Bibliography

The following is a (not complete) list of books (for the most part, mathematics-related ones) that I find interesting or useful, or that I've used as references when writing this site's material. For online resources, please see my links page.

For a list of physics-related books, please see my physics bibliography.

1. Hofstadter, Douglas R. Gödel, Escher, Bach: An Eternal Golden Braid. Basic Books, 1979.
   A Pulitzer Prize winner, this book is a true classic. Those who are interested in computability theory, philosophy of mind, and many other fields will find something of interest here. The dialogues between Achilles and the Tortoise (of Zeno's paradox fame) keep the 700+ page book interesting.
2. Maor, Eli. To Infinity and Beyond: A Cultural History of The Infinite. Boston: Birkhäuser, 1987.
3. Butterworth, Brian. What Counts: How Every Brain Is Hardwired for Math. New York: The Free Press, 1999.
4. Galotti, Dr. Kathleen M. Cognitive Psychology In and Out of the Laboratory. 4th ed. Thomson Wadsworth, 2008.
   This textbook is written well in an informal, almost chatty, tone. I enjoyed reading this book. The sections on problem solving and reasoning were of use in creating this site. The one disadvantage about this book is that, being a current textbook, it's incredibly expensive.
5. Falletta, Nicholas. The Paradoxicon. New York: John Wiley & Sons, 1990.
   I used this book for some of my paradoxes page.
6. Aristotle. On Sophistical Refutations. On Coming-to-be and Passing-away. On the Cosmos. Trans. E. S. Forster and D. J. Furley. Cambridge: Harvard University Press, 1955. Loeb Classical Library.
   My On Sophistical Refutations page is a copy of this translation. Nice-looking book; I believe that Martha Stewart used these books as decoration on her bookshelves.
7. Davis, Philip J. and William G. Chinn. 3.1416 and All That. Boston: Birkhäuser, 1985.
   An interesting and worthwhile book. Contains 25 short essays on topics relating to popular and recreational mathematics. The essays date from the 1960s and are starting to show their age in parts, but for the most part this is still a relevant book.
8. Polya, G. How to Solve It: A New Aspect of Mathematical Method. Second ed. Princeton: Princeton University Press, 1957.
   The classic book on problem solving and heuristics. I feel that this book is a "must-read" for anyone who is a student of mathematics, and it's still a worthwhile read if you're not.
9. Davis, Philip J. and Reuben Hersh. The Mathematical Experience. Boston: Birkhaüser, 1981.
   An interesting book that mediates well between being too technical and being too simplistic. In some ways (specifically its discussion of philosophical issues), I found it somewhat reminiscent of Gödel, Escher, Bach; in other ways it's quite different.
10. Pickover, Clifford. Keys to Infinity. John Wiley & Sons, 1995.
    A very interesting book which is of the same (high) calibre as all of the author's other works. Lots of food for thought here.
11. Noller, Ruth B., Ruth E. Heintz, and David A. Blauer. Creative Problem Solving in Mathematics. Buffalo: State University College at Buffalo, 1978.
    A small, cute book dealing with the fundamentals of problem solving and containing some nice examples.
12. Taplan, Margaret. "Mathematics Through Problem Solving." Math Goodies. Web. 21 Feb. 2011. <http://www.mathgoodies.com/articles/problem_solving.html>.
13. Dudley, Underwood. Mathematical Cranks. Washington: The Mathematical Association of America, 1992.
    This book is hilarious! This book contains discusses mathematical cranks (people who hold eccentric mathematical beliefs, believe they're right and the rest of the mathematical establishment is wrong, and write profusely. The book is divided into about fifty topics, which intersperse crank writing with Dudley's insightful and humourous comments. Dudley also includes a discussion of the actual mathematics, which aids in understanding the topics from a mainstream mathematical perspective. Now that we're in the Internet age, you can find crank writings all over the Internet, but they're just not as funny without Dudley's commentary.
