我绝对、百分之百举双手赞成推荐 Charles Pugh 的《Real Mathematical Analysis》（千万别错过他在第 9 和第 10 页转述他同事的那段建议，标题是“隐喻与类比”，那段话完全可以作为一篇关于……心理学论文的底稿）。
I absolutely, positively second the recommendation of "Real Mathematical Analysis" by Charles Pugh (don't miss the advice he relates from his colleague, on pages 9&10, with the heading "Metaphor and Analogy", which could easily form the basis for a dissertation on the psychology of…
…Spivak's Calculus. Some people start with Topology by Munkres, which is not a difficult book but is very abstract and rigorous so makes a good introduction. If you feel like you have ok calculus chops, maybe Real Mathematical Analysis by Charles Pugh. Other good books are Linear Algebra Done Right by Axler, or the linear algebra book by Friedberg, Insel, and Spence. Maybe even learn linear algebra first. It's so useful. Do plenty…
……去下载《Book of Proof》：http://www.people.vcu.edu/~rhammack/BookOfProof/，通读一遍并把所有奇数题都做完（书后有答案）。第 3 步：找一本 Charles Pugh 写的《Real Mathematical Analysis》，把它啃下来，尽量多刷上面的习题，注意不要图快，而是借每道题来开拓思路。第 4 步：挑下面任意一本……
…Download the Book of Proof: http://www.people.vcu.edu/~rhammack/BookOfProof/ You read through it and do all the odd numbered exercises (the solutions are at the end of the book). Step 3: Get a book called Real Mathematical Analysis by Charles Pugh and you work through that and attempt as many problems as you can, with a view not to rush through it, but to expand your mind through each problem. Step 4: Pick any of these books that…
(1) Charles Pugh 的《Real Mathematical Analysis》对于有数学偏向的工程师来说，是绝佳的纯数学入门书。封底是这样开头的：> 高中时平面几何是你最喜欢的数学课吗？……
(1) Real Mathematical Analysis, by Charles Pugh is a wonderful introduction to pure mathematics for a mathematically inclined engineer. The back cover starts like this > Was plane geometry your favourite math course in high school?…
很多书单推荐都取决于你想学什么。不过相比其他书，我读得最津津有味的是下面这几本：- 《Algebra: Chapter 0》（Aluffi）- 《Real Mathematical Analysis》（Pugh）- 《Mathematics and its History》（Stillwell）- 《An Introduction to Manifolds》（Tu）- 《Gauge Fields, Knots and Gravity》（Baez）- 《A First Look at Rigorous Probability Theory》（Rosenthal）- 《All of Statistics》……
A lot of recommendations depend on what you're trying to learn. But I've enjoyed the following texts to a larger extent than others: - Algebra: Chapter 0 (Aluffi) - Real Mathematical Analysis (Pugh) - Mathematics and its History (Stillwell) - An Introduction to Manifolds (Tu) - Gauge Fields, Knots and Gravity (Baez) - A First Look at Rigorous Probability Theory (Rosenthal) - All of Statistics…
……基础：1. 《Chapter Zero》（Carol Schumacher）2. 《Naive Set Theory》（Paul Halmos）线性代数：1. 《Finite-Dimensional Vector Space》（Paul Halmos）2. 《Linear Algebra Done Right》（Steven Axler）实分析：1. 《Real Mathematical Analysis》（Charles Pugh）2. 《Introduction to Analysis》（Maxwell Rosenlicht）代数：1. 《A first course in abstract algebra》（John Fraleigh）比起某些……，这些书更适合自学。
…Basic 1. Chapter Zero (Carol Schumacher) 2. Naive Set Theory (Paul Halmos) Linear Algebra 1. Finite-Dimensional Vector Space (Paul Halmos) 2. Linear Algebra Done Right (Steven Axler) Real Analysis 1. Real Mathematical Analysis (Charles Pugh) 2. Introduction to Analysis (Maxwell Rosenlicht) Algebra 1. A first course in abstract algebra (John Fraleigh) These books are better for self-directed reading compared to some of the…
我绝对、百分之百举双手赞成推荐 Charles Pugh 的《Real Mathematical Analysis》（千万别错过他在第 9 和第 10 页转述他同事的那段建议，标题是“隐喻与类比”，那段话完全可以作为一篇关于……心理学论文的底稿）。
