MTL729: Computational Algebra and its Applications

3 Credits (3-0-0)

Finite fields: Construction and examples. Polynomials over finite fields, their factorization/irreducibility and their applications to coding theory. Combinatorial applications. Symmetric and Public key cryptosystems particularly on Elliptic curves. Combinatorial group theory: investigation of groups on computers, finitely presented groups, coset enumeration. Fundamental problem of combinatorial group theory. Coset enumeration, Nielsen transformations. Braid Group cryptography. Automorphism groups. Computational methods for determining automorphism groups of certain finite groups. Computations of characters and representations of finite groups. Computer algebra programs. Computations of units in rings and group rings. Calculations in Lie algebras.