14. Richardson, William F. Numbering and Measuring in the Classical World. Revised Ed. Bristol: Bristol Phoenix Press, 2004.
15. Gibilisco, Stan. Puzzles, Paradoxes and Brain Teasers. Blue Ridge Summit: Tab Books, 1988.
    A very interesting book, containing short discussions on a wide variety of topics, from infinity, logic, some physics topics, and more. The format of the book (each chapter of the book is divided into small articles of about half a page or so) is quite interesting. I found parts of the book to be somewhat speculative in nature and a few little mathematical errors can be found in the text, but it's still an interesting work.
16. Euclid. The Thirteen Books of The Elements. Trans. Sir Thomas L. Heath. Second ed. Vol. 1. New York: Dover Publications, 1956.
17. Falconer, Kenneth. Fractal Geometry: Mathematical Foundations and Applications. Chichester: John Wiley & Sons, 1990.
18. Richardson, A. Stephen. "Logical Fallacies in Scientific Writing." Department of Computer Science - The University of Auckland. Web. 04 Mar. 2011. <http://www.cs.auckland.ac.nz/~cristian/i2rcs/i2rcs_docs/logic.htm>.
19. Hamblin, C. L. Fallacies. London: Methuen & Co., 1970.
20. Dudley, Underwood. Elementary Number Theory. New York: Dover, 1978.
    This is an excellent introductory textbook to number theory. Textbooks are often expensive; however, Dover now has a reprint edition of this that is very inexpensively priced.
21. Dodgson, Charles L., M.A. Pillow-Problems: Thought Out During Wakeful Hours. New York: Dover, 1958.
22. Gardner, Martin. The Universe in a Handkerchief: Lewis Carroll's Mathematical Recreations, Games, Puzzles, and Word Plays. New York: Copernicus, 1996.
23. Collins, A. Frederick. Rapid Math Without a Calculator. Secaucus: Citadel Press, 1987.
    A reprint of an older book (I assume from the 1920s) originally entitled Magic with Figures. Quite a useful book; contains lots of methods for improving your mental calculation speed. There are some inaccuracies in the book, so it is best if read critically.
24. Gardner, Martin. The Second Scientific American Book of Mathematical Puzzles and Diversions. Chicago: University of Chicago Press, 1987.
    A collection of Gardner's Scientific American columns from parts of 1958 through 1960, there are some gems here, such as the section on "Probability and Ambiguity" and "Phi: The Golden Ratio".
25. Bell, Eric Temple. The Search For Truth New York: Reynal & Hitchcock, 1934.
26. Walton, Douglas. Fallacies Arising from Ambiguity. Dordrecht: Kluwer Academic, 1996. Applied Logic Ser. 1.
27. Walton, Douglas. A Pragmatic Theory of Fallacy. Tuscaloosa: The University of Alabama Press, 1995.
28. Benson, William H. and Oswald Jacoby. New Recreations With Magic Squares. New York: Dover Publications, 1976.
29. Foundation for Critical Thinking, "Defining Critical Thinking", http://www.criticalthinking.org/aboutCT/define_critical_thinking.cfm (Retrieved August 7, 2011).
30. Ball, W. W. Rouse. A Short Account of the History of Mathematics. London: MacMillan & Co., 1912.
31. Smullyan, Raymond. The Lady or the Tiger?: and Other Logic Puzzles. New York: Alfred A. Knopf, 1982.
32. Burns, Marilyn. Math for Smarty Pants. New York: Little Brown, 1982.
33. Pappas, Theoni. The Magic of Mathematics: Discovering the Spell of Mathematics. San Carlos, CA: Wide World Publishing/Tetra, 1994.
34. Ball, W. W. Rouse. Mathematical Recreations & Essays. Eleventh Edition. London: MacMillan, 1939.
35. Groza, Vivian Shaw. A Survey of Mathematics: Elementary Concepts and Their Historical Development. New York: Holt, Rinehart and Winston, 1968.
36. Chace, Arnold Buffum. The Rhind Mathematical Papyrus Reston, VA: The National Council of Teachers of Mathematics, 1979.
37. Datta, Bibhutibhushan and Avadhesh Narayan Singh. History of Hindu Mathematics: A Source Book (Bombay: Asia Publishing House, 1962).
38. Boyer, Carl B. and Uta C. Merzbach. A History of Mathematics, second edition (New York: John Wiley & Sons, 1991). View book review for this book.
39. Posamentier, Alfred S. Math Charmers: Tantalizing Tidbits for the Mind (Amherst: Prometheus Books, 2003).

Leonard C. Bruno (ed.), Math & Mathematicians: The History of Math Discoveries Around the World. UXL (Gale), 1999.

