ADDITIVE COMBINATORICS
by Terence Tao · first published 2006
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Additive combinatorics is the theory of counting additive structures in sets. This theory has seen exciting developments and dramatic changes in direction in recent years thanks to its connections with areas such as number theory, ergodic theory and graph theory. This graduate-level 2006 text will allow students and researchers easy entry into this fascinating field. Here, the authors bring together in a self-contained and systematic manner the many different tools and ideas that are used in the modern theory, presenting them in an accessible, coherent, and intuitively clear manner, and provid
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…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
on “Math Atlas - a Gateway to modern mathematics” ↗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…
on “Mathematicians Catch a Pattern by Figuring Out How to Avoid It” ↗…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).
on “Math ∩ Programming” ↗