complex Multiplication Sundeep Balaji Jesse Silliman
    • Serre's article in Algebraic Number Theory by Cassels and Frohlich
    • Neukirch Algebraic Number Theory
    • Silverman Elliptic Curves
    • Silverman Advanced Topics in Elliptic Curves (Chapter 1)
    • some notes from Conrad and Milne
    Elliptic Curves Yiwei She Monica Pani
    • Topology from the Differentiable Viewpoint, Milnor
    Mathematical approach to quantum mechanics Wouter van Limbeek Thomas Yu
    • Faddeev, Yakubovskii - Lectures on Quantum Mechanics for Mathematics Students
    Topics in Linear Algebra Jenny Wilson Jing Miao
    • Friedberg--Insel--Spence, Linear Algebra
    Differentiable Manifolds Kathryn Mann Max Laponsky
    • do Carmo, "Differential geometry of curves and surfaces"
    Category Theory Yi-Wei Henry Chan Eric Guan
    Number theory Preston Wake Zefeng Chen
    Group Theory / Topology Bena Tshishiku Jasha Sommer-Simpson
    • Armstrong, "Groups and Symmetry"
    Statistical Mechanics / PDE Hyomin Choi Rachel McEnroe
    • Introduction to Partial Differential Equation, Strauss
    Point-set Topology Georgios Sakellaris Mishel Skenderi
    • Munkres, Topology
    Discrete Probability Jacob Perlman Tony Song
    Commutative Algebra / Algebraic Geometry Sean Howe Nathaniel Sauder
    Algebraic Number Theory Vaidehee Madhav Thatte Stanley Breitweiser

    Projects from Fall 2012

    Project Title Mentor Mentee Resources Used
    Atiyah Segal completion theorem Mona Merling Elden Elmanto
    Geometric measure theory Kathryn Mann Orest Xherija
    • Mattila, Geometry of Sets and Measures in Euclidean Spaces
    Differential equations Bobby Wilson Arindrima Datta
    Probability Wouter van Limbeek Akshat Goel
    • Introduction to Probability by Sinai
    • Exploration in Monte Carlo Methods by Shonkwiler and Mendivil.
    Basic coding theory John Wilmes Zack Witten
    Algebra/combinatorics Asilata Bapat Izaak Meckler
    Manifolds and cohomology Nick Salter Samuel Dooley
    • Janich: Vector Analysis
    • Bott/Tu: Differential Forms in Algebraic Topology
    Logic Matthew Wright Yiding Hao
    Derived category Zhouli Xu Anirudh Sankar
    Number theory Valia Gazaki Conor Mahany
    • Dummitt and Foote "Abstract Algebra"
    • Hartshorne
    • Ravi Vakil's notes on Algebraic Geometry.
    Topology Jenny Wilson Matthew Lewis
    • Friedberg--Ingel--Spence, LINEAR ALGEBRA
    • Marsden--Hoffman, BASIC COMPLEX ANALYSIS
    • Anderson, HYPERBOLIC GEOMETRY
    Knot theory Bena Tshishiku Bruno Cabral
    • Adams, The Knot Book
    Topology Yi-Wei Henry Chan Zefeng Chen

    Projects from Spring 2012

    Project Title Mentor Mentee Resources Used
    Morse theory and Bott periodicity Fedor Manin Jesse Silliman
    • Milnor, "Morse Theory" Matsumoto, "Morse Theory"
    Logic Matthew Wright Younghan Lee
    • Sipser
    Differential forms Wouter van Limbeek Arindrima Datta
    • Multidimensional Real Analysis - Integration (Duistermaat / Kolk)
    Topics in algebra Vaidehee Madhav Thatte Samuel Dooley
    • A First Course in Abstract Algebra: J.B. Fraleigh.
    • Undergraduate Commutative Algebra: M. Reid.
    Point-set topology Bena Tshishiku Orest Xherija
    • Munkres, Topology
    PDE's Markus Kliegl Bradly Stadie
    • Evans, Lawrence C. Partial Differential Equations.
    Steenrod operations Mona Merling Elden Elmanto
    Mean field games Jessica Lin Jonathan Libgober
    Introduction to smooth manifolds Asilata Bapat Zihao Jiang
    • An Introduction to Manifolds (Loring Tu)
    • Differential Topology (Victor Guillemin and Alan Pollack)
    Mathematical programming and optimization Olga Turanova Igor Vasiljevic
    • "Mathematical Programming: An Introduction to Optimization," by Melvyn W. Jeter
    Topology Jared Bass Jiaqi Jiang
    • Topology, Munkres.

