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: Public-Key Encryption using the RSA Algorithm

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