数学证明
Mathematical proofs
Gary Chartrand、Albert D. Polimeni、Zhang, Ping、Ping Zhang · 初版 2002 年
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20位读者提及
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为什么值得读
- 系统讲授通用的数学证明方法与策略
- 全面引入作为证明基础的集合论内容
- 专为通往进阶数学学习的过渡阶段设计
Mathematical Proofs: A Transition to Advanced Mathematics, 4th Edition 向学生系统介绍了证明技巧、证明分析，以及如何撰写既符合数学规范又逻辑清晰的证明过程。全书编写风格亲切易懂，扎实介绍了关系、函数和集合基数等主题，并提供了数论、组合学和微积分等可选进阶内容。书中的习题因其构思精巧和富有创意而广受读者好评，有助于学生从理解概念逐步过渡到
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……带你入门的一些参考：Richard Hammack 的《证明之书》：https://www.people.vcu.edu/~rhammack/BookOfProof/ Susanna Epp 的《离散数学》：https://www.amazon.com/Discrete-Mathematics-Applications-Sus... Chartrand 等人合著的《数学证明：通往高等数学的过渡》：https://www.amazon.com/Mathematical-Proofs-Transition-Advanc... Lara Alcock 的《如何思考分析》：https://www.amazon.com/Think-About-Analysis-Lara-Alcock/dp/0...……
…to get you started: Book of Proof by Richard Hammack: https://www.people.vcu.edu/~rhammack/BookOfProof/ Discrete Math by Susanna Epp: https://www.amazon.com/Discrete-Mathematics-Applications-Sus... Mathematical Proofs: A Transition to Advanced Mathematics by Chartrand et al: https://www.amazon.com/Mathematical-Proofs-Transition-Advanc... How to Think About Analysis by Lara Alcock: https://www.amazon.com/Think-About-Analysis-Lara-Alcock/dp/0...…
……Chartrand 等人，[3] Lara Alcock 的《如何思考分析》，[4] Nancy Rodgers 的《学会推理》[1] https://books.google.com/books?id=PPc_2qUhXrAC&pg=PA1&source... [2] https://www.amazon.com/Mathematical-Proofs-Transition-Advanc... [3] https://books.google.com/books?id=n0tuBAAAQBAJ&pg=PA4&source... [4] https://books.google.com/books?id=J9RLuhDRWGQC&pg=PR6&source... 如果你预算有限，可以看看免费的……
…Chartrand et al, [3] How to Think about Analysis by Lara Alcock, [4] Learning to Reason by Nancy Rodgers [1] https://books.google.com/books?id=PPc_2qUhXrAC&pg=PA1&source... [2] https://www.amazon.com/Mathematical-Proofs-Transition-Advanc... [3] https://books.google.com/books?id=n0tuBAAAQBAJ&pg=PA4&source... [4] https://books.google.com/books?id=J9RLuhDRWGQC&pg=PR6&source... If you're on a budget, check out the free…
……以后打算读研的话。如果想看重以证明为核心的内容覆盖，你可以用一本通用的证明策略书来辅助阅读，比如：1. Chartrand, Polimeni, Zhang 合著的《数学证明》2. Daniel Velleman 的《怎样证明它》（How to Prove It）第一本 Chartrand 等人的书更偏传统教材，在背景中对集合论做了全面的介绍……
…plan on going to graduate school later on. For a coverage of the material that emphasizes a proof-based approach, you can supplement your reading with a book on general proof strategies, such as: 1. Mathematical Proofs by Chartrand, Polmeni, Zhang 2. How to Prove It by Daniel Velleman The first book by Chartrand et al is more of a traditional textbook and gives a comprehensive introduction to set theory in the context…
去读一本证明导向的入门书吧，比如《证明之书》，或者我个人最喜欢的：https://www.amazon.ca/Mathematical-Proofs-Transition-Advance...
Read an introduction to proofs oriented book such as Book of Proof or my personal favorite: https://www.amazon.ca/Mathematical-Proofs-Transition-Advance...
Chartrand、Polimeni 和 Zhang 合著的《数学证明：通往高等数学的过渡》。这是我当年“数学证明入门”课用的教材，写得太牛了。绝对对得起昂贵的价格。另一本不错的选修书是……
Mathematical Proofs: A Transition to Advanced Mathematics by Chartrand Polimeni and Zhang. This was the textbook used in my intro to proofs course and it was fantastic. Worth the steep price. Another good one that was optional…
……Susanna Epp 著 https://www.amazon.com/Discrete-Mathematics-Applications-Sus... [2] Steve Warner 的《初学者的纯数学》https://www.amazon.com/Pure-Mathematics-Beginners-Rigorous-I... [3] Gary Chartrand 等人的《数学证明》https://www.amazon.com/Mathematical-Proofs-Transition-Advanc... [4] G.A.V. Pai 的《数据结构与算法：概念、技术与应用》https://www.amazon.com/gp/product/0070699577/ref=ppx_yo_dt_b...……
…by Susanna Epp https://www.amazon.com/Discrete-Mathematics-Applications-Sus... [2] Pure Mathematics for Beginners by Steve Warner https://www.amazon.com/Pure-Mathematics-Beginners-Rigorous-I... [3] Mathematical Proofs by Gary Chartrand et al https://www.amazon.com/Mathematical-Proofs-Transition-Advanc... [4] Data Structures and Algorithms: Concepts, Techniques and Applications by G.A.V. Pai https://www.amazon.com/gp/product/0070699577/ref=ppx_yo_dt_b...…