……https://www.amazon.com/Mathematics-Discrete-Introduction-Edw... 《The Real Analysis Lifesaver: All the Tools You Need to Understand Proofs》作者 Rafi Grinberg：https://www.amazon.com/Real-Analysis-Lifesaver-Understand-Pr... 《Linear Algebra: Step by Step》作者 Kuldeep Singh：https://www.amazon.com/Linear-Algebra-Step-Kuldeep-Singh/dp/... 《Abstract Algebra: A Student-Friendly Approach》作者 Dos Reis：https://www.amazon.com/Abstract-Algebra-Student-Friendly-Lau...……
…https://www.amazon.com/Mathematics-Discrete-Introduction-Edw... The Real Analysis Lifesaver: All the Tools You Need to Understand Proofs by Rafi Grinberg: https://www.amazon.com/Real-Analysis-Lifesaver-Understand-Pr... Linear Algebra: Step by Step by Kuldeep Singh: https://www.amazon.com/Linear-Algebra-Step-Kuldeep-Singh/dp/... Abstract Algebra: A Student-Friendly Approach by the Dos Reis: https://www.amazon.com/Abstract-Algebra-Student-Friendly-Lau...…
……在某种运算下构成半群：我们只需验证结合律。要掌握这些内容，我推荐以下书籍：Richard Hammack 的《Book of Proof》（行业工具），Kuldeep Singh 的《Linear Algebra》（严谨教程：兼具教科书的严谨性和教程的易用性），Dos Reis 的《Abstract Algebra》（严谨教程），Lara Alcock 的《Real Analysis》（这本书让人……
…form a semigroup under a certain operation: we'll just check it for associativity. To get a hang of this stuff I recommend the following books: Book of Proof by Richard Hammack (tools of the trade) Linear Algebra by Kuldeep Singh (rigorous tutorial: combines the rigor of a textbook and the ease of use of tutorial) Abstract Algebra by the Dos Reis (rigorous tutorial) Real Analysis by Lara Alcock (this books makes…
…this book you'll stop fearing the word "proof" and start demanding it wherever you go. Link: https://www.people.vcu.edu/~rhammack/BookOfProof/ 2. The book by Don Shimamoto is super trivial if you know linear algebra. The best books in the genre (imo) are (a) Linear Algebra: Step by Step by Kuldeep Singh whose secret is that he uses all the exercises from other LA books as his 100% worked out examples (which seems…
…though, as this one wasn't my first analysis encounter. This book enters the pantheon of books that were tremendously helpful to me: Learning to Reason by Nancy Rodgers, Discrete Math by Susanna Epp and Linear Algebra by Kuldeep Singh. [0] https://www.amazon.com/Real-Analysis-Long-Form-Mathematics-T...
…probability theory are very helpful. This free book [1] gives a sampling of such topics. As preparation, one can start by looking at pre-real-analysis books like the ones by Lara Alcock and Jay Cummings, Linear Algebra by Kuldeep Singh and Probability Theory by Dimitri Bertsekas/Tsitsiklis. These books are very easy to read. There are also introductory books that give a bare-bones sampling of most undergrad math subjects…
……https://www.amazon.com/Mathematics-Discrete-Introduction-Edw... 《The Real Analysis Lifesaver: All the Tools You Need to Understand Proofs》作者 Rafi Grinberg：https://www.amazon.com/Real-Analysis-Lifesaver-Understand-Pr... 《Linear Algebra: Step by Step》作者 Kuldeep Singh：https://www.amazon.com/Linear-Algebra-Step-Kuldeep-Singh/dp/... 《Abstract Algebra: A Student-Friendly Approach》作者 Dos Reis：https://www.amazon.com/Abstract-Algebra-Student-Friendly-Lau...……
…https://www.amazon.com/Mathematics-Discrete-Introduction-Edw... The Real Analysis Lifesaver: All the Tools You Need to Understand Proofs by Rafi Grinberg: https://www.amazon.com/Real-Analysis-Lifesaver-Understand-Pr... Linear Algebra: Step by Step by Kuldeep Singh: https://www.amazon.com/Linear-Algebra-Step-Kuldeep-Singh/dp/... Abstract Algebra: A Student-Friendly Approach by the Dos Reis: https://www.amazon.com/Abstract-Algebra-Student-Friendly-Lau...…
……作者 Susanna Epp 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_An... [6] Kuldeep Singh 的《Linear Algebra》 https://www.google.com/books/edition/Linear_Algebra/BJNoAgAA...
…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...
……在某种运算下构成半群：我们只需验证结合律。要掌握这些内容，我推荐以下书籍：Richard Hammack 的《Book of Proof》（行业工具），Kuldeep Singh 的《Linear Algebra》（严谨教程：兼具教科书的严谨性和教程的易用性），Dos Reis 的《Abstract Algebra》（严谨教程），Lara Alcock 的《Real Analysis》（这本书让人……
…form a semigroup under a certain operation: we'll just check it for associativity. To get a hang of this stuff I recommend the following books: Book of Proof by Richard Hammack (tools of the trade) Linear Algebra by Kuldeep Singh (rigorous tutorial: combines the rigor of a textbook and the ease of use of tutorial) Abstract Algebra by the Dos Reis (rigorous tutorial) Real Analysis by Lara Alcock (this books makes…
……读完这本书，你将不再害怕“证明”这个词，并开始在任何地方都要求给出证明。链接：https://www.people.vcu.edu/~rhammack/BookOfProof/ 2. 如果你懂线性代数，Don Shimamoto 的那本书就太琐碎了。这个类型里最好的书（在我看来）是 (a) Kuldeep Singh 的《Linear Algebra: Step by Step》，它的秘诀在于他把其他线性代数书里的所有习题都拿来当作自己 100% 详解的例题（这似乎……
…this book you'll stop fearing the word "proof" and start demanding it wherever you go. Link: https://www.people.vcu.edu/~rhammack/BookOfProof/ 2. The book by Don Shimamoto is super trivial if you know linear algebra. The best books in the genre (imo) are (a) Linear Algebra: Step by Step by Kuldeep Singh whose secret is that he uses all the exercises from other LA books as his 100% worked out examples (which seems…
……不过，因为这不是我第一次接触分析学。这本书进入了对帮助极大的书之列：《Learning to Reason》（Nancy Rodgers）、《Discrete Math》（Susanna Epp）和 Kuldeep Singh 的《Linear Algebra》。[0] https://www.amazon.com/Real-Analysis-Long-Form-Mathematics-T...
…though, as this one wasn't my first analysis encounter. This book enters the pantheon of books that were tremendously helpful to me: Learning to Reason by Nancy Rodgers, Discrete Math by Susanna Epp and Linear Algebra by Kuldeep Singh. [0] https://www.amazon.com/Real-Analysis-Long-Form-Mathematics-T...
……概率论非常有帮助。这本免费书 [1] 给出了这类主题的样本。作为准备，可以先看 Lara Alcock 和 Jay Cummings 等人写的实分析预备书、Kuldeep Singh 的《Linear Algebra》以及 Dimitri Bertsekas/Tsitsiklis 的《Probability Theory》。这些书都非常易读。还有一些入门书对大多数本科数学科目给出了最基础的样本……
…probability theory are very helpful. This free book [1] gives a sampling of such topics. As preparation, one can start by looking at pre-real-analysis books like the ones by Lara Alcock and Jay Cummings, Linear Algebra by Kuldeep Singh and Probability Theory by Dimitri Bertsekas/Tsitsiklis. These books are very easy to read. There are also introductory books that give a bare-bones sampling of most undergrad math subjects…