Here is a (not complete) list of books and other sources that I used
between 1999 and 2002 to write pages on this site. For more recent sources
used, see the main bibliography page.
Douglas R. Hofstadter, 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.
Philip J. Davis and Reuben Hersh, The Mathematical Experience. Birkhaüser Boston, 1981
An interesting book that mediates well between being too technical
and being too simplistic. It is somewhat reminiscent of (but IMHO not
quite as good as) Gödel, Escher, Bach in that it discusses
a lot of philosophical issues as well.
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.
Clifford Pickover, Keys to Infinity. John Wiley & Sons Inc., 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.
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, The Second Scientific American Book of
Mathematical Puzzles and Diversions. University of Chicago Press,
1961.
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".
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. The sections on
Egyptian Fractions and
Ticktacktoe are also quite interesting.
G. Polya, How to Solve It: A New Aspect of Mathematical
Method. Princeton University Press, 1945, 1957, 1973, 1985.
The classic book on problem solving. IMHO, a "must-read" for anyone
who is a student of mathematics, and it's still a worthwhile read if
you're not.
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.
Stan Gibilisco, Puzzles, Paradoxes and Brain Teasers.
Tab Books, Blue Ridge Summit, PA, 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.
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
exerpts 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
should be accessible even to those without much mathematical skill.
Eli Maor, To Infinity and Beyond: A Cultural History of The
Infinite. Birkhäuser, Boston, 1987.
An interesting book about infinity and its history.
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Old Bibliography