Abstract Algebra
Abstract Algebra
Lectures : Tuesday at 8:00 am, Thursday at 8:00 am and Friday at 12:00 noon.
Tutorial/Discussion : Wednesday at 12:00 noon
Mid Semester Examinations - 30% (15%+15%)
End Semester Examination - 30%
Quizzes - 30%
Assignments - 10%
Topics to be covered:
Group Theory : Review of Group theory (Symmetric Groups, Transformation Groups), Abelian groups, Sylow Theorems, nilpotent and solvable groups.Ring Theory : Rings, Polynomial Rings, Prime ideals, Maximal Ideals, Principal Ideal Domain, Unique Factorization domain, Euclidian Algorithm. Field extensions : Finite extension, algebraic extensions.Galois Theory : Galois Theory, splitting Fields, Normal extension, Fundamental Theorem of Galois Theory and its applications.References:
Dummit, D. S. and Foote, R. M., Abstract algebra, 3 Ed., Wiley, 2004.
Cohn, P. M., Basic algebra: Groups, rings and fields, 2 Ed., Springer, 2005.
Jacobson, N., Basic Algebra I, Dover Publication, 2009.
Jacobson, N., Basic Algebra II, Dover Publication, 2012.
Artin, M., Algebra, Second Edition, Pearson, 2010
Musili, C., Introduction to Rings and Modules, 2 Ed., Narosa, 1997.
Luthar, I. S. and Passi, I. B. S., Algebra Volume 4: Field Theory, Narosa, 2004.
3-January-2020 : Introduction and Brief History
7-January-2020 : Definition and Examples of Groups
8-January-2020 : Homomorphism and Isomorphism
9-January-2020 : Group action, Definition and examples
10-January-2020 : Conjugacy classes, Normal subgroups
11-January-2020 : Cyclic groups, Langrange Thoerem
21-January-2020 : Quotient groups, Isomorphism Theorems
22-January-2020 : Quiz-I
23-January-2020 : Quotient groups, Isomorphism Theorems
27-January-2020 : Burnside's Lemma, Cauchy's Theorem
28-January-2020 : The Sylow Theorems
29-January-2020 : Tutorial
30-January-2020 : The Sylow Theorems(cont.)
31-January-2020 : Generators and Relations
01-February-2020 : Nilpotent groups, Solvable groups
05-February-2020 : Mid Semester Examination-I
11-February-2020 : Definition of Ring, Examples
12-February-2020 : Subrings, Polynomial Rings
13-February-2020 : Ideals, Zorn's Lemma
17-February-2020 : Maximal Ideals and Prime Ideals
18-February-2020 : Algebra of Ideals, Quotient Rings
19-February-2020 : Ring Homomorphisms
20-February-2020 : Isomorphism Theorems
27-February-2020 : Irreducible elements, Prime elements
28-February-2020 : Tutorial on Assignment-IV
29-February-2020 : Quiz-II
2-March-2020 : Euclidean Domain
3-March-2020 : Principal Ideal Domain
4-March-2020 : Factorization Domain, UFD
5-March-2020 : Field of fractions
6-March-2020 : Primitive polynomials, Gauss Lemma
12-March-2020 : Gauss Theorem
13-March-2020 : Eisenstein's criterion
14-March-2020 : Discussion on Assignment-V
Classes shifted to online mode due to COVID