**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:

- The Euclidean Algorithm
- Unique Factorization
- Prime Numbers
- Congruences and Divisibility
- Fermat's Little Theorem
- Pseudoprimes and primality testing
- Groups and the Euler phi function
- Euler's Theorem, and Powers of Integers
- Quadratic residues and reciprocity
- Finite fields
- Elliptic Curves
- Introduction to Public Key Crypto-systems

The EGCD Algorithm

Please select a topic by

October 2. Progress report is dueOctober 20.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.

Links

- The Prime Pages
- Unsolved problems in Number Theory, Logic, and Cryptography
- Topics in 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

David Singer

Professor of Mathematics

College of Arts and Sciences

Case Western Reserve University

Cleveland, Ohio 44106-7058

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