Introduction to Group Theory

By Prof. R. Venkatesh | IISc Bangalore

Learners enrolled: 754 | Exam registration: 56

ABOUT THE COURSE:
Group theory studies symmetries. This course, designed for undergraduate students, gives a gentle introduction to the highlights of elementary group theory. The course begins with group definitions and basic properties and discusses various essential examples of groups from Geometry and Number theory. We move on to developing basic notions like homomorphisms and quotient groups. Finally, we study group actions and see various applications of group actions, including Sylow’s theorems.

PREREQUISITES: Basic Linear Algebra

Summary

Course Status :	Completed
Course Type :	Core
Duration :	12 weeks
Category :	Mathematics
Credit Points :	3
Level :	Undergraduate
Start Date :	22 Jan 2024
End Date :	12 Apr 2024
Enrollment Ends :	05 Feb 2024
Exam Registration Ends :	16 Feb 2024
Exam Date :	28 Apr 2024 IST

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

Page Visits

Course layout

Week 1: Groups: definitions and basic properties

Week 2: Examples from Geometry I: Group of isometries of a plane and their finite reflection subgroups

Week 3: Examples from Geometry II: symmetries of a cube, tetrahedron and regular n-gon

Week 4: Examples from Number theory: the additive/multiplicative group of integers modulo n

Week 5: Cyclic groups: various characterizations

Week 6: Abelian groups examples, Symmetric and alternating groups

Week 7: Group homomorphisms, Normal subgroups

Week 8: Quotient groups and isomorphism theorems

Week 9: Group actions: definition and various examples

Week 10: Application of group action: Cayley’s theorem, Lagrange’s theorem, Cauchy's theorem

Week 11: Conjugacy action, the class equation

Week 12: Sylow’s theory and its application

Books and references

1. Dummit, David; Richard Foote (2004). Abstract Algebra (3rd ed.). Wiley.
2. Eie, Minking; Chang, Shou-Te (2010). A Course on Abstract Algebra. World Scientific.
3. D. M. Burton., Elementary Number Theory, McGraw Hill.
4. M. A. Armstrong, Groups and Symmetry, Springer-Verlag.

Instructor bio

Prof. R. Venkatesh

IISc Bangalore

Prof. R. Venkatesh is working as an Assistant Professor at the Indian Institute of Science, Bengaluru from May 2017. His research work focuses on problems related to infinite dimensional Lie algebras and their representations.

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: 28 April 2024 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 IISc Bangalore .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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