Algebra III

Type of Course:

• Compulsory Yes (Cohort BA (H) Mathematics)
• Elective Yes (Cohort BA (H) other than Mathematics)

Course Coordinator and Team: Tanya Saluja (CC)

Email of course coordinator: tanya[at]aud[dot]ac[dot]in

Pre-requisites: M07

Aim: This course continues where the Algebra II course ended. It builds the theoretical base in Group theory, Ring Theory and Linear Algebra beyond what was done in M07.

Brief description of modules/ Main modules:

• Group Theory: Automorphisms, External Direct Products, Fundamental Theorem of finite abelian groups.
• Ring Theory: Polynomial rings, factorization of polynomials, divisibility in integral domains.
• Linear Algebra: Change of basis, applications to difference equations and Markov chains, eigenvalues and eigenvectors.

Refererences:

• Joseph A. Gallian, Contemporary Abstract Algebra (Fourth Edition), Narosa Publishing House, New Delhi, 1999.
• Jimmie Gilbert and Linda Gilbert, Linear Algebra and Matrix Theory (Second Edition), Brooks Cole, 2004.
• David C. Lay, Linear Algebra and its Applications (Third Edition), Pearson Education Asia, Indian Reprint, 2007.

Additional Reference:

• Bhattacharya, Jain and Nagpal, Basic Abstract Algebra (Second Edition), Cambridge, 2009.

Tentative Assessment schedule with details of weightage: