离天线设计、电磁学之类的虽然还有点距离，但我认为你必须对证明信手拈来，才能真正跟上那些内容。数学这门学科博大精深；个人情况各不相同（ymmv）。《A Transition to Advanced Mathematics》，作者 Douglas Smith、Maurice Eggen、Richard St. Andre，ISBN-13: 978-0495562023，ISBN-10: 0495562025，第 7 版。Abebooks 上能搜到，价格可能会便宜点。它……
There is some distance from this to antenna design, electromagnetism, etc, but I think you have to be fluent in proofs to actually follow along on those. Math is a big subject; ymmv. A Transition to Advanced Mathematics by Douglas Smith (Author), Maurice Eggen (Author), Richard St. Andre (Author) ISBN-13: 978-0495562023 ISBN-10: 0495562025 Edition: 7th It shows up on Abebooks which could help with the price. It's…
我小学六年级学年结束、暑假刚开始的时候读了《A Transition to Advanced Mathematics》（0-534-38214-2）。我会把这本书推荐给当年的自己，因为它是在学完高中最后一门数学课和……之间的桥梁
"A Transition to Advanced Mathematics" (0-534-38214-2) at the end of my 6th grade school year, just as summer was starting. I would give this book to myself because it's a bridge between finishing the final class in high school math and…
……Approach 2. 《Elements of Set Theory》- Enderton 2a. 《Naive Set Theory》- Halmos 3. 《Foundations of Analysis》- Landau 4. 《Basic Mathematics》- Lang 5. 《Principles of Mathematics》- Allendoerfer & Oakley 6. 《A Transition to Advanced Mathematics》 6a. 《Concept of Modern Mathematics》- Stewart 7. 《Calculus》- Apostol 或 Spivak 一本都别跳过
…Approach 2. Elements of Set Theory - Enderton 2a. Naive Set Theory - Halmos 3. Foundations of Analysis - Landau 4. Basic Mathematics - Lang 5. Principles of Mathematics - Allendoerfer & Oakley 6. A Transition to Advanced Mathematics 6a. Concept of Modern Mathematics - Stewart 7. Calculus - Apostol or Spivak Don't skip any
如果有人对数学家如何思考和做证明感兴趣，有很多很有帮助的书。比如 Chartrand 等人写的《Mathematical Proofs: A Transition to Advanced Mathematics》。Velleman 写的《How to Prove It: A Structured Approach》。Nancy Rodgers 写的《Learning to Reason: An Introduction to Logic, Sets, and Relations》。初等离散数学教材也可以……
If anyone is interested in how mathematicians think and do proofs there are many helpful books. For example, Mathematical Proofs: A Transition to Advanced Mathematics by Chartrand and others. How to Prove It: A Structured Approach by Velleman. Learning to Reason: An Introduction to Logic, Sets, and Relations by Nancy Rodgers. Elementary Discrete Math books make…
……Richard Hammack 写的《Book of Proof》：https://www.people.vcu.edu/~rhammack/BookOfProof/ Susanna Epp 写的《Discrete Math》：https://www.amazon.com/Discrete-Mathematics-Applications-Sus... Chartrand 等人写的《Mathematical Proofs: A Transition to Advanced Mathematics》：https://www.amazon.com/Mathematical-Proofs-Transition-Advanc... Lara Alcock 写的《How to Think About Analysis》：https://www.amazon.com/Think-About-Analysis-Lara-Alcock/dp/0... Learning……
…Book of Proof by Richard Hammack: https://www.people.vcu.edu/~rhammack/BookOfProof/ Discrete Math by Susanna Epp: https://www.amazon.com/Discrete-Mathematics-Applications-Sus... Mathematical Proofs: A Transition to Advanced Mathematics by Chartrand et al: https://www.amazon.com/Mathematical-Proofs-Transition-Advanc... How to Think About Analysis by Lara Alcock: https://www.amazon.com/Think-About-Analysis-Lara-Alcock/dp/0... Learning…
我也附议推荐 Chartrand 的书（我猜你指的是《Mathematical Proofs: A Transition to Advanced Mathematics》）。我当时在“过渡桥梁”课程上用了这本书，非常喜欢；它完全是从第一性原理出发，给了你大量简单例题，方便你在此基础上逐步进阶。
I can second the Chartrand book (I believe you mean "Mathematical Proofs: A Transition to Advanced Mathematics"). I used this book in a "bridge" class and loved it; it really starts from first principles and gives you a lot of simple examples that you can build on.
