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Quick Facts

Medium Of Instructions	Mode Of Learning	Mode Of Delivery
English	Self Study	Video and Text Based

Course Overview

The objective of the Groups: Motion, Symmetry and Puzzles online course by SWAYAM is to encourage learners to explore and enjoy different aspects of groups. The programme is not specifically about group theory. Instead, it is about the importance of groups and why one should study them. The course curriculum also offers a glimpse into abstraction and why it is an indispensable mathematical tool. Candidates will learn all this and more, only in four short weeks.

The Groups: Motion, Symmetry and Puzzles programme welcomes anyone and everyone interested in understanding the significance of group theory and abstractions. Be it school seniors, science and engineering undergraduates, or even Masters and Doctorate scholars; everyone is welcome.

There are several assignments that candidates can undertake to evaluate their learning. Additionally, they can take the term-end exam to earn a course certification. They can do so by paying an examination fee and visiting any one of the designated test centres to appear for the assessment.

The Highlights

Books and References
Four-week course
Undergraduate-level
Optional exam
Mathematics category
Weekly assignments
Core learning programme
Free learning
Expert faculty
E-certificate

Programme Offerings

core training
Free learning
Optional exam
e certificate
Books And References

Courses and Certificate Fees

Fees Informations	Certificate Availability	Certificate Providing Authority
INR 1000	yes	IISER Mohali

The Groups: Motion, Symmetry and Puzzles online course is a free-learning programme. However, the exam for certification is a paid feature.

Groups: motion, symmetry and puzzles programme fee structure

Training	Fees
SWAYAM’S Groups: Motion, Symmetry and Puzzles programme	NA.
Examination Fee (Optional)	Rs. 1,000

Eligibility Criteria

Working knowledge of coordinate geometry (school level) and matrices are prerequisites for the Groups: Motion, Symmetry, and Puzzles online programme.

Candidates will get four assignments during the entire duration of the programme. Their score in the best three will be averaged, 25% of which will be the ‘Average Assignment Score’. If the candidate chooses to write the term-end assessment, 75% of their obtained marks (out of 100) will become their ‘Exam Score’. The candidate’s final score is the sum of the Average Assignment Score and the Exam Score. To be eligible for certification, the candidate must satisfy BOTH the conditions listed below:

Average Assignment Score should be 10/25 or more.
Exam Score Should be 30/75 or more.

If any one of these conditions is not met, the learner will not get certified, even if their Total Score is 40/100 or more.

What you will learn

Mathematical skill

After completing the Groups: Motion, Symmetry, and Puzzles training programme, candidates should be adequately informed about the following concepts: -

Free Groups
Rubik’s Group
Counting Orbits
15-Puzzle Group
Words on Groups
Burnside’s Lemma
Action and Motion
Puzzles and Groups
Graphs and Groups
Matrices and Groups

Who it is for

Anybody interested in learning about the importance of abstraction and group theory can join this course, including:

Seniors in School
Science Undergraduates
Engineering Undergraduates

Admission Details

Step 1: Click on this link: https://onlinecourses.nptel.ac.in/noc20_ma28/preview. It will direct you to the ‘Groups: Motion, Symmetry, and Puzzles’ course page on SWAYAM’s website.

Step 2: Look for the ‘Sign-In/Register button and click on it.

Step 3: Log in to your SWAYAM account, or through your Facebook, Google, or Microsoft account. Alternatively, you can create a new account on SWAYAM.

Step 4: Follow the on-screen instructions, provide the necessary details, and complete the registration.

Application Details

Learners need not fill out any application forms to join the Groups: Motion, Symmetry and Puzzles programme. They can apply for free just by logging in to their SWAYAM account or through their Facebook/Google/Microsoft account.

The Syllabus

Introduction and purpose of the course
Action and motion
need of definition of a group
Burnside’s lemma
counting of orbits

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

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

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

Evaluation process

To get the Groups: Motion, Symmetry, and Puzzles course certificate, you will have to appear for the term-end test and pass it. You can do that by paying the examination fee (Rs. 1,000), visiting any one of the designated exam centres, writing the exam, and meeting the certification criteria specified below:

The Average Assignment Score should be a minimum of 10/25.
The Exam Score should be at least 30/75.

If the candidate fails to satisfy any one of these conditions, he/she will be ineligible for certification, even if their Total Score is more than 40/100. These scores are calculated as under:

Average Assignment Score - 25% of the average score in the three best assignments (out of four)

Exam Score - 75% of the marks obtained in the term-end, proctored examination (out of 100)

Instructors

IISER Mohali Frequently Asked Questions (FAQ's)

1: What are the prerequisites for the Groups: Motion, Symmetry and Puzzles programme?

A school-level understanding of coordinate geometry, and working knowledge of matrices, are the prerequisites for taking the Groups: Motion, Symmetry, and Puzzles certification course.

2: How can I assess my learning in the Groups: Motion, Symmetry and Puzzles programme?

There are four assignments in the curriculum to help you assess your learning. You can also opt for the term-end proctored exam, which is a paid feature.

3: Do I have to take the term-end exam?

No, the term-end exam is optional. However, if you don’t take the exam, you will be ineligible for certification.

4: Can I write the term-end exam from home?

No, you must write the term-end certification exam at one of the designated exam centres.

5: How soon can I finish the Groups: Motion, Symmetry and Puzzles online course?

You can complete the Groups: Motion, Symmetry, and Puzzles online programme in four short weeks.