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

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.
To make connections between modern algebra and other branches of mathematics, and to see some of the history of the subject.

Research

Audrey Terras, Abstract Algebra with Applications, Cambridge University Press

Nadiya Gubareni, Introduction to Modern Algebra and Its Applications, CRC Press

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.