    Projects from Winter 2012

    Project Title Mentor Mentee Resources Used
    Geometry of Surfaces Rita Jimenez Arindrima Datta
    • Stillwell. Geometry of Surfaces
    • Bonahon. Low-dimensional geometry: from euclidean surfaces to hyperbolic knots
    • Anderson. Hyperbolic Geometry
    Analysis/applied math/Fourier analysis Olga Turanova Zhe Wang
    • Vretblad, Anders. Fourier analysis and its applications
    Morse theory Wouter van Limbeek Rebecca Hoberg
    • Guillemin and Pollack. Differential topology
    • Milnor. Morse theory
    • Milnor. Topology from the Differentiable Viewpoint
    Advanced Algebraic Topology Mona Merling Elden Elmanto
    Hausdorff dimension and Fractals Daniel Studenmund Orest Xherija
    Graph Theory Vaidehee Madhav Thatte Alexandru Hostiuc
    • Roberts and Tesman. Applied Combinatorics
    • Anderson, Ian. Combinatorial Designs: Construction Methods
    • Tucker, Alan. Applied Combinatorics
    Probability/analysis Hyomin Choi Eric Guan
    • Ross, Sheldon. Stochastic Processes
    Category theory/Logic Matthew Wright Benjamin Gammage
    • Awodey. Category Theory
    Number theory Valia Gazaki Siddharth Patel
    Ergodic theory Alex Wright Sarah Peluse
    • Einsiedler and Ward. Ergodic theory with a view towards number theory
    Fourier Analysis Bena Tshishiku Joshua Bosshardt
    • Terras. Fourier Analysis on Finite Groups and Applications
    • Stein. Fourier Analysis: An Introduction
    Differential Geometry / General Relativity Markus Kliegl Savannah Thais
    • Schutz, Bernard. A First Course in General Relativity
    • Kühnel, Wolfgang. Differential Geometry: Curves - Surfaces - Manifolds
    Combinatorial Game Theory Jared Bass Zihao Jiang
    • Conway. On Numbers and Games
    • Berlekamp, Conway, and Guy. Winning Ways For Your Mathematical Plays
    Algebraic geometry - Sheaves Preston Wake McKee Krumpak

    Projects from Fall 2011

    Project Title Mentor Mentee Resources Used
    Model category theory Mona Merling Elden Elmanto
    • May. A Concise Course in Algebraic Topology
    • Dwyer and Spalinski. Homotopy Theory and Model Categories
    Elementary Topology Claire Tomesch Jasson Elliott
    • A Combinatorial Introduction to Topology by Michael Henle
    • Geometric Folding Algorithms: Linkages, Origami, Polyhedra
    • Project Origami: Activities for Exploring Mathematics
    Fourier Analysis Olga Turanova Alec Zimmer
    • Duoandikoetxea, Javier. Fourier Analysis
    Logic Matthew Wright Sam Bailey
    • Enderton.
    Analysis Max Engelstein Jesse Silliman
    Geometry Kathryn Mann McKee Krumpak
    • Thurston. Three-dimensional geometry and topology.

