Book Recommendations
Mathcamp 1999
- 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
This is a very technical subject and the books I
(Tomas) know are fairly technical and require a lot of algebra.
- 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
The last three books go at a very leisurely pace. Very few prerequisites; the abstract algebra course and ANT course from
Mathcamp should definitely be enough
- 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!
Mathcamp!
Meep, last updated Aug 2001