Park City Mathematics Institute 2008
Course Notes
Darryl Yong and Ben Sinwell with assistance from Bowen Kerins

Applications of Algebra and Geometry to the Craft of Teaching: How do you generate Pythagorean triples? Scalene triangles with integer side-lengths and a 60-degree angle? Cubic polynomials with integer zeros and extreme points? Triangles on the Cartesian plane whose vertices have integer coordinates and whose side lengths are integers? A mathematical analysis of how to design problems that "come out nice" leads to investigations into foundational ideas from number theory, algebraic geometry, and analytic geometry. We'll use this theme as a springboard into investigations of the structure of different algebraic systems and geometric curves. This applied mathematics - choosing and designing tasks - is mathematics applied to the work teachers do.

July 7, 2008
Download Day 1 [PDF file]

July 8, 2008
Download Day 2 [PDF file]

July 9, 2008
Download Day 3 [PDF file]

July 10, 2008
Download Day 4 [PDF file]

July 11, 2008
Download Day 5 [PDF file]

July 14, 2008
Download Day 6 [PDF file]

July 15, 2008
Download Day 7 [PDF file]

July 16, 2008
Download Day 8 [PDF file]

July 17, 2008
Download Day 9 [PDF file]

July 18, 2008
Download Day 10 [PDF file]

July 21, 2008
Download Day 11 [PDF file]

July 22, 2008
Download Day 12 [PDF file]

July 23, 2008
Download Day 13 [PDF file]

July 24, 2008
Download Day 14 [PDF file]

July 25, 2008
Download Day 15 [PDF file]

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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.