Course Details
Subject {L-T-P / C} : MA6647 : Abstract Algebras with its Application { 3-1-0 / 4}
Subject Nature : Theory
Coordinator : Prof. Kishor Chandra Pati
Syllabus
Background on logic and set theory, Algebraic structures: introduction to fields, rings and groups, Fields, Rings, Integral domains, Ideals and quotient rings, Special integral domains: UFDs, PIDs, and EDs, Polynomial rings, Introduction to groups. Modern applications in subjects such as Cryptography, Coding Theory, Computer Science and Physics. In particular, algorithm RSA, secret sharing algorithms, Diffie-Hellman Scheme and ElGamal cryptosystem based on discrete logarithm problem
Course Objectives
- To provide students with a good understanding of the theory of modern algebra as described in the syllabus.
- To introduce students to some of the basic methods of modern algebra.
- To develop abstract and critical reasoning by studying logical proofs and the axiomatic method as applied to modern algebra. <br />To make connections between modern algebra and other branches of mathematics, and to see some of the history of the subject.
Course Outcomes
Research
Essential Reading
- Audrey Terras, Abstract Algebra with Applications, Cambridge University Press
- Nadiya Gubareni, Introduction to Modern Algebra and Its Applications, CRC Press
Supplementary Reading
- Mahima Ranjan AdhikariAvishek Adhikari, Basic Modern Algebra with Applications, Springer
- William J. Gilbert and W. Keith Nicholson, Modern Algebra with Applications, John Wiley & Sons, Inc.