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Swayam Central

Introduction to Abstract Group Theory

By Prof.Krishna Hanumanthu   |   CMI

This course will introduce abstract groups. We will start with definitions, basic properties and constructions and cover many important theorems in basic group theory, such as Lagrange’s theorem, Cauchy’s theorem and Sylow theorems. A major emphasis of the course will be to present numerous worked-out examples and problems. A part of the lecture every week will be devoted to explicit calculations. 

INTENDED AUDIENCE: BSc, MSc students studying mathematics
PREREQUISITES:           Any BSc student who is familiar with high school mathematics can take this course
INDUSTRY SUPPORT:    NIL

Learners enrolled: 2515

SUMMARY

Course Status : Ongoing
Course Type : Core
Duration : 8 weeks
Start Date : 26 Aug 2019
End Date : 18 Oct 2019
Exam Date : 16 Nov 2019
Category :
  • Mathematics
  • Level : Postgraduate
    This is an AICTE approved FDP course

    COURSE LAYOUT


    Week 1  :  Motivation, definition, examples and basic properties
    Week 2  :   Subgroups, subgroups of integers, homomorphisms
    Week 3  : Quotient groups, isomorphism theorems
    Week 4  :  Group operations, counting formula 
    Week 5  :  Symmetric groups 
    Week 6  :  Operations of a group on itself, class equation
    Week 7  :  Sylow theorems I
    Week 8  :  Sylow theorems II

    BOOKS AND REFERENCES

    NIL

    INSTRUCTOR BIO




    Prof. Krishna Hanumanthu is an associate professor of mathematics at Chennai Mathematical Institute (CMI). He studied BSc and MSc in CMI during 1998-2003 and did his PhD in mathematics at University of Missouri during 2003-2008. He joined CMI as a faculty member in 2011 after working for 3 years at University of Kansas. His main areas of research are algebraic geometry and commutative algebra. He has been teaching for almost 15 years and taught introductory courses on abstract algebra (including group theory) many times. 

    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 centers.
    • The exam is optional for a fee of Rs 1000/- (Rupees one thousand only).
    • Date and Time of Exams: 16th November 2019, 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 6 assignments out of the total 8 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 are being discontinued from July 2019 semester and will not be dispatched.

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