(1) MTH 461 General Topology, Dr. Irwin E. Schochetman
A study of topological spaces and continuous functions. Separation and countability properties, connectedness, compactness and local properties.
A NOTE FROM PROFESSOR LIPMAN: Topology grew out of geometry. It is the foundation of analysis -- the study of functions. Topology is fun because it plays with your intuition and really encourages your mathematical creativity. It also requires clear and careful reasoning. The reward is broader horizons and a deep understanding of and appreciation for the properties of the Real numbers.
(2) APM 405 Introduction to Graph Theory, Dr. Eddie Cheng
This is a sophomore level course. Topics include paths and cycles, colouring, independent sets, spanning trees, shortest paths, planar graphs, and applications such as the game Instant Insanity, scheduling problems and facilities design.
A NOTE FROM PROFESSOR LIPMAN: I love Graph Theory. You start with an incredibly simple definition and grow rapidly to using sophisticated tools to attack important real applications. Almost any theoretical question you can answer about graphs has practical economic value. Besides, you get to draw a lot of pictures.