The purpose of this series is to introduce undergraduates to the varied areas of current

research in mathematics; and this text, of all in the series, most clearly achieves that goal. There are six essays here written by different authors. The best is the introduction to Morse theory by Forman. This author is gifted with the ability to know when to include and exclude detail so as to not lose the developing intuitive thrust. What this book recognizes, perhaps not explicitly, is that there are different learning styles amoung undergraduates and this text has something to offer in this regard. For example, many undergraduates need to see numbers computed and be connected to a physical experiment in order to grasp and motivate the math. The essay on modeling traffic flow and the one on the inquiry into plucked strings will satisfy those readers. The more legalistic undergrads will appreciate the minimal surfaces essays. Since the entire book seems to have been written by the math faculty at Rice university, it seems that whoever put that department together did a great job of eclectic casting in assembling such a talented group of teachers.

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