Past Readings

This is a list of some books used by DRP participants in previous semesters. 

Some of these books are owned by DRP and can be found in the library. Feel free to peruse these suggestions or choose topics not represented here (for instance, logic or set theory, category theory, mathematics of gerrymandering or climate change, etc.) and help us expand it.

Algebra

• Visual Group Theory, Carter

• The Symmetric Group, Sagan

• Abstract Algebra, Dummit and Foote

• Linear Algebraic Groups and Finite Groups of Lie Type, Malle and Testerman

• Algebra, Lang

• Galois' Dream, Kuga

Algebraic and Combinatorial Geometry

• Ideals, Varieties, Algorithms, by Cox, O’Shea, and Little

• Combinatorial Commutative Algebra, Miller and Sturmfels

• Foundations of Algebraic Geometry, Vakil

• Introduction to Tropical Geometry, Maclagan and Sturmfels

• An Invitation to Algebraic Geometry, Smith, Kahanpaa, Kekalainen and Traves

Analysis

• Introductory Functional Analysis with Applications, Kreyszig

• Nonlinear Dynamics and Chaos, Strogatz

• A First Course In Chaotic Dynamical Systems, Devaney

• Analysis Now, Pedersen

• Visual Complex Analysis, Needham

• Fourier Analysis, Stein and Shakarchi 

Applied Math

• Deep Learning, Goodfellow

• Pattern Formation: An Introduction to Methods, Hoyle

• Understanding and Using Linear Programming, Matousek and Gartner

• Numerical Linear Algebra, Trefethen and Bau

• A First Course in Bayesian Statistical Methods, Hoff

• Monte Carlo Strategies in Scientific Computing, Liu 

Category Theory

• Category Theory, Awodey

• Category Theory in Context, Riehl

• Category Theory for the Sciences, Spivak

• Category Theory for the Working Mathematician, Mac Lane

Combinatorics

• A Walk Through Combinatorics, Bona

• Algebraic Combinatorics, Stanley

• Discrete Mathematics, Lovasz, Pelican, and Vesztergombi

Dynamical Systems, Differential Equations and Probability

• Markov Chains, Norris

• Random Walk and the Heat Equation, Lawler

• Introduction to Stochastic Processes, Lawler

• Ordinary Differential Equations, Arnol'd

• Partial Differential Equations: Analytical and Numerical Methods, Gockenbach

• Partial Differential Equations, Evans

Graph Theory

• Introduction to Graph Theory, Trudeau

• Algebraic Graph Theory, Biggs

• A Textbook of Graph Theory, Balakrishnan and Ranganathan

Foundations

• Set Theory and Metric Spaces, Kaplansky

• The Banach-Tarski Paradox, Tomkowicz and Wagon

• Computability: An Introduction to Recursive Function Theory, Cutland

• Linear Algebra Done Right, Axler

Number Theory

• p-adic Numbers, Gouvea

• Breaking Codes: An Introduction to Cryptography, Garrett

• Rational Points on Elliptic Curves, Silverman and Tate

• Arithmetic of Elliptic Curves, Silverman

• p-adic Analysis and Zeta-Functions, Koblitz

Representation Theory

• Complex Representations of GL[2,k] for Finite Fields, Piatetski-Shapiro

• Representation Theory, Fulton and Harris

• Representation Theory of Finite Groups, Steinberg

Topology and Geometry

• Intuitive Concepts in Elementary Topology, Arnold

• Algebraic Topology, Hatcher

• Introduction to Smooth Manifolds, Lee

• Foundations of Differential Manifolds and Lie Groups, Warner

• Differential Forms and Applications, do Carmo

• The Knot Book, Adams

• Braid Groups, Kassel and Turaev

• Euclidean and Non-Euclidean Geometries, Greenberg

• Four Pillars of Geometry, Stillwell