…[1]. It follows Rudin closely and as opposed to many other analysis books meant to "better explain" stuff, it goes deep into the trenches and actually tackles the subject. [1] https://www.amazon.com/Real-Analysis-Lifesaver-Understand-Pr... I think time invested into studying real analysis pays off because then you can later study measure theory, functional analysis and more advanced probability to deal with curse of dimensionality…
……罗杰斯（Rodgers）写的：https://www.amazon.com/Learning-Reason-Introduction-Logic-Re... 爱德华·沙纳曼（Edward Scheinerman）的《数学：离散导论》：https://www.amazon.com/Mathematics-Discrete-Introduction-Edw... 拉菲·格林伯格（Rafi Grinberg）的《普林斯顿实分析读本》（The Real Analysis Lifesaver）：https://www.amazon.com/Real-Analysis-Lifesaver-Understand-Pr... 库尔迪普·辛格（Kuldeep Singh）的《线性代数：一步一步学》：https://www.amazon.com/Linear-Algebra-Step-Kuldeep-Singh/dp/...……
…Rodgers: https://www.amazon.com/Learning-Reason-Introduction-Logic-Re... Mathematics: A Discrete Introduction by Edward Scheinerman: 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/...…
…concepts of convergence and boundlessness and the latter, in addition to what Alcock does, introduces a bit of topology on the real line. Speaking of topology necessary for analysis, Rafi Grinberg's "Real Analysis Lifesaver" kicks ass. It tackles topology and convergence in the Euclidean Spaces (a leg up on the above-mentioned books). These extremely easy to read books (read in the given order) would easily prepare a dedicated…
…traditionalist Riemann integral. Because why not. Links: https://www.amazon.com/Think-About-Analysis-Lara-Alcock-eboo... https://www.amazon.com/Real-Analysis-Long-Form-Mathematics-T... https://www.amazon.com/Real-Analysis-Lifesaver-Understand-Pr... https://link.springer.com/content/pdf/10.1007%2F978-3-030-33... https://www.amazon.com/Introduction-Analysis-Number-Integral... ------------------- Now to a few examples of Indian…
……[1]。这本书紧跟鲁丁（Rudin）的编排路线，而且不像很多其他打着“更好懂”旗号的实分析教材那样浮于表面，它直面硬骨头，深入核心去攻克这些数学难点。[1] https://www.amazon.com/Real-Analysis-Lifesaver-Understand-Pr... 我觉得花时间钻研实分析是非常划算的，因为之后你再去学测度论、泛函分析以及更高阶的概率论来应对维度灾难……
…[1]. It follows Rudin closely and as opposed to many other analysis books meant to "better explain" stuff, it goes deep into the trenches and actually tackles the subject. [1] https://www.amazon.com/Real-Analysis-Lifesaver-Understand-Pr... I think time invested into studying real analysis pays off because then you can later study measure theory, functional analysis and more advanced probability to deal with curse of dimensionality…
……罗杰斯（Rodgers）写的：https://www.amazon.com/Learning-Reason-Introduction-Logic-Re... 爱德华·沙纳曼（Edward Scheinerman）的《数学：离散导论》：https://www.amazon.com/Mathematics-Discrete-Introduction-Edw... 拉菲·格林伯格（Rafi Grinberg）的《普林斯顿实分析读本》（The Real Analysis Lifesaver）：https://www.amazon.com/Real-Analysis-Lifesaver-Understand-Pr... 库尔迪普·辛格（Kuldeep Singh）的《线性代数：一步一步学》：https://www.amazon.com/Linear-Algebra-Step-Kuldeep-Singh/dp/...……
…Rodgers: https://www.amazon.com/Learning-Reason-Introduction-Logic-Re... Mathematics: A Discrete Introduction by Edward Scheinerman: 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/...…
……收敛性和无界性的概念，而后者除了涵盖奥尔科克（Alcock）讲的内容外，还引入了一点实数线上的拓扑学知识。说到实分析必备的拓扑知识，拉菲·格林伯格写的《普林斯顿实分析读本》（Real Analysis Lifesaver）简直绝了。它直接拿下了欧几里得空间里的拓扑和收敛性（比上面提到的几本书更胜一筹）。这些读起来极其通俗易懂的书（按给出的顺序阅读）完全可以轻松帮一个有毅力的……
…concepts of convergence and boundlessness and the latter, in addition to what Alcock does, introduces a bit of topology on the real line. Speaking of topology necessary for analysis, Rafi Grinberg's "Real Analysis Lifesaver" kicks ass. It tackles topology and convergence in the Euclidean Spaces (a leg up on the above-mentioned books). These extremely easy to read books (read in the given order) would easily prepare a dedicated…
……传统的黎曼积分。毕竟干嘛不学呢。链接：https://www.amazon.com/Think-About-Analysis-Lara-Alcock-eboo... https://www.amazon.com/Real-Analysis-Long-Form-Mathematics-T... https://www.amazon.com/Real-Analysis-Lifesaver-Understand-Pr... https://link.springer.com/content/pdf/10.1007%2F978-3-030-33... https://www.amazon.com/Introduction-Analysis-Number-Integral... ------------------- 下面来看几个印度的……
…traditionalist Riemann integral. Because why not. Links: https://www.amazon.com/Think-About-Analysis-Lara-Alcock-eboo... https://www.amazon.com/Real-Analysis-Long-Form-Mathematics-T... https://www.amazon.com/Real-Analysis-Lifesaver-Understand-Pr... https://link.springer.com/content/pdf/10.1007%2F978-3-030-33... https://www.amazon.com/Introduction-Analysis-Number-Integral... ------------------- Now to a few examples of Indian…