…陶哲轩（Terence Tao，我已经读完了第一卷，现在在读第二卷，不过我其实把它们当成一本书）- Stephen Abbott 的《Understanding Analysis》- Starbird 和 Su 的《Topology Through Inquiry》- George F. Simmons 的《Introduction To Topology And Modern Analysis》。陶哲轩的书到目前为止简直太棒了，是非常通俗易懂的实分析（Real Analysis）入门教材。Abbott 的书也是很多人极力推荐的，从我读的前两章来看，我能…
…Terence Tao (I finished the first volume and am now on the second, but I consider them really one book) - "Understanding Analysis" by Stephen Abbott - "Topology Through Inquiry" by Starbird and Su - "Introduction To Topology And Modern Analysis" by George F. Simmons The Terence Tao books are amazing so far. Extremely readable introduction to Real Analysis. Abbott also came highly recommended and from reading the first couple chapters I can…
Simmons？哇！他可是个严肃认真的数学家，比如看他的 George F. Simmons《Introduction to Topology and Modern Analysis》（拓扑与现代分析引论）就知道了。我有一年夏天在范德堡大学参加 NSF 项目时学过这本书。当时我就觉得，他写数学书真的写得太牛了。
Simmons? WOW! He's a serious mathematician, e.g., as in his George F. Simmons, Introduction to Topology and Modern Analysis. I studied it one summer in an NSF program at Vanderbilt. Then I concluded that he is one heck of a good math writer.
…and Complex Analysis》，ISBN 07-054232-5，McGraw-Hill，纽约，1966年。---------------------------------------- 想要轻松搞懂度量空间（metric space），一本极为优雅的入门书是 George F. Simmons 的《Introduction to Topology and Modern Analysis》，McGraw Hill，纽约，1963年。======================================== 常微分方程（Ordinary Differential Equations）---------------------------------------- 线性代数很重要，在某些节点甚至至关重要，对于…
…and Complex Analysis', ISBN 07-054232-5, McGraw-Hill, New York, 1966. ---------------------------------------- An elegant introduction to how to get comfortable in metric space is George F. Simmons, 'Introduction to Topology and Modern Analysis', McGraw Hill, New York, 1963. ======================================== Ordinary Differential Equations ---------------------------------------- Linear algebra is important, as some points crucial, for…
…对偶的对偶，并在等号成立时称原空间是自反的（reflexive）。接着他们又想定义弱拓扑（weak topology）和弱*拓扑（weak* topology）等等。你可以在比如 G. Simmons 的《Introduction to Topology and Modern Analysis》里看到一部分这些内容，写得超级棒，虽然我从来没见过它有什么实际应用。在线性代数里捣鼓对偶性可以推导出伴随变换（adjoint transformations）。对我来说，这最后变成了大量细致的…
…duals of duals, and when there is equality say that the original space is reflexive. Then they want to define the weak topology and the weak* topology, etc. Can see some of this in, say, G. Simmons, Introduction to Topology and Modern Analysis, super nicely written book although I have never seen any applications for it. Pushing around duality in linear algebra can get to adjoint transformations. To me it turns out to be a lot of careful…
…纯数专业。如果在哪里学过一门抽象代数课，比如带一点群论，那可能会有帮助！研究生阶段：可能会从比如 Simmons 的《Introduction to Topology and Modern Analysis》里多学一点拓扑。所以，先把度量空间搞扎实，再开始学对偶性。接下来的重要一步是测度论和泛函分析课程。Simmons 的书会有所帮助。《Baby Rudin》将至关重要；Halmos 的…
…pure math major. If somewhere take a course in abstract algebra, e.g., with a little group theory, then that might help! Graduate School. Might learn a little more about topology, say, from Simmons, 'Introduction to Topology and Modern Analysis'. So, get good with metric spaces and get started on duality. The next big step is a course in measure theory and functional analysis. The Simmons work will help. Baby Rudin will be crucial; Halmos…
…在家里和办公室都备着：Rudin 的《Real and Complex Analysis》、Halmos 的《Finite Dimensional Vector Spaces》、Billingsley 的《Probability and Measure》、Kelley 的《General Topology》、Lang 的《Undergraduate Algebra》、Simmons 的《Introduction to Topology and Modern Analysis》、Parthasarathy 的《Probability Measures on Metric Spaces》、Whinston、Green 和 Mas-Colell 的《Microeconomic Theory》
…at both home and work: Rudin, Real and Complex Analysis Halmos, Finite Dimensional Vector Spaces Billingsley, Probability and Measure Kelley, General Topology Lang, Undergraduate Algebra Simmons, Introduction to Topology and Modern Analysis Parthasarathy, Probability Measures on Metric Spaces Whinston, Green and Mas-Colell, Microeconomic Theory
