…1. 微积分预备：Axler 的《微积分预备：微积分序曲》 2. 微积分：Ash 的《微积分辅导书》。大学部分：3. 大学高阶数学准备：3a. 高阶数学通用准备：Alcock 的《如何学好数学专业》（How to Study as a Mathematics Major） 3b. 证明写作：Velleman 的《如何证明：结构化方法》或者 Hammack 的《证明之书》（第2版）（这本书是免费的！） 4. 数学分析：4a. 分析学的优质准备：How to Think…
…1. Precalculus: Precalculus: A Prelude to Calculus - Axler 2. Calculus: The Calculus Tutoring Book - Ash. College: 3. Preparation for Collegel-level maths: 3a. General prep for high level maths: How to Study as a Mathematics Major - Alcock 3b. Proof writing: How to Prove It - A Structured Approach - Velleman OR Book of Proof (2nd ed) - Hammack (it's free!) 4. Mathematical Analysis: 4a. Good prep for Analysis: How to Think…
…在进入第一门基于证明的线性代数或数学分析课程之前，先搞懂自然数/有理数/实数/可数性等概念：- Kevin Houston 的《如何像数学家一样思考》 - Keith Devlin 的《数学思维导论》 - Lara Alcock 的《如何学好数学专业》（不知道为什么，她/牛津出版社有两本书内容看似完全一样，只是书名分别叫 Math Major 和 Math Degree）
…natural/rationals/reals/countability etc before heading into your first proof based LA or analysis sequence: - Kevin Houston "How to Think Like a Mathematician" - Keith Devlin "Intro Mathematical Thinking" - "How to Study as a Mathematics Major" Lara Alcock (for some reason, she/Oxford Press has 2 books with seemingly identical content under Math Major and Math Degree titles)
…to get up to speed on the research literature for the non-mathematics part of the research problem, in order to properly understand its constraints and bigger-picture significance. Lara Alcock's book "How to Study as a Mathematics Major" touches upon this topic more directly. She encourages readers not to be too intimidated if other students in a course seem really smart: much of the time, the reason is not due to an innate difference…
…1. 微积分预备：Axler 的《微积分预备：微积分序曲》 2. 微积分：Ash 的《微积分辅导书》。大学部分：3. 大学高阶数学准备：3a. 高阶数学通用准备：Alcock 的《如何学好数学专业》（How to Study as a Mathematics Major） 3b. 证明写作：Velleman 的《如何证明：结构化方法》或者 Hammack 的《证明之书》（第2版）（这本书是免费的！） 4. 数学分析：4a. 分析学的优质准备：How to Think…
…1. Precalculus: Precalculus: A Prelude to Calculus - Axler 2. Calculus: The Calculus Tutoring Book - Ash. College: 3. Preparation for Collegel-level maths: 3a. General prep for high level maths: How to Study as a Mathematics Major - Alcock 3b. Proof writing: How to Prove It - A Structured Approach - Velleman OR Book of Proof (2nd ed) - Hammack (it's free!) 4. Mathematical Analysis: 4a. Good prep for Analysis: How to Think…
…在进入第一门基于证明的线性代数或数学分析课程之前，先搞懂自然数/有理数/实数/可数性等概念：- Kevin Houston 的《如何像数学家一样思考》 - Keith Devlin 的《数学思维导论》 - Lara Alcock 的《如何学好数学专业》（不知道为什么，她/牛津出版社有两本书内容看似完全一样，只是书名分别叫 Math Major 和 Math Degree）
…natural/rationals/reals/countability etc before heading into your first proof based LA or analysis sequence: - Kevin Houston "How to Think Like a Mathematician" - Keith Devlin "Intro Mathematical Thinking" - "How to Study as a Mathematics Major" Lara Alcock (for some reason, she/Oxford Press has 2 books with seemingly identical content under Math Major and Math Degree titles)
…以便跟上该研究问题中非数学部分的研究文献进展，从而正确理解其约束条件和更宏观的意义。Lara Alcock 的书《如何学好数学专业》更直接地探讨了这个话题。她鼓励读者在课程中如果觉得其他同学看起来绝顶聪明，千万不要太受打击：很多时候，原因根本不是天赋上的差异……
…to get up to speed on the research literature for the non-mathematics part of the research problem, in order to properly understand its constraints and bigger-picture significance. Lara Alcock's book "How to Study as a Mathematics Major" touches upon this topic more directly. She encourages readers not to be too intimidated if other students in a course seem really smart: much of the time, the reason is not due to an innate difference…