Teacher resources and professional development across the curriculum

Teacher professional development and classroom resources across the curriculum

Monthly Update sign up
Mailing List signup
Follow The Annenberg Learner on LinkedIn Follow The Annenberg Learner on Facebook Follow Annenberg Learner on Twitter

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).

back to top

HomeVideo CatalogAbout UsSearchContact Us

© Annenberg Foundation 2013. All rights reserved. Privacy Policy