Proof patterns /

There is no shortage of books for introductory courses, but far too few are "second books." Joshi (Univ. of Melbourne, Australia) has written a companion to the standard introductory proofs course for undergraduates. It presents a "new pattern-based approach to learning proof methods," and its examples are drawn from various topics far beyond the standard set and number theory proofs. The premise of his book is brilliant, relevant, and essential but completely unoriginal. Many introductory texts follow a similar proof-template approach, including Edward Scheinerman's clever text on discrete mathematics. Joshi presents each new proof pattern in its own separate chapter. Unfortunately, only half the chapters present actual proof patterns. The remaining chapters are tangential excursions into algebra, analysis, and game theory, and are more distracting than helpful. Only one pattern ("Intersection-Enclosure and Generation") is actually beyond the topics of a first-semester course. There are few examples and fewer exercises, most of which focus on frivolous details unrelated to their patterns. Without a thorough explanation of how the patterns can be used outside the author's examples, readers will be left on their own to learn any effective proof templates. Summing Up: Not recommended. --Andrew Misseldine, Southern Utah University