    Projects from Spring 2011

    Project Title Mentor Mentee Resources Used
    Complex Analysis and Probability Brent Werness Gideon Dresdner
    Stochastic analysis Marcelo Alvisio Greg Mitseas
    • Shreve, Steven. Stochastic Calculus for Finance: Continuous-Time Models.
    • Oksendal, Bernt. Stochastic Differential Equations: An Introduction with Applications
    Automorphic forms on $GL(2)$ Swarnendu Datta Neel J. Patel
    • Professor Ngo's course on automorphic forms.
    Advanced algebraic topology Mona Merling Jay Shah
    • May, Peter. A Concise Course in Algebraic Topology.
    • Dwyer and Spalinski. Homotopy Theories and Model Categories
    Combinatorial Game Theory Jared Bass Eric Guan
    • Conway. On Numbers and Games.
    • Berlekamp, Conway, and Guy. Winning Ways For Your Mathematical Plays
    Number theory Preston Wake Sam Bailey
    • The Gamma Function - Emil Artin
    Lie groups Kathryn Mann James Murphy
    • Lee, John C. Introduction to smooth manifolds
    Set theory Matthew Wright Daping Weng
    • Jech. Set Theory
    Linear algebra up to the spectral theorem Fedor Manin Zihao Jiang
    • Axler, Sheldon. Linear Algebra Done Right

    Projects from Winter 2011

    Project Title Mentor Mentee Resources Used
    The BGG category O Aaron Marcus Neel J. Patel
    • Humphreys, James. Representations of Semisimple Lie Algebras in the BGG Category O
    Probability Marcelo Alvisio Anil Vaitla
    • Williams, David. Probability with Martingales
    • Rudin, Walter. Real and Complex Analysis
    Reverse math Damir Dzhafarov Noah Schweber
    Number theory Preston Wake Watson Ladd
    Categorical logic Emily Riehl Nick Ramsey
    • Lambek and Scott
    • Awodey. Category Theory
    Randomness David Diamondstone William Chan
    • André Nies, Computability and Randomness, Oxford University Press, 2009.

    Projects from Fall 2010

    Project Title Mentor Mentee Resources Used
    Introduction to characteristic classes Rita Jimenez Jay Shah
    • Bott and Tu. Differential Forms in Algebraic Topology.
    • Milnor and Stasheff. Characteristic Classes.
    • Hatcher. Vector Bundles and K-Theory
    Representation Theory Charles Staats Neel J. Patel
    • Fulton and Harris. Representation Theory: A first course
    Number Theory Thomas Church Moira Cassidy
    Algebraic Curves Ian Shipman Samuel Bloom
    • Fulton, William. Algebraic Curves
    Homological Algebra Jonathan Sun Donald Laackman
    • Weibel. An Introduction to Homological Algebra
    • Gelfand and Manin. Methods of Homological Algebra
    Topoi and Logic Jonathan Stephenson Paige North
    • Maclane and Moerdijk. Sheaves in Geometry and Logic
    Category Theory Jared Bass Watee Srinin
    • Awodey. Category Theory
    Probability Marcelo Alvisio Zhongtian Dai
    • Williams, David. Probability with Martingales.
    • Cohn, Donald. Measure Theory
    Logic Matthew Wright William Chan
    • Jech. Set theory

    Projects from Spring 2010

    Project Title Mentor Mentee Resources Used
    Reverse math and knowledge spaces Damir Dzhafarov Noah Schweber
    Model theory David Diamondstone Caroline Terry
    • Chang, C. C. and Keisler, H. Jerome. Model Theory
    • Marker, David. Model Theory
    Geometry Rita Jimenez David M Price
    • Iversen, Birger. Hyperbolic Geometry. Anderson, James W. Hyperbolic Geometry
    Logic Matthew Wright Jasper DeAntonio
    • Enderton.
    Young tableaux and representations of the symmetric group Vipul Naik John Wiltshire-Gordon
    • Kerov.
    Compact Lie Groups Daniele Rosso Neel J. Patel
    • Baker. Matrix groups, an introduction to Lie groups
    • Simon. Representations of Finite and Compact groups
    Special (co)limits and Kan extensions Emily Riehl Donald Laackman
    Elliptic curves and applications Aaron Marcus Cong Han Lim
    Elementary mathematics John Lind Maxwell Stolarski
    • Conway. On Numbers and Games
    Analytic Number Theory Shawn Drenning Dylan Allegretti
    • Serre. A Course in Arithmetic
    Riemann surfaces Hyomin Choi Wolfgang Schmaltz
    • Miranda. Algebraic Curves and Riemann Surfaces
    Algebraic Geometry Kathryn Mann Tengren Zhang
    • Smith. An invitation to Algebraic Geometry

