Daniel J. Velleman's How to Prove It: A Structured Approach
Proofs play a central role in advanced
Mathematics and theoretical computer science, yet many students struggle the first time they take a course in which proofs play a significant role. This bestselling text's third edition helps students transition from solving problems to proving theorems by teaching them the techniques needed to read and write proofs. Featuring over 150 new exercises and a new chapter on number
Theory, this new edition introduces students to the world of advanced
Mathematics through the mastery of proofs. The book begins with the
Basic concepts of
Logic and set
Theory to familiarize students with the language of
Mathematics and how it is interpreted. These concepts are used as the basis for an analysis of techniques that can be used to build up complex proofs step by step, using detailed 'scratch work' sections to expose the
Machinery of proofs about numbers, sets, relations, and functions. Assuming no background beyond standard high school
Mathematics, this book will be useful to anyone interested in
Logic and proofs: computer scientists, philosophers, linguists, and, of course, mathematicians.
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Advanced Mathematics
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