Math 303 - Fall 2024

Instructor: Professor David Singer
Office: Yost 307
Extension: x2892
E-mail: david.singer@case.edu

Description. MATH 303 is a one-semester, three credit-hour course in number theory and its application to cryptology. The prerequisite for the course in MATH 122 or its equivalent.

Detailed Information can be found in this document.

Text: A Friendly Introduction to Number Theory, 4th Edition, by Joseph H. Silverman, 2012. (ISBN 978-0-321-81619-1)

Syllabus: The general goal of the course is to introduce basic ideas in number theory and their application to modern cryptology. Here is an approximate list of the topics to be covered:

1. The Euclidean Algorithm
2. Unique Factorization
3. Prime Numbers
4. Congruences and Divisibility
5. Fermat's Little Theorem
6. Pseudoprimes and primality testing
7. Groups and the Euler phi function
8. Euler's Theorem, and Powers of Integers
9. Quadratic residues and reciprocity
10. Finite fields
11. Elliptic Curves
12. Introduction to Public Key Crypto-systems

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The EGCD Algorithm

Please select a topic by September 30 . Progress report is due October18.

List of suggested topics for project. Important note on references.

Midterm Exam is Wednesday, October 16.

Final Exam is Wednesday, December 11, 8:00 - 11:00AM.

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Links

Sage Calculator

• The Prime Pages
• Unsolved problems in Number Theory, Logic, and Cryptography
• Topics in Number Theory
• Topics in Algebraic Number Theory
• Online Notes in Number Theory
• Great Internet Mersenne Prime Search : 2^82,589,933 - 1 is now the largest known Mersenne prime!!
• Prime Puzzles and Problems
• On-Line Encyclopedia of Integer Sequences
• Andrew Granville's Papers
• PARI: number theory calculator
• David Joyce History of Mathematics pages
• Women Mathematicians
• MathWorld from Wolfram
• Lists
• Top 20