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 input-output 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.

June 30 - July 3, 2003
Download Week 1 [PDF file]

June 30 - 11, 2003
Download Weeks 1 and 2 [PDF file]

 

July 14 - 18, 2003
Download    Day 9 [PDF file]     Day 10 [PDF file]     Day 11 [PDF file]

       

Download     Day 12 [PDF file]     Day 13 [PDF file]     Day 14 [PDF file]

       

 

Download:

TI-89 Notes on Algebra [text file]        TI-89 Notes on Taylor Series [text file]

NOTE: As you select any of the links listed above, they will download as PDF files. To open PDF files use Adobe Acrobat Reader, available free from Adobe:

_____________________________________
PCMI@MathForum Home || IAS/PCMI Home
_____________________________________

© 2001 - 2014 Park City Mathematics Institute
IAS/Park City Mathematics Institute is an outreach program of the Institute for Advanced Study, 1 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 and Grant No. ESI-0554309. 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.