    Projects from Winter 2010

    Project Title Mentor Mentee Resources Used
    Categorical Logic Josh Grochow Noah Schweber
    • Chagrov and Zakharyachev. Modal Logic
    Group Theory Adam Allan Neel J. Patel
    Flows on manifolds Ariel Barton Alex Korbonits
    • Hamilton's papers on the Ricci flow.
    Lie Groups Alex Wright Jonathan James Gleason
    • Hassani, Sadri. Mathematical Physics: A Modern Introduction to Its Foundations
    Geometry and differential forms Rita Jimenez Nick Ramsey
    • do Carmo. Differential forms and applications
    • Bachman, David. A Geometric Approach to Differential Forms
    • Morita, Shigeyuchi. Geometry of Differential Forms
    Probability Zachary Madden Ryan Wang
    Manifolds and Lie Groups Kathryn Mann Tengren Zhang
    • Lee, John M. Introduction to Smooth Manifolds
    Algebra Alan Anders John Reilly
    • Tate and Silverman. Rational Points on Elliptic Curves
    Combinatorial Game Theory Jared Bass Paige North
    • Conway. On Numbers and Games
    • Berlekamp, Massey, Guy. Winning Ways For Your Mathematical Plays
    Young Tableaux Daniele Rosso David M Price
    • Fulton. Young Tableaux: With Applications to Representation Theory and Geometry
    • Fulton and Harris. Representation Theory: A First Course
    Algebraic Topology Anna Marie Bohmann Melissa Lynn
    • Aguilar et al. Algebraic Topology from a Homotopical Viewpoint.
    • May, J.P. A Concise Course in Algebraic Topology
    Category Theory Aaron Marcus Daniel Genovessylvan
    • Awodey. Category Theory
    Local class field theory via Lubin-Tate theory Takashi Suzuki Vladislav Vladilenov Petkov
    • Iwasawa, Kenkichi. Local class field theory. Oxford Science Publications, 1986
    • Yoshida, Teruyoshi. Local class field theory via Lubin-Tate theory. Ann. Fac. Sci. Toulouse Math. (6) 17 (2008), no. 2, 411--438.

    Projects from Fall 2009

    Project Title Mentor Mentee Resources Used
    Algebra Alan Anders Jay Shah
    • Bergman. An Invitation to General Algebra and Universal Constructions
    Logic Matthew Wright Scott Messick
    • Jech. Set Theory
    Harmonic analysis Timur Akhunov Dennis Kriventsov
    • Stein. Harmonic Analysis
    Topology Grigori Avramidi Valer Popa
    • Bott and Tu. Differential Forms in Algebraic Topology
    A first course in math culture. Strom Borman Rebecca Hoberg
    • Laczkovich, Miklos. Conjecture and Proof
    Mathematical Physics Evan Jenkins Jonathan James Gleason
    • Hassani, Sadri. Mathematical Physics
    Category Theory Rolf Hoyer Noah Schweber
    • Goldblatt. Topoi: The categorial analysis of logic
    • Borceaux. Handbook of categorical algebra I
    • MacLane, Moerdijk. Sheaves in Geometry and Logic
    • Awodey. Category Theory
    • McClarty. Elementary Category Theory
    Elementary Number Theory Daniele Rosso Nick Ramsey
    • Jones and Jones. Elementary Number Theory
    Group Theory Adam Allan Wolfgang Schmaltz
    • Holt, Dereck. Handbook of Computational Group Theory
    Partial Differential Equations Spencer Dowdall Valeriya Talovikova
    • Strauss, Walter A. Partial Differential Equations: An Introduction
    Category Theory Aaron Marcus David M Price
    • Awodey. Category Theory
    • Maclane. Categories for the Working Mathematician.
    • May. A Concise Course in Algebraic Topology
    Manifolds Jared Bass Jason Quinones
    • Guillemin and Pollack. Differential Topology
    Geometry/topology Thomas Church Kathy Snyder
    • do Carmo. Differential Geometry of Curves and Surfaces
    • do Carmo. Riemannian Geometry

