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: Public-Key Encryption using the RSA Algorithm

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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.