
Park City Mathematics Institute 2003
Course Notes
Number Theory  Bowen Kerins, Ben Sinwell, and Brian Hopkins

Sums and Differences: the Art and Craft of Adding and Subtracting: How do you find a polynomial function of smallest degree that agrees with a table of data? What's the sum of the fourth powers of all the integers between 1 and 100? What's the sum of the reciprocals of the perfect squares? What's the sum of the squares of all the complex numbers whose fifth power is 1? Why, if the third differences in an inputoutput table are constant, is there a cubic polynomial fit? What's the probability that two integers, chosen at random, have no common factor? And, most importantly, what do all these questions have to do with one another? This course looks at the calculus of finite differences as a unifying theme for these questions and others that connect to the middle and high school curriculum.
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© 2001  2013 Park City Mathematics Institute
IAS/Park City Mathematics Institute is an outreach program of the School of Mathematics at the Institute for Advanced Study, Einstein Drive, Princeton, NJ 08540
Send questions or comments to: Suzanne Alejandre and Jim King

With program support provided by Math for America
This material is based upon work supported by the National Science Foundation under Grant No. 0314808.
Any opinions, findings, and conclusions or recommendations expressed
in this material are those of the author(s) and do not necessarily reflect
the views of the National Science Foundation.
