…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 - A Straightforward Approach (2nd ed) - Binmore (has full solutions) 5. Discrete Mathematics…
…viable options include "Calculus" by Spivak (it's really a book on real analysis at a level somewhere between a typical freshman calculus book and "baby Rudin"), "Real Mathematical Analysis" by Pugh, or "Yet Another Introduction to Analysis" by Bryant.
既然你提到了分析学，我推荐维克多·布莱恩特的《又一本数学分析导论与度量空间》（Yet Another Introduction to Analysis and Metric Spaces）。难度应该刚刚好，而且非常有趣。另一本关于分析学的建议是H.S. Wall写的《创造性数学》（Creative Mathematics）。这是一本引导高中水平学生……
Since you mention analysis, I recommend Yet Another Introduction to Analysis and Metric Spaces by Victor Bryant. They should be at the right level and a lot of fun. Another analysis suggestion is Creative Mathematics by H.S. Wall. It is a book that walks a high school level student…
…there are fantastic preparatory books like "Linear Algebra: Step by Step" by Kuldeep Singh which one needs because Rudin considers Euclidean Spaces proper, not just the reals. Other helpful books include "Yet Another Introduction to Analysis" by Bryant, "How to Think About Analysis" by Lara Alcock, "A First Course in Mathematical Analysis" by Brannan, "Real Analysis: A Long-Form Mathematics Textbook by Jay Cummings" etc. None of these books…
……Velleman著，或者《证明之书》（第2版）- Hammack著（免费的！）4. 数学分析：4a. 适合分析学的入门准备书：《如何思考分析学》- Alcock著 4b. 《理解分析》（第2版）- Abbott著，或者《又一本数学分析导论》- Bryant著（配有完整答案），或者《单变量微积分的来龙去脉》- Sasane著，或者《数学分析：简明方法》（第2版）- Binmore著（配有完整答案）5. 离散数学……
…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 - A Straightforward Approach (2nd ed) - Binmore (has full solutions) 5. Discrete Mathematics…
……可行的选择包括斯皮瓦克（Spivak）的《微积分》（它本质上是一本实分析教材，难度介于典型大一微积分教材和“小Rudin”之间），普格（Pugh）的《实数学分析》，或者布莱恩特（Bryant）的《又一本数学分析导论》。
…viable options include "Calculus" by Spivak (it's really a book on real analysis at a level somewhere between a typical freshman calculus book and "baby Rudin"), "Real Mathematical Analysis" by Pugh, or "Yet Another Introduction to Analysis" by Bryant.
既然你提到了分析学，我推荐维克多·布莱恩特的《又一本数学分析导论与度量空间》（Yet Another Introduction to Analysis and Metric Spaces）。难度应该刚刚好，而且非常有趣。另一本关于分析学的建议是H.S. Wall写的《创造性数学》（Creative Mathematics）。这是一本引导高中水平学生……
Since you mention analysis, I recommend Yet Another Introduction to Analysis and Metric Spaces by Victor Bryant. They should be at the right level and a lot of fun. Another analysis suggestion is Creative Mathematics by H.S. Wall. It is a book that walks a high school level student…
……有很多极棒的预备书籍，比如库尔迪普·辛格（Kuldeep Singh）的《线性代数：循序渐进》，这本书很有必要，因为Rudin讨论的是真正的欧氏空间，而不仅仅是实数集。其他有用的书还包括布莱恩特的《又一本数学分析导论》、拉拉·阿尔考克的《如何思考分析学》、布兰南的《数学分析第一门课》、杰伊·卡明斯的《实分析：长篇数学教材》等等。这些书没有一本……
…there are fantastic preparatory books like "Linear Algebra: Step by Step" by Kuldeep Singh which one needs because Rudin considers Euclidean Spaces proper, not just the reals. Other helpful books include "Yet Another Introduction to Analysis" by Bryant, "How to Think About Analysis" by Lara Alcock, "A First Course in Mathematical Analysis" by Brannan, "Real Analysis: A Long-Form Mathematics Textbook by Jay Cummings" etc. None of these books…