    Projects from Spring 2009

    Project Title Mentor Mentee Resources Used
    Models of Peano Arithmetic David Diamondstone Robert Sare
    Differential Forms in Algebraic Topology Claire Tomesch Donald Laackman
    • Bott and Tu. Differential Forms in Algebraic Topology.
    Differential Geometry Tam Nguyen Hikaru Kiyo
    Logic Damir Dzhafarov Noah Schweber
    Stochastic Processes Brent Werness Daniel Smith
    • Williams. Probability with Martingales.
    Commutative algebra and algebraic geometry Vipul Naik Ariel Hafftka
    • Dummit and Foote. Abstract Algebra, 3rd Edition.
    • Eisenbud. Commutative Algebra
    Topos Theory in Physics Evan Jenkins John Dougherty
    Complex analysis Timur Akhunov Isaac Davis
    • Stein and Shakarchi. Complex Analysis
    Algorithms of Algebra and Number Theory Aaron Marcus Cong Han Lim
    • Cox, Little, and O'Shea. Ideals, Varieties, and Algorithms
    • ?. Modern Computer Algebra
    Topology from the Differential Viewpoint Strom Borman Wolfgang Schmaltz
    • Milnor
    • Guillemin and Pollack. Differential Topology
    Number theory Michael Miller Jasper DeAntonio
    • Silverman, Joseph. A Friendly Introduction to Number Theory
    Linear Algebra Daniele Rosso Shiv Subramaniam
    • Axler. Linear Algebra Done Right.
    • Artin. Algebra
    Complex algebraic curves Sundeep Balaji Vladislav Vladilenov Petkov
    • Kirwan, Francis. (?)
    Introduction to Logic John Lind Zhongtian Dai
    • Robbin. Mathematical Logic: A First Course
    Visual Introduction to Complex Analysis Rita Jimenez Zsolt Terdik
    • Needham, Tristan. Visual Complex Analysis. Oxford University Press
    Fourier analysis Shawn Drenning Seth Weidman
    • Stein. Fourier Analysis
    The Spectral Theorem Catalin Carstea Jonathan James Gleason
    • Hassani, S. Mathematical Physics
    • Reed and Simon. Methods of Modern Mathematical Physics
    Combinatorial Game Theory Jared Bass Korei Klein
    • Conway. On Numbers and Games
    The Prime Number Theorem Burton Newman Jay Shah
    • Apostol. Analytic Number Theory
    Differential manifolds Matthew Thibault Je-ok Choi
    Existence and Uniqueness for Ordinary Differential Equations Francis Chung Jonathan Libgober
    • Gamelin and Greene. Introduction to Topology
    Algebraic K-theory Thanos Papaioannou Adam Kaye
    Knot Theory Emily Riehl Paige North
    • The Knot Book
    • Munkres. Topology
    Linear Differential Equations Alan Anders McKee Krumpak

