抽象代数
Abstract algebra
David S. Dummit · 初版 1991 年
11人推荐
26位读者提及
27次提及
为什么值得读
- 例题极为丰富而非充斥枯燥的符号推演
- 内容全面扎实，适合自学者作为核心参考
- 不留给读者过多推导断层，利于稳步掌握
本书旨在让读者领略数学不同领域之间丰富交融所带来的力量与美感。书中细致阐述了不同代数结构的理论，从基础定义层层递进到某些深刻结论，并辅以大量例题与习题帮助读者理解。通过这种方式，读者能够真切体会到数学结构及其相互作用如何在众多不同情境下引出强有力的结论与深刻见解。
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……http://math.stanford.edu/~vakil/216blog/FOAGapr2915public.pd... 可能还有 Milne 关于 etale cohomology（平展上同调）的讲义：http://www.jmilne.org/math/CourseNotes/LEC210.pdf。如果你觉得这些看不懂，那就先从 Dummit 和 Foote 的《抽象代数》（Abstract Algebra，从头到尾通读一遍）、Neukirch 的《代数数论》（Algebraic Number Theory）、Atiyah 和 Macdonald 的《交换代数》（Commutative Algebra），以及 Fulton 和 Harris 的《表示论》（Representation Theory）开始。如果你真想把这些都读完，你还不如……
…http://math.stanford.edu/~vakil/216blog/FOAGapr2915public.pd... and maybe Milne on etale cohmology: http://www.jmilne.org/math/CourseNotes/LEC210.pdf If you find that incomprehensible, start with Dummit and Foote's Abstract Algebra (read it cover to cover), Neukirch's Algebraic Number Theory, Atiyah and Macdonald's Commutative Algebra, and Fulton and Harris's Representation Theory. If you indeed want to read all that, you may as…
自学抽象代数的话，我推荐 Dummit & Foote。我当年拿它当本科代数课的补充教材，感觉非常管用。相比之下，像 Artin 那样的书给读者留了太多空白要自己推导，……
For self study of abstract algebra, I recommend Dummit & Foote. I used it as a supplement to my undergrad algebra classes and found it to be very useful. This is in contrast to some books like Artin which leave a lot to the readers,…
如果你想看懂 Peluse 的论文，我认为最直接相关的背景读物是 Tao 和 Vu 的《加法组合学》（Additive Combinatorics）。Dummit 和 Foote 的《抽象代数》（Abstract Algebra）是一本绝佳的好书——哪怕它跟加法组合学并不是那么直接相关。分析学背景也会很有用，比如 Stein 和 Shakarchi 系列里的内容。一些入门级的组合数学……
If you want to understand Peluse's paper, I think the most directly relevant background reading would be Tao and Vu's Additive Combinatorics. Dummit and Foote's Abstract Algebra is an excellent book -- even if not very directly relevant to additive combinatorics. Analysis background would be useful, such as to be found in Stein and Shakarchi's series. Some introductory combinatorics…
大多数人都喜欢 Dummit & Foote 的书；它往往包含大量的例题和示例，而不是一堆密密麻麻的符号推导：http://www.amazon.com/Abstract-Algebra-Edition-David-Dummit/... 不过我学的时候用的是这本 Dover 出版的书，更便宜实惠：http://www.amazon.com/Elements-Abstract-Algebra-Dover-Mathem...
Most people like the Dummit & Foote book; it tends to be loaded with examples rather than a lot of dense symbolic arguments: http://www.amazon.com/Abstract-Algebra-Edition-David-Dummit/... When I learned it, though, it was from this Dover book, which is more affordable: http://www.amazon.com/Elements-Abstract-Algebra-Dover-Mathem...
……我上群论和环论课时买的教材[1]。它相当贵，习题也非常有挑战性，但如果你是个有自觉性的学生，光从这一本书里就能学到海量的抽象代数知识。在深入学习之前，如果你已经很久没碰线性代数了，可能需要先复习一下。你可以在网上找到许多习题的解答，不过我没法保证它们……
…textbook I bought for the course I took on group theory and ring theory [1]. It’s pretty expensive and the exercises are very challenging but if you’re a self-motivated student, you can learn a TON of abstract algebra from this one book. You may want to review some linear algebra before you dive in, if you haven’t done so in a while. You can find solutions to many of the exercises online though I can’t vouch for their…
Dos Reis 写的《抽象代数：适合学生的入门方法》（Abstract Algebra: A Student-Friendly Approach）。平装本的排版感觉像练习册，不会让人望而生畏——对新手非常友好
Abstract Algebra: A Student-Friendly Approach by Dos Reis Paperback layout feels like a workbook, not overwhelming-- beginner friendly