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Motion, Symmetry and Puzzles

  • Course level: Beginner

Description

Motion, Symmetry, and Puzzles

The goal of this course is to encourage participants to learn about and enjoy different elements of groups.

The focus of the course is on why groups should be studied rather than group theory. The course would also provide insight into why abstraction is such an important technique in mathematics that it demands more attention.

COURSE PLAN

WEEK 1:  INTRODUCTION AND PURPOSE OF THE COURSE Action and motion, the necessity to define a group, Burnside’s lemma, and orbit counting

Week 2: Parity verifying groupings, groups, and problems Groups and graphs, Rubik’s group, 15-puzzle group, Words about groups, unrestricted groups

Week 3: Review of Rubik’s group, introduction to GAP Representations of groups, groups, and matrices Linear transformations and groups are two things that come to mind while thinking about linear transformations

Week 4: From Kourovka’s book: Platonic solids and associated symmetry groups, Groups in several disciplines of mathematics

TARGET AUDIENCE: Anyone interested in learning about the importance of group theory. These may be senior high school students, science and engineering undergraduates, or anyone interested in learning why abstraction is useful.

Topics for this course

17 Lessons

Introduction_Groups:Motion, Symmetry & Puzzles

Introduction to the Course00:00:00
Parity and puzzles 0500:00:00
Groups and parity 0400:00:00
Groups acting on a set an object 0200:00:00
Cosets, quotients and homomorphisms 0700:00:00
Cosets, quotients and homomorphisms 0700:00:00
GAP through Rubik’s cube 1200:00:00
Generators and relations 0600:00:00
Introduction to GAP 1100:00:00
Rotational symmetries of platonic solids 0900:00:00
Symmetries of plane and wallpapers 1000:00:00
Cayley graphs of groups 0800:00:00
Representing abstract groups00:00:00
A quick introduction to group representations00:00:00
Rotations and quaternions00:00:00
Rotational symmetries of platonic solids00:00:00
Finite subgroups of SO(3)00:00:00
Free

Enrolment validity: Lifetime

Requirements

  • Basic coordinate geometry and matrices knowledge