Algebra - I

By Prof. S. Viswanath, Prof. Amritanshu Prasad | IMSc

Learners enrolled: 1903

ABOUT THE COURSE:
Foundational PG level course in algebra, suitable for M.Sc and first year PhD students in Mathematics.

INTENDED AUDIENCE : Any Interested Learners

PREREQUISITES : BSc-level linear algebra

INDUSTRIES SUPPORT : Not Applicable

Summary

Course Status :	Completed
Course Type :	Core
Duration :	12 weeks
Category :	Mathematics
Credit Points :	3
Level :	Postgraduate
Start Date :	25 Jul 2022
End Date :	14 Oct 2022
Enrollment Ends :	08 Aug 2022
Exam Date :	30 Oct 2022 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

IMSc

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: 30 October 2022 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.

CRITERIA TO GET A CERTIFICATE

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

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