Algebra - I

By Prof. S. Viswanath, Prof. Amritanshu Prasad   |   IMSc
Learners enrolled: 2424
Foundational PG level course in algebra, suitable for M.Sc and first year PhD students in Mathematics.

Any Interested Learners
PREREQUISITES BSc-level linear algebra
Course Status : Completed
Course Type : Core
Duration : 12 weeks
Category :
  • Mathematics
Credit Points : 3
Level : Postgraduate
Start Date : 26 Jul 2021
End Date : 15 Oct 2021
Enrollment Ends : 09 Aug 2021
Exam Date : 24 Oct 2021 IST

Note: This exam date is subjected to change based on seat availability. You can check final exam date on your hall ticket.

Page Visits

Course layout

Week 1: Permutation groups, group axioms, order and conjugacy, subgroups
Week 2: Group actions, homomorphisms, isomorphisms, quotient groups, products
Week 3: Orbit counting theorem, fixed points, Sylow's theorems
Week 4: Sylow's theorems (continued), free groups
Week 5: Generators and relations
Week 6: Rings, Euclidean domains, ideals and factorization
Week 7: Examples of commutative and non-commutative rings, quotients by ideals
Week 8: Tensor and exterior algebras, modules
Week 9: Sums, quotients and homomorphisms of modules
Week 10: Free modules, determinants, primary decomposition
Week 11:Finitely generated modules and the Noetherian condition
Week 12: Smith form, structure theorem for finitely generated modules over a PID, Jordan canonical form

Books and references

Algebra, by Michael Artin
Abstract Algebra, by Dummit and Foote

Instructor bio

Prof. S. Viswanath

S Viswanath is a faculty at The Institute of Mathematical Sciences, Chennai. His research interest is in representation theory.

Prof. Amritanshu Prasad

Amritanshu Prasad is a faculty at The Institute of Mathematical Sciences, Chennai. His research interest is in representation theory.

Course certificate

The course is free to enroll and learn from. But if you want a certificate, you have to register and write the proctored exam conducted by us in person at any of the designated exam centres.
The exam is optional for a fee of Rs 1000/- (Rupees one thousand only).
Date and Time of Exams: 24 October 2021 Morning session 9am to 12 noon; Afternoon Session 2pm to 5pm.
Registration url: Announcements will be made when the registration form is open for registrations.
The online registration form has to be filled and the certification exam fee needs to be paid. More details will be made available when the exam registration form is published. If there are any changes, it will be mentioned then.
Please check the form for more details on the cities where the exams will be held, the conditions you agree to when you fill the form etc.


Average assignment score = 25% of average of best 8 assignments out of the total 12 assignments given in the course.
Exam score = 75% of the proctored certification exam score out of 100

Final score = Average assignment score + Exam score

YOU WILL BE ELIGIBLE FOR A CERTIFICATE ONLY IF AVERAGE ASSIGNMENT SCORE >=10/25 AND EXAM SCORE >= 30/75. If one of the 2 criteria is not met, you will not get the certificate even if the Final score >= 40/100.

Certificate will have your name, photograph and the score in the final exam with the breakup.It will have the logos of NPTEL and IIT Madras .It will be e-verifiable at nptel.ac.in/noc.

Only the e-certificate will be made available. Hard copies will not be dispatched.

Once again, thanks for your interest in our online courses and certification. Happy learning.

- NPTEL team

MHRD logo Swayam logo


Goto google play store