# the Directed Reading Program

## Archive of Past Readings

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.

### 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

### 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

### Analysis:

• Introductory Functional Analysis with Applications, Kreyszig
• Nonlinear Dynamics and Chaos, Strogatz
• A First Course In Chaotic Dynamical Systems, Devaney

### Applied Math:

• Partial Differential Equations, Evans
• Deep Learning, Goodfellow
• Markov Chains, Norris
• Pattern Formation: An Introduction to Methods, Rebecca Hoyle

### Topology and Geometry:

• 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

### Graph Theory:

• Introduction to Graph Theory, Trudeau
• Algebraic Graph Theory, Biggs
• A Textbook of Graph Theory, Balakrishnan and Ranganathan

### Category Theory

• Category Theory, Awodey
• Category Theory in Context, Riehl

### Representation Theory:

• Complex Representations of GL$[2,\mathbb{k}]$ for Finite Fields $\mathbb{k}$, 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.

## Other suggested books:

### Algebraic and Combinatorial Geometry

• Ideals, Varieties, Algorithms, by Cox, O’Shea, and Little
• Combinatorial Commutative Algebra, Miller and Sturmfels

### Topology

• The Knot Book, Adams
• Braid Groups, Kassel and Turaev

### Foundations

• Set Theory and Metric Spaces, Kaplansky
• The Banach-Tarski Paradox, Tomkowicz and Wagon
• Computability: An Introduction to Recursive Function Theory, Cutland

### Category Theory

• Category Theory for the Sciences, Spivak
• Category Theory for the Working Mathematician, Mac Lane