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Graph theory is a young and exciting area of discrete mathematics. For our purposes, a graph is just a bunch of dots together with lines or curves joining certain pairs of these dots. Though at first glance graphs may seem like simple objects to study, the field of graph theory contains some of the deepest and most beautiful mathematics of the last fifty years. Being an extremely visual field, many problems in graph theory are easily stated, yet have complex solutions with far reaching implications and applications. Problem solving, class discussions, and student examples will guide our exploration not only of the mathematics of graph theory, but also illustrate how graph theory arises in fields such as computer science, linguistics, chemistry, game theory, and many others.
Rough class notes: One, Two, Three, Four, Five, Six, Seven, Eight, Nine, Ten, Eleven, Twelve Picture-Hanging Puzzles |