加性组合学
ADDITIVE COMBINATORICS
Terence Tao · 初版 2006 年
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Additive combinatorics 是研究集合中加法结构计数的理论。近年来，得益于它与 number theory、ergodic theory 和 graph theory 等领域的联系，该理论取得了令人振奋的进展，研究方向也发生了巨大转变。这本出版于 2006 年的研究生水平教材将使学生和研究人员能够轻松进入这一引人入胜的领域。在本书中，作者以自成体系且系统化的方式，汇集了现代理论中使用的诸多不同工具与思想，以易读、连贯且直观清晰的方式呈现出来，并提供……
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……组合学与分析学（进而包括偏微分方程 PDE）之间的联系，以及再与群论的关联。有些非常酷的问题只能通过一种巧妙奇特的技术融合来解决。http://www.amazon.com/Additive-Combinatorics-Cambridge-Advan... 陶哲轩（Terry Tao）和范武（Van Vu）合著的那本加性组合学（Additive Combinatorics）的书给出了非常棒的例子
…relationship between combinatorics and analysis (and hence pde) and thence with group theory. There's some really cool problems that can only be answered via a funky fusion of technique. http://www.amazon.com/Additive-Combinatorics-Cambridge-Advan... the additive combinatorics book by terry tao and van vu give some amazing examples of this
如果你想读懂 Peluse 的论文，我认为最直接相关的背景阅读材料是 Tao 和 Vu 的《Additive Combinatorics》。Dummit 和 Foote 的《Abstract Algebra》是一本极好的书——哪怕它跟加性组合学的关系不算非常直接。分析学背景也会很有用，比如 Stein 和 Shakarchi 的……
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…
……接着看一本概率算法书，把你在 CS 里学到的东西用上（不过我当时是上了一门课，所以不能保证哪本书最好），另外你也可以翻翻 Tao 和 Vu 的《Additive Combinatorics》，看看怎么在数论中应用概率（概率方法是书里的第一章）。
…continue with both some probabilistic algorithm book to apply what you've learned in CS (I did take a course in that, though, so I can't vouch for the best book out there) and you could also grab Tao, Vu's Additive Combinatorics for how to apply probability in number theory (probabilistic method is chapter one in there).