Park City Mathematics Institute 2005
Course Notes
Bowen Kerins and Ben Sinwell

Developing Mathematics: Doing it with Differences: Focused on learning mathematics by working problems together, this course explores the fundamental mathematics on a topic that has its roots in the secondary level, and is related to the mathematical theme of the Institute. Careful work on this topic allows teachers (and students) to understand exactly how elementary and more advanced procedures in the specific content area are derived and generalized.

The course is structured so that each participant can work at his/her own level. Those who are more mathematically advanced may be asked to help those with less preparation. The course is conducted by teacher leaders from the PROMYS program at Boston University. The focus of this strand is entirely on mathematics, although opportunity is provided within the course for reflection on the approach used by the instructors and to consider the implications of such an approach for teaching in secondary classrooms.

The topic for the summer is: Many situations, from monthly payments on a car loan to the absorption of drugs into the bloodstream, to Fibonacci numbers, to models of population growth can be described with "difference equations," equations that relate one term in a sequence to previous terms in a regular way. This course will develop several general-purpose methods for dealing with difference equations, including methods that use algebra, matrix algebra, combinatorics, and the theory of equations. Little by way of background is assumed, but we promise new and beautiful results by the end of week three.

June 27, 2005
Download Day 1 [PDF file]

June 28, 2005
Download Day 2 [PDF file]

June 29, 2005
Download Day 3 [PDF file]

June 30, 2005
Download Day 4 [PDF file]

July 1, 2005
Download Day 5 [PDF file]

July 5, 2005
Download Day 6 [PDF file]

July 6, 2005
Download Day 7 [PDF file]

July 7, 2005
Download Day 8 [PDF file]

July 8, 2005
Download Day 9 [PDF file]

July 11, 2005
Download Day 10 [PDF file]

July 12, 2005
Download Day 11 [PDF file]

July 13, 2005
Download Day 12 [PDF file]

July 14, 2005
Download Day 13 [PDF file]

July 15, 2005
Download Day 14 [PDF file]

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© 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.