Don't let the minor factual errors put you off this two-volume series designed for younger readers. It chronicles the lives of many famous mathematicians and is interspersed with discussions about mathematical concepts. A good source for adding spice to lesson plans.

David Wells, The Penguin Dictionary of Curious and Interesting Numbers. Penguin Books, 1986.

Just as the title says, a dictionary of interesting numbers, from -1 to Graham's Number. Has discussions on perfect numbers, prime numbers, and many other concepts.

John H. Conway and Richard K. Guy, The Book of Numbers. Springer-Verlag, New York, 1996.

A really interesting book on number theory by some of the giants in the field. I would definitely recommend reading it.

Martin Gardner, Fractal Music, Hypercards and More...: ...Mathematical Recreations from Scientific American Magazine. W. H. Freeman and Company, New York, 1992.

Another collection of Gardner's (later) Scientific American columns. The section "Does Time Ever Stop? Can the Past Be Altered" is very deep and makes worthwhile reading. I used sections in the book about Egyptian Fractions and Ticktacktoe in creating some of my pages.

A. K. Dewdney, The Magic Machine: A Handbook of Computer Sorcery. W. H. Freeman and Company, New York, 1990.

A collection of Dewdney's "Computer Recreations" columns from Scientific American magazine. I found this book quite enjoyable.

Marshall Claget, Greek Science in Antiquity. MacMillan Publishing Co. Ltd., New York, 1963.

A book containing a fairly detailed history and overview of Greek science. I really enjoyed the sections on philosophy and science in Late Antiquity, since I'm rather interested in that time period.

Jacob Bronowski, The Ascent of Man. British Broadcasting Company, 1973.

A book about the history of humankind. Not a lot of mathematics stuff in this book, but I got the idea for my presentation of the proof of the Pythagorean theorem from this book.

Jack Gilbert, Numbers: Shortcuts and Pastimes. Tab Books, 1993.

Talks both practical (calculation shortcuts) and theoretical (some number theory concepts) mathematics. I enjoyed this book.

David Blatner, The Joy of π. Penguin Books, London, 1997.

An interesting book about the history of pi, calculating the value of pi, and pi in general. Contains many anecdotes about pi's properties. As well, one million decimal digits of pi are printed throughout the book. I really enjoyed the cartoon on page 54. You can visit the book's website at http://www.joyofpi.com/.

Ivan Niven, Numbers: Rational and Irrational. Mathematical Association of America, Washington, D.C., 1961

A small book, more technical in nature than most of the books listed here. Discusses rational, irrational, and transcendental numbers. Proofs are presented clearly and are valuable in understanding the material. The author is Canadian, too.

Calvin C. Clawson, Mathematical Mysteries: The Beauty and Magic of Numbers. Perseus Books, Cambridge, Mass., 1999.

I find Clawson's books well-written and understandable. This book is no exception. This book concerns itself with numbers in themselves, in other words number theory. I have never seen a more-clear presentation of Riemann's hypothesis that even the uninitiated can understand.

Charles Seife, Zero: The Biography of a Dangerous Idea. Viking Books, New York, NY, USA, 2000

A book about the origins of zero that is interesting and insightful.

Martin Gardner, The Night Is Large: Collected Essays, 1938-1995. St. Martin's Press, New York, 1996.

The sections on "Mathematics" and "Philosophy" contain a lot of math-related material, and the entire collection makes for good reading.

Ivar Ekelund , The Broken Dice: And Other Mathematical Tales of Chance. University of Chicago Press, Chicago, 1993.

An interesting book about probability. I really enjoyed the many excerpts from the Sagas and other medieval manuscripts.

Robert Kaplan, The Nothing That Is: A Natural History of Zero. Oxford University Press, 2000.

A book about the origins of the concept of zero. I enjoyed it a fair bit.

James Newman (ed.), The World of Mathematics. Simon and Schuster, New York, NY, 1956.

A four-volume work that highlights the wide range of mathematics. Some of the historical information in Volume I was useful to me in writing my Ancient Egyptian mathematics page.

Kitty Ferguson, Measuring the Universe: Our Historic Quest to Chart the Horizons of Space and Time. Walker Publishing, 1999.

An interesting book. I particularly enjoyed the chapter on Eratosthenes.

Calvin C. Clawson, The Mathematical Traveler: Exploring the Grand History of Numbers. Plenum Press, New York, 1994.

A great book that details the history of numbers. Well-written and accessible.