This is a list of some books used by DRP participants in previous semesters. You are welcome to flip through these books in the library for inspiration, 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.
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
ppp-adic Numbers, Gouvea
Breaking Codes: An Introduction to Cryptography, Garrett
Rational Points on Elliptic Curves, Silverman and Tate
Arithmetic of Elliptic Curves, Silverman
Introductory Functional Analysis with Applications, Kreyszig
Nonlinear Dynamics and Chaos, Strogatz
A First Course In Chaotic Dynamical Systems, Devaney
Partial Differential Equations, Evans
Deep Learning, Goodfellow
Markov Chains, Norris
Pattern Formation: An Introduction to Methods, Rebecca Hoyle
Algebraic Topology, Hatcher
Introduction to Smooth Manifolds, Lee
Foundations of Differential Manifolds and Lie Groups, Warner
Differential Forms and Applications, do Carmo
Foundations of Algebraic Geometry, Vakil
Introduction to Graph Theory, Trudeau
Algebraic Graph Theory, Biggs
A Textbook of Graph Theory, Balakrishnan and Ranganathan
Category Theory, Awodey
Category Theory in Context, Riehl
Complex Representations of GL[2,k][2,\mathbb{k}][2,k] for Finite Fields k\mathbb{k}k, Piatetski-Shapiro
More book suggestions are available on the DRP Network’s webpage. Some pairs have also opted to use online notes or various references.
Ideals, Varieties, Algorithms, by Cox, O’Shea, and Little
Combinatorial Commutative Algebra, Miller and Sturmfels
The Knot Book, Adams
Braid Groups, Kassel and Turaev
Set Theory and Metric Spaces, Kaplansky
The Banach-Tarski Paradox, Tomkowicz and Wagon
Computability: An Introduction to Recursive Function Theory, Cutland
Category Theory for the Sciences, Spivak
Category Theory for the Working Mathematician, Mac Lane