Introduction to graph theory including the basic definitions and theorems and some more advanced topics which drive much current research in graph theory: Ramsey's Theorem, random graph theory and, if time permits, Szemeredi's regularity lemma. Graphs will be studied as abstract objects; however graph theory is also of interest to applied mathematicians because graphs are natural models for networks (social, electric,...). Prerequisite: Math 310 or a roughly equivalent course, or permission of instructor. Students should know what a proof is and how to produce one. Some informal understanding of probability will be helpful, but students need not have taken a probability course.
Course Attributes: FA NSM; AR NSM; AS NSM