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Groups: Motion, symmetry and puzzles

Indian Institute of Science Education and Research, Mohali and NPTEL via Swayam


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.


Week 1 : Introduction and purpose of the course, Action and motion, need of definition of a group, Burnside’s lemma, counting of orbitsWeek 2 : Groups in parity checking, groups and puzzles, Rubik’s group, 15-puzzle group, groups and graphs ,Words on groups, free groupsWeek 3 : Introduction to GAP, revisiting Rubik’s group,Groups and matrices, representations of groups,Linear transformations and groupsWeek 4 : Platonic solids and their symmetry groups,Groups across various branches of mathematics, From Kourovka’s book

Taught by

Prof. Amit Kulshrestha

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