Course Details
Subject {L-T-P / C} : MA3101 : Introduction to Algebra: Group and Ring Theory { 3-1-0 / 4}
Subject Nature : Theory
Coordinator : Dr. Ranjit Mehatari
Syllabus
Groups, Subgroups, Cyclic groups, Normal Subgroups and Quotient groups, Lagrange’s theorem, Centralizers, Normalizers, Homomorphisms, Isomorphism theorems, Symmetric groups, Simplicity of the Alternating group, Matrix groups, Direct products of groups, Fundamental theorem of finitely generated abelian groups, Sylow Groups, Rings, Integral Domains, Ideals, Ring of fractions, Ring homomorphisms, Polynomial rings, Fields.
Course Objectives
- To get basic idea of groups and rings.
- Concepts of binary operations via definition and examples.
Course Outcomes
Students will be able to understand the notion of groups and rings. They will have an abstract visualization of binary operations. They will be able to understand how isomorphism preserves the structure.
Essential Reading
- I. N. Herstein, Abstract Algebra, 3rd Edition, John Wiley and Sons, 1996.
- J. A. Gallian, Contemporary Abstract Algebra, 4th Edition, Narosa, 2019.
Supplementary Reading
- D. S. Dummit & R. M. Foote, Abstract Algebra, John Wiley and Sons, 2003.
- J. J. Rotman, An Introduction to the Theory of Groups, Springer, 1995.