……《Equations》做得很好，对于几乎任何可能遇到的应用来说可能都足够了。如果你做交流/直流电路理论或确定性最优控制，会需要一些这方面的内容。对于基础抽象代数，Herstein 的《Topics in Algebra》通常就够了，而且写得很好。有了这些，就能为比如代数编码理论做好充分准备，后者实际上有一些重要的应用。一旦有了测度论的基础，……
…Equations is nicely done and likely enough for nearly any applications might encounter. Will want some of this if do A/C circuit theory or deterministic optimal control. For basic abstract algebra Herstein, Topics in Algebra should usually be enough and is well written. With that will be well prepared for, say, algebraic coding theory which actually has some important applications. Once have a background in measure theory,…
……集合的概念。然后你就可以学“群”，也就是稍微多了一点结构的集合，如果你愿意这么理解的话。然后接着是“环”。再然后是“域”。对于所有这些内容，赶紧去买 Herstein 的《Topics in Algebra》。这绝对是市面上最好的教材，没有之一。我也就学到了这一步。我猜后面肯定还有一堆好玩的东西（数论？图论和网络理论？），但我对那些就一无所知了。
…that of a set. And then you can learn about "groups", which are sets with a little more structure, if you will. And then you go on to "rings". And then "fields". For all this stuff, go get Herstein's "Topics in Algebra". It's far and away the best text. That's as far as I got. I suspect there's a ton of other fun things out there (number theory? graph and network theory?), but I don't know anything about it.
……Rudin 的《数学分析原理》就是一堆完全没有背景动机或展开解释的真命题大杂烩，自己一个人看根本看不懂。而在另一端，像 Herstein 的《Topics in Algebra》就会把每件事的前因后果讲得清清楚楚，读起来是一种享受。大多数书都介于两者之间，所以如果某本书你看得不顺手，不妨换一本讲同一主题的书试试。
…Rudin's "Principles of Mathematical Analysis" is a collection of true statements with zero motivation or exposition, and it's impossible to follow on your own. On the other end, something like Herstein's "Topics in Algebra" clearly spells out the reason for everything and is a joy to read. Most books are somewhere in between, so if a certain book isn't working for you, try something else on the same topic.
赞同这个。学代数的话，强烈推荐 Herstein 的《Topics in Algebra》。语言优美流畅，每章末尾的习题在巩固知识点方面效果极好。
This. For Algebra, look for Topics in Algebra by Herstein. It reads beautifully, and the problems at the end of each chapters are very good at solidifying the knowledge.
……一次又一次地重读它（以及它的一些续作）。培养系统性思维的心态。在分析问题时寻找瓶颈，然后想办法突破这一瓶颈。2. I. N. Herstein 的《Topics in Algebra》。大一暑假的时候，我决定从头到尾把这本书啃完，并做完书里的每一道习题。我确实做到了。遗憾的是，二十年过去了，我的代数水平现在菜得很。不过那次……
…returning to it (and some of its sequels) again and again. Adopting a systems thinking mindset. When analysing problems looking for the bottleneck, then figuring out how to elevate that constraint. 2. Topics in Algebra/ I. N. Herstein. During the first summer at Uni I decided to read this book cover to cover and solve every single problem in it. Which I did. Sadly, twenty years on, my algebra game is poor. But that…
……《Equations》做得很好，对于几乎任何可能遇到的应用来说可能都足够了。如果你做交流/直流电路理论或确定性最优控制，会需要一些这方面的内容。对于基础抽象代数，Herstein 的《Topics in Algebra》通常就够了，而且写得很好。有了这些，就能为比如代数编码理论做好充分准备，后者实际上有一些重要的应用。一旦有了测度论的基础，……
…Equations is nicely done and likely enough for nearly any applications might encounter. Will want some of this if do A/C circuit theory or deterministic optimal control. For basic abstract algebra Herstein, Topics in Algebra should usually be enough and is well written. With that will be well prepared for, say, algebraic coding theory which actually has some important applications. Once have a background in measure theory,…
……集合的概念。然后你就可以学“群”，也就是稍微多了一点结构的集合，如果你愿意这么理解的话。然后接着是“环”。再然后是“域”。对于所有这些内容，赶紧去买 Herstein 的《Topics in Algebra》。这绝对是市面上最好的教材，没有之一。我也就学到了这一步。我猜后面肯定还有一堆好玩的东西（数论？图论和网络理论？），但我对那些就一无所知了。
…that of a set. And then you can learn about "groups", which are sets with a little more structure, if you will. And then you go on to "rings". And then "fields". For all this stuff, go get Herstein's "Topics in Algebra". It's far and away the best text. That's as far as I got. I suspect there's a ton of other fun things out there (number theory? graph and network theory?), but I don't know anything about it.
……Rudin 的《数学分析原理》就是一堆完全没有背景动机或展开解释的真命题大杂烩，自己一个人看根本看不懂。而在另一端，像 Herstein 的《Topics in Algebra》就会把每件事的前因后果讲得清清楚楚，读起来是一种享受。大多数书都介于两者之间，所以如果某本书你看得不顺手，不妨换一本讲同一主题的书试试。
…Rudin's "Principles of Mathematical Analysis" is a collection of true statements with zero motivation or exposition, and it's impossible to follow on your own. On the other end, something like Herstein's "Topics in Algebra" clearly spells out the reason for everything and is a joy to read. Most books are somewhere in between, so if a certain book isn't working for you, try something else on the same topic.
赞同这个。学代数的话，强烈推荐 Herstein 的《Topics in Algebra》。语言优美流畅，每章末尾的习题在巩固知识点方面效果极好。
This. For Algebra, look for Topics in Algebra by Herstein. It reads beautifully, and the problems at the end of each chapters are very good at solidifying the knowledge.
Herstein 的《Topics in Algebra》，或者是 Dummit 和 Foote 的书。
Herstein Topics in Algebra or Dummit and Foote.
……一次又一次地重读它（以及它的一些续作）。培养系统性思维的心态。在分析问题时寻找瓶颈，然后想办法突破这一瓶颈。2. I. N. Herstein 的《Topics in Algebra》。大一暑假的时候，我决定从头到尾把这本书啃完，并做完书里的每一道习题。我确实做到了。遗憾的是，二十年过去了，我的代数水平现在菜得很。不过那次……
…returning to it (and some of its sequels) again and again. Adopting a systems thinking mindset. When analysing problems looking for the bottleneck, then figuring out how to elevate that constraint. 2. Topics in Algebra/ I. N. Herstein. During the first summer at Uni I decided to read this book cover to cover and solve every single problem in it. Which I did. Sadly, twenty years on, my algebra game is poor. But that…