case western reserve university

Math 303 - Fall 2023

Instructor: Professor David Singer
Office: Yost 307
Extension: x2892

my home

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

The EGCD Algorithm

Please select a topic by October 2 . Progress report is due October 20.

Topics Already Chosen

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

Midterm Exam is Wednesday, October 18.

Final Exam is Wednesday, December 13, 8:00 - 11:00AM.


Sage Calculator



David Singer
Professor of Mathematics
College of Arts and Sciences
Case Western Reserve University
Cleveland, Ohio 44106-7058


Legal Information | © 2020 Case Western Reserve University | Contact Prof. Singer