Course page for CS5610 - Computational Number Theory and Algebra
The course will focus on the three related topics of prime numbers, polynomials and finite fields.
Some applications to coding theory and cryptography will be seen as well.
Some of the specific topics to be covered (in no particular order):
Distribution of prime numbers, primality testing algorithms (including AKS), quadratic residues, primitive roots,
finite fields, polynomial factorization, Reed-Solomon codes, BCH codes, RSA, integer factoring.
1. Victor Shoup: A computational introduction to number theory and algebra
2. Neal Koblitz: A course in number theory and cryptography
3. Crandall and Pomerance: Prime numbers - A computational perspective
Other recommended books on Number Theory:
4. The Higher Arithmetic by Henry Davenport,
5. A Concise Introduction to the Theory of Numbers by Alan Baker,
6. An Introduction to the Theory of Numbers by Hardy and Wright
Division of credit:
Midsem: 30%, Endsem: 40%.