Zeitz Paul. The Art and Craft of Mathematical Problem Solving

The Great Courses, 2010. — 151 p.This course is devoted to the systematic development of investigation methods, strategies, and tactics. Besides this “problemsolvingology,” I will introduce you to mathematical folklore: classic problems as well as mathematical disciplines that play an important role in the problem-solving world. For example, no course on problem solving is complete without some discussion of graph theory, which is an important branch of math on its own but is also a very accessible laboratory for exploring problem-solving themes. Many of the lectures will include small amounts of new mathematics that we will build up and stitch together as the course progresses. The topics are largely drawn from discrete mathematics (graph theory, integer sequences, number theory, and combinatorics), because this branch of math does not require advanced skills such as calculus. That does not mean it is easy, but we will move slowly and develop new ideas carefully. A small but important part of the course explores the culture of problem solving. I will draw on my experience as a competitor, coach, and problem writer for various regional, national, and international math contests, to make the little-known world of math Olympiads come to life. And I will discuss the recent educational reform movement (in which I am a key player) to bring Eastern European–inspired mathematical circles to the United States.