Explore the fascinating world of graph theory through a comprehensive series of lectures covering various topics from the Handshaking Lemma to Kirchhoff's Theorem. Delve into the mathematical concepts behind social distancing, analyze Eulerian and Hamiltonian paths, and uncover the intricacies of non-planar graphs. Investigate famous theorems such as the Four Color Theorem and Cayley's Tree Theorem, while also examining the philosophical significance of these mathematical principles. Apply graph theory to real-world scenarios, including understanding the spread of coronavirus, and gain insights into the structure and properties of different types of graphs, from simple planar graphs to complex polyhedra.
Overview
Syllabus
Making Sense of Coronavirus with Graph Theory.
Graph Theory 1: Handshaking Lemma.
Stand 6 ft apart! Social Distancing and Graph Theory.
Graph Theory 2: Eulerian Paths & Circuits.
Graph Theory 3: Hamiltonian Paths & Ore's Theorem.
Graph Theory 4: Non-Planar Graphs & Kuratowski's Theorem.
Graph Theory 5: Polyhedra, Planar Graphs, & F-E+V=2.
Graph Theory 6: Simple, Planar Graphs.
Graph Theory 7: Five Color Theorem.
Graph Theory 8: Four Color Theorem (Kempe's Proof).
Graph Theory 9: Philosophical Signifance of Four Color Theorem.
Graph Theory 10: Coloring Theorem for Sphere, Torus, and More.
Graph Theory 11: Trees.
Graph Theory 12: Cayley's Tree Theorem.
Graph Theory 13: Spanning Trees and Kirchhoff's Theorem.
Taught by
math at andrews
