如何思考分析
How to Think About Analysis
Lara Alcock · 初版 2014 年
15人推荐
16位读者提及
16次提及
为什么值得读
- 适合作为进入数学分析前的过渡读物
- 并非习题教材而是学习方法指南
- 提供掌握高级数学分析的有效建议
Analysis 是大多数本科数学专业的核心课程。它优美、精妙且学有所得，但也很难。即使是最优秀的学生也会觉得它充满挑战，而毫无准备的人往往起初会觉得晦涩难懂。本书旨在确保没有任何学生需要打无准备之仗。
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……Mathematics Major - Alcock 3b. 证明书写：How to Prove It - A Structured Approach - Velleman 或 Book of Proof（第2版）- Hammack（免费的！）4. 数学分析：4a. 分析学的优质前置准备：How to Think About Analysis - Alcock 4b. Understanding Analysis（第2版）- Abbott 或 Yet Another Introduction to Analysis - Bryant（有完整解答）或 The How and Why of One Variable Calculus - Sasane 或 Mathematical Analysis……
…Mathematics Major - Alcock 3b. Proof writing: How to Prove It - A Structured Approach - Velleman OR Book of Proof (2nd ed) - Hammack (it's free!) 4. Mathematical Analysis: 4a. Good prep for Analysis: How to Think About Analysis - Alcock 4b. Understanding Analysis (2nd ed) - Abbott OR Yet Another Introduction to Analysis - Bryant (has full solutions) OR The How and Why of One Variable Calculus - Sasane OR Mathematical Analysis…
……自学的话是 Abbott 的《Understanding Analysis》，尤其是如果你能搞到答案手册的话，我觉得里面对证明的讲解非常透彻。3）我还会推荐 Lara Alcock 的《How to Think About Analysis》，这不是一本教科书，但里面有很多关于如何学好分析学的实用信息和建议。另外，虽然显而易见但也值得再强调一遍：如果你啃教材时看一页花的时间少于一小时，那……
…for self-study is Abbott, “Understanding analysis” particularly if you can get the solutions manual, I think the explanations of the proofs are very good. 3) I would also recommend Lara Alcock’s book “How to think about analysis”, which is NOT a textbook, but has a lot of useful information and advice on how to learn analysis. Also, obvious but worth repeating, if you are taking less than one hour per page to get through an…
……https://www.amazon.com/Discrete-Mathematics-Applications-Sus... Chartrand 等人的《Mathematical Proofs: A Transition to Advanced Mathematics》：https://www.amazon.com/Mathematical-Proofs-Transition-Advanc... Lara Alcock 的《How to Think About Analysis》：https://www.amazon.com/Think-About-Analysis-Lara-Alcock/dp/0... Nancy Rodgers 的《Learning to Reason: An Introduction to Logic, Sets, and Relations》：https://www.amazon.com/Learning-Reason-Introduction-Logic-Re...……
…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... Learning to Reason: An Introduction to Logic, Sets, and Relations by Nancy Rodgers: https://www.amazon.com/Learning-Reason-Introduction-Logic-Re...…
……而且最有趣的会是离散数学入门，或者所谓的“过渡（transition）”类书籍。比如，可以看看 [1] Susanna Epp 的《Discrete Math》、[2] Gary Chartrand 等人的《Transition to Advanced Math》、[3] Lara Alcock 的《How to Think about Analysis》、[4] Nancy Rodgers 的《Learning to Reason》 [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...……
…and funnest would be intro to discrete math or the so called "transition" books. For example, check out [1] Discrete Math by Susanna Epp, [2] Transition to Advanced Math by Gary 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...…
……Proof》（Richard Hammack 著）。网上有免费版：https://www.people.vcu.edu/~rhammack/BookOfProof/ [4] Susanna Epp 的《Discrete Math》https://www.google.com/books/edition/Discrete_Mathematics_wi... [5] Lara Alcock 的《How to Think About Analysis》https://www.google.com/books/edition/How_to_Think_about_Anal... [6] Kuldeep Singh 的《Linear Algebra》https://www.google.com/books/edition/Linear_Algebra/BJNoAgAA...
…Proof" by Richard Hammach. It's online free. https://www.people.vcu.edu/~rhammack/BookOfProof/ [4] "Discrete Math" by Susanna Epp https://www.google.com/books/edition/Discrete_Mathematics_wi... [5] "How to Think About Analysis" by Lara Alcock https://www.google.com/books/edition/How_to_Think_about_Anal... [6] "Linear Algebra" by Kuldeep Singh https://www.google.com/books/edition/Linear_Algebra/BJNoAgAA...
……有一阵子没碰代数了（比如 Strang 或者 Singh 的《Linear Algebra: Step by Step》）。然后是：线性代数 - Friedberg 等著；《Linear Algebra Done Right》- Axler；《Linear Algebra》- Hoffman & Kunze。实分析：《How to Think About Analysis》- Alcock；《Understanding Analysis》- Abbott；陶哲轩的 Analysis 教材；《Principles of Mathematical Analysis》- Rudin。拓扑学：《Topology》- Munkres；《Topology A Categorical Approach》- Tai-Danae Bradley, Tyler Bryson……
…algebra in a while (e.g. Strang or Linear Algebra: Step by Step by Singh). Then: Linear Algebra - Friedberg, et al Linear Algebra Done Right - Axler Linear Algebra - Hoffman & Kunze Real Analysis: How to Think About Analysis - Alcock Understanding Analysis - Abbott Tao's Analysis text Principles of Mathematical Analysis - Rudin Topology: Topology - Munkres Topology A Categorical Approach - Tai-Danae Bradley, Tyler Bryson,…