Mathcamp 1999

- General Purposes
- Geometry
- Fourier Series
- Basic Number Theory
- Algebraic Number Theory
- P-adics
- Graph Theory, Random Walks, Ramsey Theory
- Combinatorics
- Algorithms
- Probability
- Toy Universes
- Linear Algebra
- Complex Numbers
- Fractals
- Riemann Surfaces / Algebraic Geometry
- Weird Numbers
- Calculus
- Topology
- Ethnomathematics
- Representation Theory

- Bell, E.T.,
**Men of Mathematics***-- history; entertaining, though it reportedly contains many inaccuracies* - Conway and Guy,
**Book of Numbers** - Dummit and Foot,
**Algebra** - Golomb,
**Polyominoes** - Gunning,
**Modular Forms** - Hardy, G.H.,
**A Mathematician's Apology** - Hilbert,
**Geometry and the Imagination** - Hofstadter, Douglas,
**Godel, Escher, Bach** - Lakatos,
**Proofs and Refutations***--philosophy of math* - Lozansky and Roussea,
**Winning Solutions** - Vick,
**Homology Theory**

- Coxeter,
**Geometry** - Coxeter and S.L. Greitzer,
**Geometry Revisited***--and anything else on geometry by Coxeter* - Greenberg, Marvin J.,
**Euclidean and Non-Euclidean Geometry**

- Oppenheim,
**Signals and Systems***--it is not a math book*

- Niven, I. and Zuckerman, H.S.,
**An Introduction to the Theory of Numbers***--what the class followed during Mathcamp* - Davenport, H.,
**The Higher Arithmetic** - Dudley, U.,
**Elementary Number Theory** - Guy, R.,
**Unsolved Problems in Number Theory** - Hardy, G.H. and Wright, E.M.,
**An Introduction to the Theory of Numbers** - Ireland, K. and Rosen, M.,
**A Classical Introduction to Modern Number Theory** - Ore, O.,
**Number Theory and its History** - Shanks, D.,
**Solved and Unsolved Problems in Number Theory** - Silverman, J.,
**A Friendly Introduction to Number Theory**

- Ireland and Rosen,
**Introduction to Modern Number Theory** - Marcus,
**Number Fields** - Hartley and Hawkes,
**Rings, Modules and Linear Algebra**: Chapman and Hall Mathematics Series - Stewart and Tall,
**Algebraic Number Theory** - Stewart, I.,
**Galois Theory**

- Gouvea, Fernando,
**P-adic Numbers**

- Bollobas, B.,
**Modern Graph Theory**, GTM Series, Springer.*This book pretty much contains everything you would want to know; not many prerequisites, but it is very concise. Don't be scared by the exercises -- many of them are hard, even those marked as easy.* - Doyle, Peter and Snell, J. Laurie,
**Random Walks and Electric Networks**

- Graham, R.L., Grotschel, M. and Lovasz, Laszlo,
**Handbook of Combinatorics** - Lovasz, Laszlo,
**Combinatorial Problems and Exercises**

- Cormen, Thomas H., Leiserson, Charles E., and Rivest, Ronald L.,
**Introduction to Algorithms** - Sedgewick, Robert,
**Algorithms in C**

- Feller, William,
**An Introduction to Probability Theory and its Applications***has some good random walk calculations* - Mosteller, Frederick,
**Fifty Challenging Problems in Probability**, Dover Books, 1956.*-- archetypal problems* - Scarne, John,
**Scarne's New Complete Guide to Gambling**, Simon and Schuster, 1986.*--everything from sports betting to casino games* - Von Mises, Richard,
**Probability, Statistics, and Truth**, Dover Books, 1957.*--lots of discussions on probability*

- Burger, Dionys,
**Sphereland***general relativity by analogy* - Gamow, George,
**Mr. Thompkins in Paperback***--see what happens when you have quantum effects on pool tables or when the speed of light is 65 mph* - Herbert, Nick,
**Quantum Reality: Beyond the New Physics***--extremely easy to read for a metaphysics book* - Rucker, Rudy,
**The 4th Dimension**

- Axler, Sheldon,
**Linear Algebra Done Right***-- for theory* - Strang, Gilbert,
**Linear Algebra***--for applications/computations*

- Conway, John B.,
**Functions of One Complex Variable** - Nehari, Zeev,
**Conformal Mapping** -
**Straub's Outline for Complex Variables**

- Barnsley, Michael,
**Fractals Everywhere** - Beitger, Jergens and Saupe,
**Fractals in the Classroom***--this comes in two volumes and are much easier to read than Barnsley's book*

- Miranda, Rick,
**Introduction to Riemann Surfaces** - Silverman and Tate,
**Rational Points on Elliptic Curves***--particularly the appendix* - Bix, Robert,
**Conics and Cubics** - Cox, Little, and O'Shea,
**Ideals, Varieties, and Algorithms**

- Conway, Guy, and Berlekamp,
**Winning Ways for Your Mathematical Plays***--out of print, but can find in university libraries; best book in the world* - Knuth, Donald,
**Surreal Numbers**

- Spivak, Michael,
**Calculus***--look for jokes in the index*

- Massey,
**Algebraic Topology: An Introduction**

- Ascher, Marcia,
**Ethnomathematics** - Eglash, Ron,
**African Fractals** - Powell and Frankenstein,
**Ethnomathematics: Challenging Eurocentrism in Mathematics Education**

- James and Liebeck,
**Representations of Finite Groups***--Very nicely paced, explains almost everything you need, and covers a lot of material. Definitely accessible if you've gone to Linear Algebra and Abstract Algebra!*

Meep, last updated Aug 2001