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Unit 3

How Big is Infinity?





Aristotle. (Edited by: Richard McKeon, Introduction by C.D. Reeve) The Basic Works of Aristotle. New York: Modern Library, 2001.

Benjamin, Arthur T and Jennifer J. Quinn. Proofs that Really Count: The Art of Combinatorial Proof (Dolciani Mathematical Expositions). Washington, D.C.: Mathematical Association of America, 2003.

Berlinghoff, William P. and Fernando Q. Gouvea. Math Through the Ages : A Gentle History for Teachers and Others. Farmington, ME: Oxton House Publishers, 2002.

Berlinghoff, William P. and Kerry E. Grant. A Mathematics Sampler: Topics for the Liberal Arts, 3rd ed. New York: Ardsley House Publishers, Inc., 1992.

Boyer, Carl B. (revised by Uta C. Merzbach). A History of Mathematics, 2nd ed. New York: John Wiley and Sons, 1991.

Burton, David M. History of Mathematics: An Introduction, 4th ed. USA : WCB/ McGraw-Hill, 1999.

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

Du Sautoy, Marcus. The Music of the Primes: Searching To Solve the Greatest Mystery in Mathematics. New York: Harper Collins, 2003.

Gazale, Midhat. Number: From Ahmes to Cantor. Princeton, NJ: Princeton University Press, 2000.

Gross, Benedict and Joe Harris. The Magic of Numbers. Upper Saddle River, NJ: Pearson Education, Inc./ Prentice Hall, 2004.

Henle, J.M. "Non-nonstandard analysis: Real infinitesimals," Mathematical Intelligencer, vol. 21 Issue 1 (Winter 1999).

Joseph, George Gheverghese. Crest of the Peacock: The Non-European Roots of Mathematics. Princeton, NJ: Princeton University Press, 2000.

Mueckenheim, W. "On Cantor's Important Proofs." Cornell University Library. http://arxiv.org/abs/math/0306200 (accessed 2007).

Mueckenheim, W. "The Meaning of Infinity." Cornell University Library. http://arxiv.org/abs/math/0403238 (accessed 2007).

Newman, James R. Volume 1 of The World of Mathematics: A Small Library of the Literature of Mathematics from A'h-mose the Scribe to Albert Einstein. New York: Simon and Schuster, 1956.

Poonen, Bjorn. "Infinity: Cardinal Numbers." Berkeley Math Circle, UC Berkeley. http://mathcircle.berkeley.edu/bmcarchivepages/handouts/1998_1999.html (accessed 2007).

Schechter, Eric. "Potential Versus Completed Infinity: Its History and Controversy." Department of Mathematics, Vanderbilt University. http://www.math.vanderbilt.edu/~schectex/ http://www.math.vanderbilt.edu/~schectex/courses/thereals/potential.html (accessed 2007).

Schumacher, Carol. Chapter Zero: Fundamental Notions of Abstract Mathematics. Reading, MA: Addison-Wesley Higher Mathematics, 1996.

Stewart, Ian. From Here to Infinity: A Guide to Today's Mathematics. New York: Oxford University Press, 1996.

Tannenbaum, Peter. Excursions in Modern Mathematics, 5th ed. Upper Saddle River, NJ: Pearson Education, Inc., 2004.

Tanton, James. "Arithmetic, Algebra and Abstraction," Text in preparation, to appear 2009.

Weisstein, Eric W. "Newton's Iteration." Wolfram Research http://mathworld. wolfram.com/NewtonsIteration.html (accessed 2007).

Weisstein, Eric W. "Pythagoras's Constant." Wolfram Research. http:// mathworld.wolfram.com/PythagorassConstant.html (accessed 2007).

White, Michael. "Incommensurables and Incomparables: On the Conceptual Status and the Philosophical Use of Hyperreal Numbers," Notre Dame Journal of Formal Logic, vol. 40, no. 3 (Summer 1999).

Zeno, of Elea. [translated by H.D.P. Lee] Zeno of Elea. A Text, with translation from the Greek and notes. Amsterdam: A. M. Hakkert, 1967.


Allen, G. Donald. "Lectures on the History of Mathematics: The History of Infinity." Department of Mathematics, Texas A&M University. http://www.math.tamu.edu/~dallen/masters/index.htm http://www.math.tamu.edu/~don.allen/history/m629_97a.html (accessed 2007).

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