Groups: Motion, symmetry and puzzles

By Prof. Amit Kulshrestha | IISER Mohali

Learners enrolled: 1332

The purpose of this course is to motivate participants to explore and enjoy various aspects to groups. The course is not about group theory, but rather about why groups should be studied. The course would also give a glimpse into why abstraction in mathematics is an important tool that deserves its due attention.

INTENDED AUDIENCE : Anyone who is willing to understand the importance of group theory. These could be senior school students, undergraduates of science and engineering or anyone interested in knowing why abstraction is useful.

INDUSTRY SUPPORT : Basic school level co-ordinate geometry and familiarity with matrices.

Summary

Course Status :	Completed
Course Type :	Core
Duration :	4 weeks
Category :	Mathematics
Credit Points :	1
Level :	Undergraduate
Start Date :	14 Sep 2020
End Date :	09 Oct 2020
Enrollment Ends :	25 Sep 2020
Exam Date :	18 Dec 2020 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 : Introduction and purpose of the course, Action and motion, need of definition of a group, Burnside’s lemma, counting of orbits

Week 2 : Groups in parity checking, groups and puzzles, Rubik’s group, 15-puzzle group, groups and graphs ,Words on groups, free groups

Week 3 : Introduction to GAP, revisiting Rubik’s group,Groups and matrices, representations of groups,Linear transformations and groups

Week 4 : Platonic solids and their symmetry groups,Groups across various branches of mathematics, From Kourovka’s book

Books and references

Groups and symmetry by Armstrong. Groups and platonic solids / AFS school notes by Amit Kulshrestha

Instructor bio

Prof. Amit Kulshrestha

IISER Mohali

Dr. Amit Kulshrestha is an Associate Professor in the Department of Mathematical Sciences at IISER Mohali, where he has been teaching mathematics for almost a decade. He works in the broader area of algebra and loves to interact with students and teachers at all levels.

TEACHING ASSISTANTS:

Dr. Dishari Choudhuri
Postdoctoral Fellow Department of Mathematical Sciences, IISER Mohali

Mr. Puneeth Deraje
Final Year Postgraduate Student Department of Mathematical Sciences, IISER Mohali

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: 18 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 3 assignments out of the total 4 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.