Motion, Symmetry and Puzzles

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About Course

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.

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Course Content

Introduction_Groups:Motion, Symmetry & Puzzles

  • Introduction to the Course
    00:00
  • Parity and puzzles 05
    00:00
  • Groups and parity 04
    00:00
  • Groups acting on a set an object 02
    00:00
  • Cosets, quotients and homomorphisms 07
    00:00
  • Cosets, quotients and homomorphisms 07
    00:00
  • GAP through Rubik’s cube 12
    00:00
  • Generators and relations 06
    00:00
  • Introduction to GAP 11
    00:00
  • Rotational symmetries of platonic solids 09
    00:00
  • Symmetries of plane and wallpapers 10
    00:00
  • Cayley graphs of groups 08
    00:00
  • Representing abstract groups
    00:00
  • A quick introduction to group representations
    00:00
  • Rotations and quaternions
    00:00
  • Rotational symmetries of platonic solids
    00:00
  • Finite subgroups of SO(3)
    00:00

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