    Projects from Winter 2009

    Project Title Mentor Mentee Resources Used
    Reverse math and proof theory Damir Dzhafarov Noah Schweber
    Combinatorial Topology Jim Fowler Erin Molloy
    Algebraic K-theory Thanos Papaioannou Adam Kaye
    Riemann Surfaces and elliptic curves Vipul Naik Ryan Julian
    • Silverman. Elliptic Curves
    Category Theory Claire Tomesch Donald Laackman
    • Maclane. Categories for the Working Mathematician
    Descriptive set theory and determinacy Matthew Wright Alex Rosenfeld
    Hyperbolic Geometry Aaron Marcus Last Feremenga
    • Anderson. Hyperbolic Geometry
    Algebraic Curves Swarnendu Datta Vladislav Vladilenov Petkov
    Probability Zachary Madden Jia Lin Chen
    Harmonic analysis Tomasz Zamojski William C Abram
    • Stein. Singular Integrals
    Applied mathematics David Chudzicki ?
    Riemann Surfaces Jared Bass Peter Nelson
    • Miranda. Algebraic Curves and Riemann Surfaces
    • Lecture notes from Schlag's first-year graduate complex analysis course.
    Algebra Emily Norton Riley Heckel
    Number theory and combinatorics Burton Newman John Binder
    • Apostol. Analytic number theory
    Galois theory of differential equations Rita Jimenez Guilherme Nettesheim
    Algebraic Number Theory Daniele Rosso Wolfgang Schmaltz
    • Jones and Jones. Elementary Number Theory
    Complex algebraic geometry Michael Miller Wai Lee Chin Feman

    Projects from Fall 2008

    Project Title Mentor Mentee Resources Used
    Geometry of Surfaces Ian Biringer Noah Schweber Neil Raman
    Sheaves, complex analysis and GAGA Alan Anders Elan Bechor
    Complexity theory Matthew Wright Mark Stoehr
    • http://www.cs.princeton.edu/theory/index.php/Compbook/Draft
    • Kearns and Vazirani. An Introduction to Computational Learning Theory
    The Fundamental Group Jared Bass ?
    Introduction to Manifolds Strom Borman Patrick Greene
    • Janich, Klaus. Vector Analysis
    • Lee, John. Introduction to Smooth Manifolds
    Van der Waerden's Theorem Burton Newman Conor Hughes
    Reverse math Damir Dzhafarov Alex Rosenfeld
    • Simpson, Stephen. Subsystems of Second Order Arithmetic
    Gröbner bases Daniele Rosso Youlian Simidjiyski
    • Cox, Little, and O'Shea. Ideals, Varieties, and Algorithms.
    Number theory Aaron Marcus Michael LeFors
    • Erdos and Suranyi. Topics in Number Theory
    Matrix groups Vipul Naik Tom Milnor
    • Morton L. Curtis, Matrix Groups
    Category theory Emily Riehl Donald Laackman
    Fourier analysis Timur Akhunov Aaron McKnight
    • Stein. Fourier Analysis
    Fractals Shawn Drenning Dustin Hedmark
    • Falconer. Fractal Geometry
    Topological Genericity Tomasz Zamojski Melissa Yeung
    • Hochman. Genericity in topological dynamics. (paper)

