
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.
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 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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Unless otherwise indicated all of these materials are licensed under a Creative Commons AttributionNonCommercialShareAlike
4.0 International License.
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© 2001  2018 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 major funding from Math for America
With generous support from Robert and Lynn Johnston
