Book Recommendations for the Directed Reading Program

This is an old list of books created by past DRP organizers. These books have not all been used in the DRP, but are a good source of project ideas. Whoever created the list has given books ratings based on how advanced they are:

G: Any level

PG: Needs basic calculus and high school algebra

PG-13: Needs a few mid-level undergraduate math courses

R: Needs some high-level undergraduate math courses

Algebra, Algebraic Geometry and Number Theory

• Linear Representations of Finite Groups, by Jean-Pierre Serre (R)
• The Geometry of Schemes, by Eisenbud and Harris (R)
• Linear Algebra Done Right, by Axler (PG)
• Galois' Dream, by Kuga (G)
• Groups: A Path to Geometry, by R. P. Burns (PG)
• Algebraic Curves, by Fulton (PG-13)
• Elliptic Curves and Cryptography, by Washington (PG-13)
• Primes of the Form x^2 + ny^2, by Cox (PG-13)
• The Sensual (Quadratic) Form, by John Conway (PG)
• The Higher Arithmetic: An Introduction to the Theory of Numbers, by Davenport (G)
• Geometry of Numbers, by Gruber and Lekkerkerker (R)
• Rational Points of Elliptic Curves, by Tate and Silverman (R)
• A Course in Arithmetic, by J. P. Serre (R)
• Principles of Algebraic Geometry, by Griffiths and Harris (R)
• An Invitation to Algebraic Geometry, by Smith, Kahanpaa, Kekalainen and Traves (R)
• Introduction to Tropical Geometry, by Maclagan and Sturmfels (PG-13)
• Representation Theory, by Fulton and Harris (R)
• Ideals, Varieties, and Algorithms, by Cox, Little, and O'Shea (PG-13)
• Rational Points on Elliptic Curves, by Silverman (PG-13)

Topology

• Chapter 13 of Thurston's The Geometry and Topology of 3-Manifolds, and learning how to classify wallpaper groups using orbifolds. (R)
• Topology, by Klaus Jänich (PG-13)
• Counterexamples in Topology, by Steen and Seebach (R)
• Intuitive Concepts in Elementary Topology, by Arnold (G)
• A Basic Course in Algebraic Topology, by Massey (R)

Analysis and Geometry

• Analysis Now, by Gert Pedersen (R)
• Geometric Transformations, by Yaglom (PG-13)
• Fourier Analysis, by Körner (PG - PG-13)

Applied and Computational Mathematics

• Numerical Linear Algebra, by Trefethen and Bau (Rating pending)
• Partial Differential Equations: Analytical and Numerical Methods,by Gockenbach (Rating pending)
• A First Course in Bayesian Statistical Methods, by Hoff (Rating pending)
• Monte Carlo Strategies in Scientific Computing, by Liu (Rating pending)

Dynamical Systems, Differential Equations and Probability

• Random Walk and the Heat Equation by Lawler (PG - PG-13)
• Introduction to Stochastic Processes by Lawler (PG - PG-13)
• Ordinary Differential Equations, by Arnol'd (PG)

Logic

• Naive Set Theory, by Halmos (PG)
• A Mathematical Introduction to Logic, by Enderton (G)
• Book of Proof, by Richard Hammack (G)
• Forcing for Mathematicians, by Weaver (PG+?)

Graph Theory and Combinatorics

• On Numbers and Games, by John Conway (PG)
• The Probabilistic Method, by Alon and Spencer (PG-13)

Other

• Euclidean and Non-Euclidean Geometries, by Greenberg (PG)
• Proofs from the Book, by Aigner and Ziegler (G)