离天线设计、电磁学之类的虽然还有点距离，但我认为你必须对证明信手拈来，才能真正跟上那些内容。数学这门学科博大精深；个人情况各不相同（ymmv）。《A Transition to Advanced Mathematics》，作者 Douglas Smith、Maurice Eggen、Richard St. Andre，ISBN-13: 978-0495562023，ISBN-10: 0495562025，第 7 版。Abebooks 上能搜到，价格可能会便宜点。它……
There is some distance from this to antenna design, electromagnetism, etc, but I think you have to be fluent in proofs to actually follow along on those. Math is a big subject; ymmv. A Transition to Advanced Mathematics by Douglas Smith (Author), Maurice Eggen (Author), Richard St. Andre (Author) ISBN-13: 978-0495562023 ISBN-10: 0495562025 Edition: 7th It shows up on Abebooks which could help with the price. It's…
我小学六年级学年结束、暑假刚开始的时候读了《A Transition to Advanced Mathematics》（0-534-38214-2）。我会把这本书推荐给当年的自己，因为它是在学完高中最后一门数学课和……之间的桥梁
"A Transition to Advanced Mathematics" (0-534-38214-2) at the end of my 6th grade school year, just as summer was starting. I would give this book to myself because it's a bridge between finishing the final class in high school math and…
……Approach 2. 《Elements of Set Theory》- Enderton 2a. 《Naive Set Theory》- Halmos 3. 《Foundations of Analysis》- Landau 4. 《Basic Mathematics》- Lang 5. 《Principles of Mathematics》- Allendoerfer & Oakley 6. 《A Transition to Advanced Mathematics》 6a. 《Concept of Modern Mathematics》- Stewart 7. 《Calculus》- Apostol 或 Spivak 一本都别跳过
…Approach 2. Elements of Set Theory - Enderton 2a. Naive Set Theory - Halmos 3. Foundations of Analysis - Landau 4. Basic Mathematics - Lang 5. Principles of Mathematics - Allendoerfer & Oakley 6. A Transition to Advanced Mathematics 6a. Concept of Modern Mathematics - Stewart 7. Calculus - Apostol or Spivak Don't skip any
如果有人对数学家如何思考和做证明感兴趣，有很多很有帮助的书。比如 Chartrand 等人写的《Mathematical Proofs: A Transition to Advanced Mathematics》。Velleman 写的《How to Prove It: A Structured Approach》。Nancy Rodgers 写的《Learning to Reason: An Introduction to Logic, Sets, and Relations》。初等离散数学教材也可以……
If anyone is interested in how mathematicians think and do proofs there are many helpful books. For example, Mathematical Proofs: A Transition to Advanced Mathematics by Chartrand and others. How to Prove It: A Structured Approach by Velleman. Learning to Reason: An Introduction to Logic, Sets, and Relations by Nancy Rodgers. Elementary Discrete Math books make…
……Richard Hammack 写的《Book of Proof》：https://www.people.vcu.edu/~rhammack/BookOfProof/ Susanna Epp 写的《Discrete Math》：https://www.amazon.com/Discrete-Mathematics-Applications-Sus... Chartrand 等人写的《Mathematical Proofs: A Transition to Advanced Mathematics》：https://www.amazon.com/Mathematical-Proofs-Transition-Advanc... Lara Alcock 写的《How to Think About Analysis》：https://www.amazon.com/Think-About-Analysis-Lara-Alcock/dp/0... Learning……
…Book of Proof by Richard Hammack: https://www.people.vcu.edu/~rhammack/BookOfProof/ Discrete Math by Susanna Epp: https://www.amazon.com/Discrete-Mathematics-Applications-Sus... Mathematical Proofs: A Transition to Advanced Mathematics by Chartrand et al: https://www.amazon.com/Mathematical-Proofs-Transition-Advanc... How to Think About Analysis by Lara Alcock: https://www.amazon.com/Think-About-Analysis-Lara-Alcock/dp/0... Learning…
我也附议推荐 Chartrand 的书（我猜你指的是《Mathematical Proofs: A Transition to Advanced Mathematics》）。我当时在“过渡桥梁”课程上用了这本书，非常喜欢；它完全是从第一性原理出发，给了你大量简单例题，方便你在此基础上逐步进阶。
I can second the Chartrand book (I believe you mean "Mathematical Proofs: A Transition to Advanced Mathematics"). I used this book in a "bridge" class and loved it; it really starts from first principles and gives you a lot of simple examples that you can build on.