Group Theory For Children (Updating)
1. Groups of integers:
Primes and Groups.
- What are primes? What are primes less than 100?
- Groups
, , . Identities and Inverses. Commutativity. - Primitive elements (aka. generators) in
. (Try .)
2. Dihedral groups and Platonic solids:
Regular n-gons and polyhedrons.
- Geometry of Triangles: Regular Triangles and its angles (
). PDF with its multiplication table. This is the first non-commutative group! PDF - Angles, n-gons and circles.
- There are ONLY 5 regular polyhedrons. See: https://gogeometry.com/solid/platonic-solids-html5-animation-ipad-nexus-7.htm
- Euler characteristics:
for all polyhedrons.
3. Linear algebra and General linear group
Matrix
1. Identity matrix:2. Symmetric matrix:
3. Echelon matrix:
4. Upper/lower triangle matrix:
Matrix and vectors, linear space of
Multiplications, non-community.
Visualization of matrix and Vectors:
Group Theory For Children (Updating)
http://jules-zhu.github.io/danny/GroupTheoryForChildren.html