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Park City Mathematics Institute 2001
Course Notes
Number Theory - Ryota Matsuura and Bowen Kerins
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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.
These course materials are licensed under a Creative Commons Attribution-NonCommercial-ShareAlike
4.0 International License.
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
NOTE: As you select any of the links listed above, they will download as PDF files. To open PDF files use Adobe Acrobat Reader, available free from Adobe:
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Unless otherwise indicated all of these materials are licensed under a
Creative Commons Attribution-NonCommercial-ShareAlike
4.0 International License.
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© 2001 - 2020 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
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With major funding from Math for America
With generous support from Robert and Lynn Johnston
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