Course Code: MATH-203

Algebra-I

Prerequisite(s): None

Credit Hours: 3+0

Objectives of the course:

Prerequisites: Elements of Set Theory and Mathematical Logic

Objectives of the course: This course introduces basic concepts of groups and their homomorphisms. The main objective of this course is to prepare students for courses which require a good back ground in group theory like Rings and Modules, Linear Algebra, Group Representation, Galois Theory etc.

Course Contents:

Groups: Definition of a group, subgroup, subgroup generated by a set. The cyclic groups, Cosets and Lagrange’s theorem. normalizer,centralizer, center of a group, equivalence relation in a group, conjugacy classes, normal subgroups, quotient group.

Grouphomomorphism: Homomorphism, isomorphism and automorphism, kernel and image of homomorphism, isomorphism theorems, permutation groups, cyclic decomposition of a permutation group, Cayley’s theorem, direct product of two groups and examples.

Recommended Books:

1. Galllian J. A. Contemporary Abstract Algebra, 8th Ed, 2013.

2.  Rose J. A Course on Group Theory, Cambridge University Press, 1978.

3. Herstein I. N. Topics in Algebra, 2nd Ed., Xerox Publishing Company, 1964.

4. Cohn P. M. Algebra, John Wiley and Sons, London, 1974.

5. Bhattacharya P. B, Jain S. K. and Nagpaul S. R. Basic Abstract Algebra, 

    Cambridge University Press, 1986.

6. Fraleigh J. B. A First Course in Abstract Algebra, Addison-Wesley Publishing

    Company, 2002.

7. Vivek Sahai and Vikas Bist. Algebra, Narosa Publishing House, 1999.

8. Dummit D. S and Foote R. M. Abstract Algebra, 3rd Edition, Addison-Wesley

    Publishing Company, 2004.

9. Malik D.S, Mordeson J. M., Sen M.K. Fundamentals of Abstract Algebra,

    McGraw-Hill, 1997.