Abstract Algebra
Abstract Algebra
Lectures : Monday, Wednesday and Friday at 8:00 am
Tutorial/Discussion : Tuesday or Thursday at 12:00 (Once a week)
Mid Semester Examinations - 30% (15%+15%)
End Semester Examination - 30%
Quizzes - 40%
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.
4-January-2020 : Introduction and Brief History
9-January-2020 : Definition and Examples of Groups (Lecture conducted by Dr. Mandira Mondal)
10-January-2020 : Tutorial - I (Conducted by Mr. Pushpendra Singh)
11-January-2020 : Group Actions (Lecture conducted by Dr. Mandira Mondal)
13-January-2020 : More on Group Actions (Lecture conducted by Dr. Mandira Mondal)
16-January-2020 : Cayley Theorem, Class equation, Lagrange Theorem
18-January-2020 : Orbit Stablizer Lemma, Group homomorphisms and First Isomorphism Theorem
23-January-2020 : Second and Third Isomorphism Theorems.
24-January-2020 : Quiz -I and Tutorial -II (Conducted by Mr. Pushpendra Singh)
27-January-2020 : Burniside's Lemma and Cauchy's Theorem
30-January-2020 : First and Second Sylow Theorems.
1-February-2020 : Second Sylow Theorem and applications
2-February-2020 : Tutorial -III (Conducted by Mr. Pushpendra Singh)
6-February-2020 : Commutator subgroup and Solvable groups
7-February-2020 : Nilpotent groups and Fundamental theorem of finite ablian groups
8-February-2020 : Tutorial -IV (Conducted by Mr. Pushpendra Singh)
9-February-2020 : Mid Semester Examination - I
13-February-2020 : Rings, Nilpotent elements, Zero Divisors, Unity and Units
15-February-2020 : Characteristic of Ring, Integral domain
Dr. Mandira Mandal taught the second part of this course.