# Books

The following books have not all been used in the DRP, but are a good source of project ideas. Difficulty and background required are marked as follows:

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)