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Algebra - I

By Prof. S. Viswanath, Prof. Amritanshu Prasad   |   IMSc
Learners enrolled: 3888
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
Start Date : 14 Sep 2020
End Date : 04 Dec 2020
Exam Date : 20 Dec 2020 IST
Enrollment Ends : 25 Sep 2020
Category :
  • Mathematics
Credit Points : 3
Level : Postgraduate



Course layout

Week 1:Permutation Groups, symmetries of graphs
Week 2:Abstract Groups, homomorphism, isomorphism, subgroup, quotient group
Week 3:Group actions
Week 4:Sylow theorems
Week 5:Examples and definition of rings
Week 6:Homomorphisms, ideals, quotients, integral domains, fraction fields
Week 7:Principal ideal domains, Unique factorization domains and Euclidean domains
Week 8:Modules, definition and examples, submodules, simplicity, indecomposability
Week 9:Tensor products
Week 10:Jordan-Holder and Krull-Schmidt theorems
Week 11:Classification of finitely generated modules over PID’s
Week 12:Applications of classification to finitely generated abelian groups and 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: 20 December 2020, 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.


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