Department of Mathematics
INDIAN INSTITUTE OF SCIENCE
Faculty Publications (by author)
Academic Review Reports
NMI Distinguished Associates
Inspire Fellows/DST Young Scientists
Current & Upcoming
Final Examination Schedule
Integrated Ph.D. Programme
Student Information Handbook
Scheme of Instruction
Undergrad Scheme of Instruction
News & Events
Bangalore Probability Seminar
Algebra & Combinatorics Seminar
Geometry & Topology Seminar
IISc Course Registration
Changed E-mails (at IISc)
NBHM Regional Library
Offices and Phone Numbers
IISc SAP S/4 HANA
MA 212: Algebra I
Prerequisite courses for Undegraduates: UM 203
Groups: definitions & basic examples;
Normal subgroups, quotients;
Three isomorphism theorems;
Centralizer and normalizer of a subset, centre of a group;
Permutations, symmetrc groups and Cayley’s theorem;
Group actions and their applications, Sylow’s theorems.
Rings and ideals: basic definitions, quotient rings;
The Chinese Remainder Theorem;
Maximal and prime ideals;
Unique factorization, unique factorization domains, principal ideal domains, Euclidean domains, polynomial rings;
Modules: basic definitions and examples, Hom and tensor products, the Structure Theorem for finitely generated modules over PIDs;
Fields: basic definitions and examples, algebraic & trancendental numbers;
Finite fields, characteristic, the order of a finite field.
Suggested books and references:
, M. Prentice-Hall of India, 1994.
Dummit, D. S. and Foote, R. M.,
, McGraw-Hill, 1986.
Herstein, I. N.,
Topics in Algebra
, John Wiley & Sons, 1995.
Algebra (3rd Ed.)
, Springer, 2002.
+91 (80) 2293 2711, +91 (80) 2293 2265 ;
Last updated: 17 Sep 2019