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Algebra - I

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

Learners enrolled: 3888

SUMMARY

Course Status : Ongoing
Course Type : Core
Duration : 12 weeks
Start Date : 14 Sep 2020
End Date : 04 Dec 2020
Exam Date : 20 Dec 2020
Enrollment Ends : 25 Sep 2020
Category :
  • Mathematics
  • Level : Postgraduate
    This is an AICTE approved FDP course

    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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