This course on Graph Theory aims to help learners understand and apply various concepts and theorems in graph theory. By the end of the course, students will be able to analyze and solve problems related to handshaking lemma, Eulerian paths, Hamiltonian paths, planar graphs, coloring theorems, trees, and spanning trees. The course teaches skills such as graph visualization, theorem proving, and problem-solving. The teaching method includes lectures, examples, and practical exercises. This course is intended for individuals interested in mathematics, computer science, or related fields who want to deepen their understanding of graph theory concepts and their applications.
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
