Many students have trouble the first time they take a mathematics course in which proofs play a significant role. This new edition of Velleman's successful text will prepare students to make the transition from solving problems to proving theorems by teaching them the techniques needed to read and write 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 a step-by-step breakdown of the most important techniques used in constructing proofs. The author shows how complex proofs are built up from these smaller steps, using detailed 'scratch work' sections to expose the machinery of proofs about the natural numbers, relations, functions, and infinite sets. To give students the opportunity to construct their own proofs, this new edition contains over 200 new exercises, selected solutions, and an introduction to Proof Designer software. No background beyond standard high school mathematics is assumed. This book will be useful to anyone interested in logic and proofs: computer scientists, philosophers, linguists, and of course mathematicians.
發表於2024-11-21
How to Prove It 2024 pdf epub mobi 電子書 下載
圖書標籤: 數學 思維 Mathematics 數理邏輯 數學證明 邏輯學 方法論 證明論
還在豆瓣時讀瞭一半的書,最近終於撿起來讀完。最後一章關於 infinity 的一些定理證明還是看不太懂,過段時間再讀一遍好瞭。書後麵有答案,不過我答的題不是很多,畢竟每道題都寫的話,早晨一下子就用光瞭,唉 ……
評分可能是由於高中及之前數學學習方式殘留的習慣,感覺這本書對解數學證明題幫助並沒那麼大,盡管作者寫得不厭其煩甚至有些囉嗦。就培養所謂mathematical maturity, only God knows...權當作補邏輯和素樸集閤論基礎的教材使瞭(感謝老師放慢進度救我狗命)。但可能對於中學生來說還是挺有價值的。
評分坑爹的殺手。。。
評分坑爹的殺手。。。
評分還在豆瓣時讀瞭一半的書,最近終於撿起來讀完。最後一章關於 infinity 的一些定理證明還是看不太懂,過段時間再讀一遍好瞭。書後麵有答案,不過我答的題不是很多,畢竟每道題都寫的話,早晨一下子就用光瞭,唉 ……
How to Prove It 2024 pdf epub mobi 電子書 下載