Algebra I

Type of Course:

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

Course Coordinator and Team: Balchand Prajapati (CC)

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

Pre-requisites: Mathematics of the 10 + 2 level

Aim: The aim of the course is to offer a gentle introduction to very basic concepts of complex numbers, groups, rings and linear mappings and some applications of these.

Real-life examples, hands-on projects, presentations, case studies, visualisation and basic computing tools will be used to reinforce skills of group theory and linear algebra.

Brief description of modules/ Main modules:

• Classical Algebra
• Group Theory
• Ring Theory
• Linear Algebra

Refererences:

• Paul E. Bland, The Basics of Abstract Algebra, W. H. Freeman and Company, 2002.
• Bhattacharya, Jain and Nagpal, Basic Abstract Algebra (Second Edition), Cambridge, 2009.
• Peter J. Cameron, Introduction to Algebra (Second Edition), Oxford University Press, 2008.
• Neal H.Mc Coy, Introduction to Modern Algebra (Fifth Revised Edition), Brown (William C.) Co, U.S., 1992.
• John R. Durbin, Modern Algebra, An Introduction (Fifth Edition), John Wiley and Sons (Asia) Pte. Ltd, 200
• 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.

Tentative Assessment schedule with details of weightage: