Maths: The Fun Parts
summary
Shows sets, groups and graphs using TypeScript examples and light Rust attempt, proves an Eulerian circuit iff every vertex has even degree, and builds a Hamiltonian circuit finder (implemented as a petgraph Rust pull request using Frank Rubin 1974 rules) to solve Secret Santa as a directed Hamiltonian cycle; notes bugs in naive graph code, that a Rubik’s Cube group has about 43 quintillion Rubik's Cube states, and that the Rust PR works but remains unmerged.
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chapters (20)
- 0:00Introduction
- 1:46Clear thinking with shared language
- 3:52Sets as membership
- 7:21Set intersections and unions
- 12:37Subsets defined
- 15:50Infinite sets properties
- 19:44Groups as arithmetic systems
- 23:40Group closure and modular
- 25:44Group identity necessity
- 29:34Group inverses role
- 33:50Non-commutative groups and symmetries
- 42:48Graphs as dots and lines
- 47:08Connected and disconnected graphs
- 51:21Vertex degrees calculation
- 52:24Eulerian circuits
- 58:54Directed graphs and Secret Santa
- 1:03:05Hamiltonian circuits complexity
- 1:08:02Infinite sets and Russell's Paradox
- 1:11:34Monster group and Four Color theorem
- 1:15:53Q&A
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