…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 well enroll in a Ph.D. program in math....
…gets on you for it." But I have not experienced this myself, nor heard this complaint from anyone until this article. Moreover I can think of lots of well-known books that are loaded with exposition. Representation Theory by Fulton and Harris comes particularly to mind. Of course, there are many books which are notoriously terse as well. (Any HN'ers tried to hack their way through Baby Rudin?) Indeed, there are many mathematicians…
…Prentice-Hall，1991年。* 推荐阅读：Halmos，《朴素集合论》（Naive Set Theory），Springer-Verlag，1974年。* 同样有用：Halmos，《有限维向量空间》（Finite-Dimensional Vector Spaces），Springer-Verlag，1987年。* 同样有用：Fulton 与 Harris，《表示论：第一门课程》（Representation Theory: A First Course），Springer-Verlag，1991年。特别参见附录 B。* 同样有用：Bott 与 Tu，《代数拓扑中的微分形式》（Differential forms in Algebraic Topology），Springer-Verlag，1982年。特别参见第 1 章。Math55b *…
…Prentice-Hall, 1991. * Recommended: Halmos, Naive Set Theory, Springer-Verlag, 1974. * Also useful: Halmos, Finite-Dimensional Vector Spaces, Springer-Verlag, 1987. * Also useful: Fulton and Harris, Representation Theory: A First Course, Springer-Verlag, 1991. See especially Appendix B. * Also useful: Bott and Tu, Differential forms in Algebraic Topology, Springer-Verlag, 1982. See especially Chapter 1. Math55b *…
Sagan's book on the symmetric group is a great introduction to algebraic combinatorics, tracing the combinatorial approach to understanding the representation theory of the symmetric group. For more depth in that direction, Fulton & Harris' 'Representation Theory' builds the connections with Lie groups. Algebraic combinatorics dances in the intersection of a number…
…那么晦涩难懂，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）开始吧。如果你真打算把这些全读完，你还不如直接去读个数学博士学位呢……
…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 well enroll in a Ph.D. program in math....
…会因此数落你。”但我自己没经历过这事，在这篇文章之前也没听任何人抱怨过。而且我能想到很多包含大量叙述性解释的名著。Fulton 和 Harris 的《表示论》（Representation Theory）尤其浮现在脑海中。当然，也有很多书以极其简练晦涩而闻名。（有 HN 网友试过硬啃《小 Rudin》（Baby Rudin）吗？）事实上，很多数学家…
…gets on you for it." But I have not experienced this myself, nor heard this complaint from anyone until this article. Moreover I can think of lots of well-known books that are loaded with exposition. Representation Theory by Fulton and Harris comes particularly to mind. Of course, there are many books which are notoriously terse as well. (Any HN'ers tried to hack their way through Baby Rudin?) Indeed, there are many mathematicians…
…Prentice-Hall，1991年。* 推荐阅读：Halmos，《朴素集合论》（Naive Set Theory），Springer-Verlag，1974年。* 同样有用：Halmos，《有限维向量空间》（Finite-Dimensional Vector Spaces），Springer-Verlag，1987年。* 同样有用：Fulton 与 Harris，《表示论：第一门课程》（Representation Theory: A First Course），Springer-Verlag，1991年。特别参见附录 B。* 同样有用：Bott 与 Tu，《代数拓扑中的微分形式》（Differential forms in Algebraic Topology），Springer-Verlag，1982年。特别参见第 1 章。Math55b *…
…Prentice-Hall, 1991. * Recommended: Halmos, Naive Set Theory, Springer-Verlag, 1974. * Also useful: Halmos, Finite-Dimensional Vector Spaces, Springer-Verlag, 1987. * Also useful: Fulton and Harris, Representation Theory: A First Course, Springer-Verlag, 1991. See especially Appendix B. * Also useful: Bott and Tu, Differential forms in Algebraic Topology, Springer-Verlag, 1982. See especially Chapter 1. Math55b *…
Sagan 关于对称群的那本书是代数组合学极好的入门书，梳理了用组合学方法来理解对称群的表示论。如果想在这个方向上进一步深入，Fulton 和 Harris 的《表示论》（Representation Theory）构建了与李群的联系。代数组合学恰好游走在好几个…的交汇处
Sagan's book on the symmetric group is a great introduction to algebraic combinatorics, tracing the combinatorial approach to understanding the representation theory of the symmetric group. For more depth in that direction, Fulton & Harris' 'Representation Theory' builds the connections with Lie groups. Algebraic combinatorics dances in the intersection of a number…