Faculty Name: Dr. Mrinmoy Datta
Course Name: Algebra I - Groups and Rings (MA 3070)
Course Period: 28 th Jul to 20 th Nov 2025 (Tuesday 04:00 PM to 05:25 PM; Friday 02:30 PM to 03:55 PM)
Number of Credits: 3 credits
Course Contents:
Permutation groups, Cayley’s theorems. Direct and semidirect product of groups. Group actions and Sylow Theorems.
Definition of Rings, Examples and basic properties, Zero divisors, Integral domains,
Fields,Characteristic of a ring, Quotient field of an integral domain. Subrings, Ideals, Quotient
rings, Isomorphism theorems. Ring of polynomials. Prime, Irreducible elements and their
properties, Unique Factorization Domains, Principal Ideal Domains, and Euclidean domains.
Prime ideal, Maximal ideal, Prime avoidance theorem, Chinese remainder theorem.
What you'll learn:
A student attending the course seriously will get
familiarity with Groups and Rings, the two most fundamental topics of algebra. The students
will build a strong foundation in abstract mathematics, which will allow them to pursue more
advanced topics of Algebra such as Fields and Galois Theory, Commutative algebra, Algebraic
Geometry, Number Theory, Representation Theory etc.
About the Instructor: Dr. Mrinmoy Datta is currently working as an assistant professor at the
Mathematics Department at IIT Hyderabad since July 2020. His research interest lies in the
domain of Algebraic Geometry and their applications to Coding Theory.
Definition of Groups, subgroups, normal subgroups, group homomorphisms, isomorphism theorems, Lagrange's Theorem, and an open mind to pick up these prerequisites as and when required.
Assessment may consist of assignments and/or quizzes and/or viva and/or exams.
Fee: Rs.15,000/- Plus GST
Apply Here
Last Date for Registration and Payment: TBA