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Description
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This text provides a systematic approach for teaching undergraduate and graduate students how to read, understand, think about, and do proofs. The approach is to catagorize, identify, and explain (at the student's level) the various techniques that are used repeatedly in all proofs, regardless of the subject in which the proofs arise. How to Read and Do Proofs 4/e also explains when each technique is likely to be used, based on certain key words that appear in the problem under consideration. Doing so enables students to choose a technique consciously, based on the form of the problem. Students are taught how to read proofs that arise in textbooks and other mathematical literature by understanding which techniques are used and how they are ap-plied. It shows how any proof can be understood as a sequence of the individual techniques. The goal is to enable students to learn advanced mathematics on their own. This book is suitable as: (1) a text for a transition-to-advanced-math course, (2) a supplement to any course involving proofs, and (3) self-guided teaching.
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