Book Recommendations
Mathcamp 2000

• Downing, Douglas, Dalculus the Easy Way. This is the book that I (Meep) taught myself calculus from. I liked the stories.
• Spivak, Calculus. Look for jokes in the index. This book is about the theory of calculus.
• Apostol, Mathematical Analysis: A Modern Approach to Advanced Calculus.

• Churchill, Brown and Vehey, Functions of a Complex Variable.
• Straub's Outline for Complex Variables.
• Nehari, Zeev, Conformal Mapping.
• Conway, John B., Functions of One Complex Variable. From Meep -- There's a proof in here with the punchline 1/72 that just killed my intro class. It was the funniest thing we heard all semester. You just had to be there.
• Beardon, Alan, Complex Analysis: the Argument Principle in Analysis and Topology. Out of print, but worth tracking down from a library.

Analysis, Measure, and Category

• Gelbaun and Olmsted, Counterexamples in Analysis. Wild n woolly functions -- find out that you really have no good idea of what a continuous function looks like.
• Oxtoby, Measure and Category. It's a graduate text, so it's difficult to read.
• Korner, Tom, Fourier Analysis. There's also a companion "Exercises on Fourier Analysis".
• Bartle and Sherbert, Introduction to Real Analysis. People in the epsilon-delta class: this is the textbook with the K-epsilon game.

Geometry

Euclidean and Non-Euclidean

• Coxeter, Geometry.
• Coxeter and Greitzer, Geometry Revisited. A must! Pretty much look at anything by Coxeter on geometry.
• Hornsberger, Episodes in Nineteenth and Twentieth Century Euclidean Geometry.
• Vossen, Hilbert-Cohn, Geometry of Imagination.
• Greenberg, Marvin, Euclidean and Non-Euclidean Geometry.
• Japanese Temple Geometry.

Projective

• Hughes and Piper, Projective Planes. This is a graduate text, so enter at your own risk.
• Samuel, Projective Geometry.

Analytic

• Liang-Sham Hahn, Complex Numbers and Geometry.

Algebraic

• Silverman and Tate, Rational Points on Elliptic Curves.
• Bix, Robert, Conics and Cubics.
• Reid, Undergraduate Algebraic Geometry.
• Kirwan, Complex Algebraic Curves. Uses a manifolds and topology approach.

Combinatorics of Words

• Salomaa, Arto, Jewels of Formal Language Theory, Computer Science Press, 1981.
• Lothaire, M., Combinatorics on Words, vol. 17 of Encyclopedia of Mathematics and its Applications, Addison-Wesley, 1983.
• Sturmian: Web link.
• Lothair, Algebraic Combinatorics on Words.

Problem Solving

• Cofman, Judita, What to Solve? Problems and Suggestions for Young Mathematicians.
• Polya, How to Solve It: A New Aspect of Mathematical Method.
• Larson, Loren, Problem-solving Through Problems.
• Gilbert, Larson and Krusemeyer (That's Mark!), The Wohascum County Problem Book.
• Shklarsky, et.al., The USSR Olympiad Problem Book: Selected Problems and Theorems of Elementary Mathematics.
• Yaglom and Yaglom, Challenging Mathematical Problems with Elementary Solutions, vol. 1.
• Holton, Derek, Let's Solve Some Math Problems.
• Gardiner, Anthony, The Mathematical Olympiad Handbook: an Introduction to Problem Solving Based on the First 32 British Mathematical Olympiads 1965-1996. Nice book, providing a brief introduction with some methods, and giving hints to most of the problems, in addition to full solutions.

Logic

Proof Techniques

• Garnier and Taylor, 100% Mathematical Proof. Good intro to logic in math proofs and simple proof techniques. If you're shaky on how to prove things rigorously through logic, this is a good place to start.
• Solow, Daniel, How to Read an Do Proofs.
• Polya, Mathematics and Plausible Reasoning. A somewhat more difficult book on logic and proofs.

Logic Puzzles

• Smullyan, R., Any of his books. If you're really into insane and sane liars and truthtellers, he's your man.
• Games Magazine or Games World of Puzzles, Paint by Numbers. The cutest logic puzzles one ever did see. Interestingly, the two-color puzzles are easier than the one-color ones (once you get the hang of things).

False Proofs, Cranks, and General Misuse of Math

• Dudley, U., Mathematical Cranks. Some of this is very funny indeed.
• Dudley, U., 200% of Nothing. The very unfunny way math is misrepresented in real life.
• Huff, D., How to Lie with Statistics. An old book, but much of what is described inside still goes on with reporting of statistics. You need the standard deviation! Review by Meep

Paradox

• Gardner, Martin, Gotcha!. Easy to read, and contains descriptions of many important paradoxes.
• Barwise and Etchemendy, The Liar: An Essay on Truth and Circularity. Much more advanced book dealing with Russell's paradox (the Liar...used in diagonal arguments).
• Stalker, D., ed., Grue!. Collection of articles on Hempel's paradox -- a paradox of scientific (as opposed to mathematical) induction. Rather difficult.

Other

Weird Numbers and Nim-like Games

• Knuth, D.E., Surreal Numbers.
• Conway, Guy, and Berlekamp, Winning Ways for your Mathematical Plays. Out of print, but many math libraries at universities have this.

Cool Physics and Higher Dimensions

• Burger, Dionys, Sphereland. And those Victorians thought Flatland was wild...
• Gamow, George, Mr. Thompkins in Paperback. See what happens when you have quantum effects on pool tables or the speed of light is 65 mph (no more need for state troopers!)
• Herbert, Nick, Quantum Reality: Beyond the New Physics. Extremely easy to read for metaphysics.
• Feynman, Richard, The Character of Physical Law. For the man on the street.
• Rucker, Rudy, The 4th Dimension. I can see it! I can really see it!

Linear Algebra

• Strang, Gilbert, Linear Algebra. For applications/computations
• Gelfand, I., Linear Algebra.
• Sapir, Mark, Web book on Linear Algebra.
• Bretscher, Otto, Linear Algebra.
• Axler, Sheldon, Linear Algebra Done Right. for theory.
• Schaum's Outlines for Linear Algebra. For reference. Lots and lots of solved problems!
• Hoffman and Kunze, Linear Algebra. REally good!

Information Theory

• McEliece, Robert, Information Theory.
• Thomas and Cover, Introduction to Information Theory.
• Shannon, Claude, His original paper on information theory is on the web. Go find it.

Magazines

• Scientific American. Used to have a math column with Ian Stewart, but now it's just short problems. Often there's articles on developments in math.
• American Mathematical Monthly. Journal put out by the Mathematical Association of America. Has problems and articles on undergraduate-level math.
• Math Horizons.
• Crux Mathematicorum with Mathematical Mayhem. Dave writes for this.
• Quantum. High school level math magazine. Neat puzzles and problems.
• Mathematics Magazine. by MAA again.

Typesetting Math (aka LaTeX)

• Donald E. Knuth, The TeXbook. A dense, but definitive, description of the TeX system. One of the best descriptions of typesetting mathematics in TeX available.
• Helmut Kopka and Patrick W. Daly, A Guide to LaTeX: Document Preparation for Beginners and Advanced Users (3rd ed.). A very nice book describing the standard LaTeX macro package; this is used by almost everyone. A much easier read than Knuth, but if you want to advanced things, you'll need the TeXbook. The coverage of typesetting math is much more basic than in The TeXbook as well.
• The TeX Users' Group. This has links to all sorts of useful information, such as where you can get a working TeX system for your machine. There are both free and commercial implementations available for most platforms; TeX and LaTeX themselves are free.