I absolutely, positively second the recommendation of "Real Mathematical Analysis" by Charles Pugh (don't miss the advice he relates from his colleague, on pages 9&10, with the heading "Metaphor and Analogy", which could easily form the basis for a dissertation on the psychology of…
……Spivak 的《Calculus》。有些人是从 Munkres 的《Topology》起步的，那本书倒不算难，但非常抽象且严谨，所以是很棒的入门读物。如果你觉得自己微积分底子还可以，也许可以看看 Charles Pugh 的《Real Mathematical Analysis》。其他好书还有 Axler 的《Linear Algebra Done Right》，或者 Friedberg、Insel 和 Spence 合著的那本线性代数。甚至可以考虑先学线性代数，它太有用了。多做……
…Spivak's Calculus. Some people start with Topology by Munkres, which is not a difficult book but is very abstract and rigorous so makes a good introduction. If you feel like you have ok calculus chops, maybe Real Mathematical Analysis by Charles Pugh. Other good books are Linear Algebra Done Right by Axler, or the linear algebra book by Friedberg, Insel, and Spence. Maybe even learn linear algebra first. It's so useful. Do plenty…
……去下载《Book of Proof》：http://www.people.vcu.edu/~rhammack/BookOfProof/，通读一遍并把所有奇数题都做完（书后有答案）。第 3 步：找一本 Charles Pugh 写的《Real Mathematical Analysis》，把它啃下来，尽量多刷上面的习题，注意不要图快，而是借每道题来开拓思路。第 4 步：挑下面任意一本……
…Download the Book of Proof: http://www.people.vcu.edu/~rhammack/BookOfProof/ You read through it and do all the odd numbered exercises (the solutions are at the end of the book). Step 3: Get a book called Real Mathematical Analysis by Charles Pugh and you work through that and attempt as many problems as you can, with a view not to rush through it, but to expand your mind through each problem. Step 4: Pick any of these books that…
(1) Charles Pugh 的《Real Mathematical Analysis》对于有数学偏向的工程师来说，是绝佳的纯数学入门书。封底是这样开头的：> 高中时平面几何是你最喜欢的数学课吗？……
(1) Real Mathematical Analysis, by Charles Pugh is a wonderful introduction to pure mathematics for a mathematically inclined engineer. The back cover starts like this > Was plane geometry your favourite math course in high school?…
很多书单推荐都取决于你想学什么。不过相比其他书，我读得最津津有味的是下面这几本：- 《Algebra: Chapter 0》（Aluffi）- 《Real Mathematical Analysis》（Pugh）- 《Mathematics and its History》（Stillwell）- 《An Introduction to Manifolds》（Tu）- 《Gauge Fields, Knots and Gravity》（Baez）- 《A First Look at Rigorous Probability Theory》（Rosenthal）- 《All of Statistics》……
A lot of recommendations depend on what you're trying to learn. But I've enjoyed the following texts to a larger extent than others: - Algebra: Chapter 0 (Aluffi) - Real Mathematical Analysis (Pugh) - Mathematics and its History (Stillwell) - An Introduction to Manifolds (Tu) - Gauge Fields, Knots and Gravity (Baez) - A First Look at Rigorous Probability Theory (Rosenthal) - All of Statistics…
……基础：1. 《Chapter Zero》（Carol Schumacher）2. 《Naive Set Theory》（Paul Halmos）线性代数：1. 《Finite-Dimensional Vector Space》（Paul Halmos）2. 《Linear Algebra Done Right》（Steven Axler）实分析：1. 《Real Mathematical Analysis》（Charles Pugh）2. 《Introduction to Analysis》（Maxwell Rosenlicht）代数：1. 《A first course in abstract algebra》（John Fraleigh）比起某些……，这些书更适合自学。
…Basic 1. Chapter Zero (Carol Schumacher) 2. Naive Set Theory (Paul Halmos) Linear Algebra 1. Finite-Dimensional Vector Space (Paul Halmos) 2. Linear Algebra Done Right (Steven Axler) Real Analysis 1. Real Mathematical Analysis (Charles Pugh) 2. Introduction to Analysis (Maxwell Rosenlicht) Algebra 1. A first course in abstract algebra (John Fraleigh) These books are better for self-directed reading compared to some of the…