ADDITIVE COMBINATORICS

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1. impendiaDec 2019
   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 would also be good (e.g. Stanley's Enumerative Combinatorics, or Van Lint and Wilson).

   Finally, analytic number theory would also be good to learn. For example, you might read Davenport's Multiplicative Number Theory. (Especially if you want to see integrals come into the picture.)

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2. NotOscarWildeMay 2013
   Some general hints: don't be afraid to skip. It may happen that some books have an intersection, even though they complement each other -- usually the authors try to be self-contained.

   Also, most of the books I mentioned have about 50% dedicated to core ideas in the field and 50% dedicated to some specific tools that may not be that useful to you. More often than not the second 50% is the latter part of the book, but in say Concrete Mathematics it is spread throughout the book entirely. I know it's hard to find the balance between reading fast (and then realizing you don't remember anything from the basic tools and you can't even apply them well) and reading slow (and realizing you're trying to memorize some obscure recurrence involving binomial coefficients). Reading is hard.

   Now, for the tips for the CS/discrete math students among you. Feel free to add some of yours, I'm hardly the veteran educator here.

   Knuth, Graham, Patashnik's Concrete Mathematics, after a few chapters, goes well with Flajolet, Sedgewick's Analytic Combinatorics. You should mix that up with some Discrete Mathematics introductory book, especially one dealing with counting objects, so you can apply the techniques almost immediately on simpler examples.

   Papadimitrou, Dasgupta, Vazirani's Algorithms is one of the better books on algorithms out there, in my opinion. As for the graph theory books I read, I liked Bondy, Murty's Graph Theory style the most, so I'd probably go with that, though I haven't really read them in parallel yet.

   For the discrete math students out there, after learning the basics of probablistic method (Alon, Spencer's Probabilistic Method being the seminal textbook, I think), you could 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).

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3. carterschonwaldMay 2009
   really? I've come to find a huge 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

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