How to Prove It: A Structured Approach (Paperback)

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.

證明在高等數學和理論計算機科學中扮演著核心角色，然而許多學生在第一次修讀需要大量證明的課程時會遇到困難。這本暢銷書的第三版幫助學生從解決問題轉向證明定理，教授他們閱讀和撰寫證明所需的技巧。這個新版增加了150多個新練習題和一個關於數論的新章節，通過掌握證明的技巧，引導學生進入高等數學的世界。本書從邏輯和集合論的基本概念開始，使學生熟悉數學的語言和解釋方式。這些概念被用作分析建立複雜證明的技巧的基礎，逐步使用詳細的“草稿”部分揭示有關數字、集合、關係和函數的證明機制。假設讀者除了標準高中數學之外沒有其他背景知識，本書對於任何對邏輯和證明感興趣的人都很有用：計算機科學家、哲學家、語言學家和當然還有數學家。