
Park City Mathematics Institute 2001
Course Notes
Number Theory  Ryota Matsuura and Bowen Kerins

The Euclidean algorithm and its applications to algebra and the theory of numbers: Focused exclusively on learning mathematics by working problems together, this course explores the fundamental algorithm on which much of arithmetic and algebra is based.
Files to Download
 Syllabus
 Session 1, July 9: Decimal Expansion
 Session 2, July 10: Base Conversion using the Division Algorithm
 Session 3, July 11: Base Conversion (Part Deux) and Modular Arithmetic
 Session 4, July 12: Euclid's Algorithm
 Session 5, July 13: Linear Diophantine Equations
 Session 6, July 16: Magic Box and its Applications
 Session 7, July 17: The Fundamental Theorem of Arithmetic
 Session 8, July 18: Units, Orders, and Fermat's Little Theorem
 Session 9, July 19: Decimal Expansion Revisited, Euclid's Algorithm for Polynomials
 Session 10, July 20: The Chinese Remainder Theorem
 Session 11, July 23: Curve Fitting
 Session 12, July 24: Properties of Gaussian Integers
 Session 13, July 25: Applications of Gaussian Integers
Handout for Session 13
 Session 14, July 26: Prime Gaussian Integers, Encryption
Handout for Session 14
 Session 15, July 27: PublicKey Encryption using the RSA Algorithm
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© 2001  2015 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 DMS0940733 and DMS1441467. 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.