    Projects from Spring 2008

    Project Title Mentor Mentee Resources Used
    Representation theory and quantum mechanics Richard Cudney Vladislav Vladilenov Petkov
    • Linearity, Symmetry, and Prediction in the Hydrogen Atom. Springer UTM
    Tropical Geometry Elizabeth Beazley Youlian Simidjiyski
    • Speyer, David, and Sturmfels, Bernd. Tropical Mathematics
    • Richter-Gebert, Sturmfels, and Theobald. First Steps in Tropical Geometry
    Logic Damir Dzhafarov Noah Schweber
    • standard reference by Ebinghaus for Lindstrom's theorem
    Introduction to Probability Hanna Bennett Kelly Kennedy
    Algebraic curves and Riemann surfaces Tam Nguyen Matthew Woolf
    • Miranda. Algebraic curves and Riemann surfaces.
    Ergodic Theory in Number Theory Tomasz Zamojski Elan Bechor
    • Pollicott. (book on dynamical systems of ergodic theory)
    First-order logic and model theory David Diamondstone Dylan Allegretti
    • Marker, David. Model Theory: An Introduction. Springer-Verlag, New York, 2002.
    • Mileti, Joseph R. Mathematical Logic for Mathematicians. Course notes, 2007
    Zeta functions of number fields Nicolas Ojeda Bar Adam Kaye
    Number theory Burton Newman Robert Bishop
    First order logic John Lind Cong Han Lim
    Fourier analysis Timur Akhunov Bo Peng
    • Stein. Fourier Analysis
    Fourier analysis Shawn Drenning Umnouy Ponsukcharoen
    • Stein. Fourier Analysis
    Topology/analysis Khalid Bou-Rabee ?
    • Jones, Frank. Lebesgue Integration on Euclidean Space
    Combinatorics Ian Biringer Carmel Levy
    Elliptic curves and cryptography Aaron Marcus Tom Milnor
    • Koblitz. A Course in Cryptography and Number Theory
    Game theory Jim Fowler Minhao Benjamin Chen
    Linear algebra Adam Allan Angelica Wong
    Representation theory Saravanan Thiyagarajan ?
    Computability and Algorithmic Information: Quantitative Versions of Godel Incompleteness Josh Grochow Wai Lee Chin Feman

    Projects from Winter 2008

    Project Title Mentor Mentee Resources Used
    Axiomatic set theory Damir Dzhafarov Noah Schweber
    • Mileti, Joseph R. Mathematical Logic for Mathematicians. Course notes, 2007
    The Borsuk Ulam Theorem Niles Johnson Peter Nelson
    • Matousek, Jiri. Using the Borsuk-Ulam Theorem
    Graph colorings Ian Biringer Alex Korbonits
    Differential geometry and general relativity Tam Nguyen Jesse Marshall
    Algebraic graph theory Josh Grochow William C Abram
    • Biggs, N. Algebraic Graph Theory
    • Godsil and Royle. Algebraic Graph Theory.
    Nonstandard analysis Michael Shulman Dylan Allegretti
    • Goldblatt. Lectures on the Hyperreals.
    • Henle and Kleinberg. Infinitesimal Calculus
    Fourier analysis Ed Wallace Chenchuan Li
    • Korner. Fourier Analysis
    Bass-Serre theory Thomas Church Nicolas Ford
    • Serre. Trees
    • Scot and Wall. Topological Methods in Group Theory.
    • Farb. Notes from Geometric Literacy.
    P-adic analysis Marius Beceanu Bo Peng
    Elliptic curves Michael Broshi Vladislav Vladilenov Petkov
    • Tate and Silverman. Rational Points on Elliptic Curves
    • Koblitz. A Course in Number Theory and Cryptography
    Mordell's Theorem Bert Guillou Robert Bishop
    Algebraic number theory Adam Allan Melissa Lynn
    • Milne. Notes on algebraic number theory.
    Euler characteristic and Gauss-Bonnet theorem Travis Schedler Elizabeth DeYoung
    • Do Carmo. Differential Geometry of Curves and Surfaces
    Riemann surfaces John Lind Lisa Wang
    • Kirwin. Complex Algebraic Curves
    • Miranda. Algebraic Curves and Riemann Surfaces.
    • Farkas and Kra. Riemann Surfaces.
    Number Fields and Class Groups Sundeep Balaji Joseph Herbert
    • Borevich and Shafarevich. Number Theory
    • Marcus, Daniel. Number Fields
    Stochastic Processes Shawn Drenning Daniel Beksha
    • Lawler, Gregory. Introduction to Stochastic Processes
    Lie groups and geometry Matthew Day Adam Anderson
    Optimization theory Timur Akhunov David Palm
    • Sundaram, Rangarajan K. A First Course in Optimization Theory