…陶哲轩（Terence Tao，我已经读完了第一卷，现在在读第二卷，不过我其实把它们当成一本书）- Stephen Abbott 的《Understanding Analysis》- Starbird 和 Su 的《Topology Through Inquiry》- George F. Simmons 的《Introduction To Topology And Modern Analysis》。陶哲轩的书到目前为止简直太棒了，是非常通俗易懂的实分析（Real Analysis）入门教材。Abbott 的书也是很多人极力推荐的，从我读的前两章来看，我能…
…Terence Tao (I finished the first volume and am now on the second, but I consider them really one book) - "Understanding Analysis" by Stephen Abbott - "Topology Through Inquiry" by Starbird and Su - "Introduction To Topology And Modern Analysis" by George F. Simmons The Terence Tao books are amazing so far. Extremely readable introduction to Real Analysis. Abbott also came highly recommended and from reading the first couple chapters I can…
Simmons？哇！他可是个严肃认真的数学家，比如看他的 George F. Simmons《Introduction to Topology and Modern Analysis》（拓扑与现代分析引论）就知道了。我有一年夏天在范德堡大学参加 NSF 项目时学过这本书。当时我就觉得，他写数学书真的写得太牛了。
Simmons? WOW! He's a serious mathematician, e.g., as in his George F. Simmons, Introduction to Topology and Modern Analysis. I studied it one summer in an NSF program at Vanderbilt. Then I concluded that he is one heck of a good math writer.
…and Complex Analysis》，ISBN 07-054232-5，McGraw-Hill，纽约，1966年。---------------------------------------- 想要轻松搞懂度量空间（metric space），一本极为优雅的入门书是 George F. Simmons 的《Introduction to Topology and Modern Analysis》，McGraw Hill，纽约，1963年。======================================== 常微分方程（Ordinary Differential Equations）---------------------------------------- 线性代数很重要，在某些节点甚至至关重要，对于…
…and Complex Analysis', ISBN 07-054232-5, McGraw-Hill, New York, 1966. ---------------------------------------- An elegant introduction to how to get comfortable in metric space is George F. Simmons, 'Introduction to Topology and Modern Analysis', McGraw Hill, New York, 1963. ======================================== Ordinary Differential Equations ---------------------------------------- Linear algebra is important, as some points crucial, for…
…对偶的对偶，并在等号成立时称原空间是自反的（reflexive）。接着他们又想定义弱拓扑（weak topology）和弱*拓扑（weak* topology）等等。你可以在比如 G. Simmons 的《Introduction to Topology and Modern Analysis》里看到一部分这些内容，写得超级棒，虽然我从来没见过它有什么实际应用。在线性代数里捣鼓对偶性可以推导出伴随变换（adjoint transformations）。对我来说，这最后变成了大量细致的…
…duals of duals, and when there is equality say that the original space is reflexive. Then they want to define the weak topology and the weak* topology, etc. Can see some of this in, say, G. Simmons, Introduction to Topology and Modern Analysis, super nicely written book although I have never seen any applications for it. Pushing around duality in linear algebra can get to adjoint transformations. To me it turns out to be a lot of careful…
…纯数专业。如果在哪里学过一门抽象代数课，比如带一点群论，那可能会有帮助！研究生阶段：可能会从比如 Simmons 的《Introduction to Topology and Modern Analysis》里多学一点拓扑。所以，先把度量空间搞扎实，再开始学对偶性。接下来的重要一步是测度论和泛函分析课程。Simmons 的书会有所帮助。《Baby Rudin》将至关重要；Halmos 的…
…pure math major. If somewhere take a course in abstract algebra, e.g., with a little group theory, then that might help! Graduate School. Might learn a little more about topology, say, from Simmons, 'Introduction to Topology and Modern Analysis'. So, get good with metric spaces and get started on duality. The next big step is a course in measure theory and functional analysis. The Simmons work will help. Baby Rudin will be crucial; Halmos…
…在家里和办公室都备着：Rudin 的《Real and Complex Analysis》、Halmos 的《Finite Dimensional Vector Spaces》、Billingsley 的《Probability and Measure》、Kelley 的《General Topology》、Lang 的《Undergraduate Algebra》、Simmons 的《Introduction to Topology and Modern Analysis》、Parthasarathy 的《Probability Measures on Metric Spaces》、Whinston、Green 和 Mas-Colell 的《Microeconomic Theory》
…at both home and work: Rudin, Real and Complex Analysis Halmos, Finite Dimensional Vector Spaces Billingsley, Probability and Measure Kelley, General Topology Lang, Undergraduate Algebra Simmons, Introduction to Topology and Modern Analysis Parthasarathy, Probability Measures on Metric Spaces Whinston, Green and Mas-Colell, Microeconomic Theory