Generatingfunctionology
by Herbert S. Wilf · first published 2005
69% recommend31% neutral
Why HN recommends it
Teaches strategies for actually solving counting and discrete math problems with generating functions, which is rare in theorem-heavy texts; well written and rewarding for working mathematicians and serious learners.
Summarised by Claude from recommending comments
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I really recommend Generatingfunctionology by Herbert Wilf https://www.math.upenn.edu/~wilf/gfologyLinked2.pdf
on “Discrete Mathematics: An Open Introduction, 3rd edition” ↗…challenge, and solutions can definitely help there. --- Personally, if I look back at books I went through a good fraction of as a self-learner (and loved), there's an even mix: • Concrete Mathematics and Generatingfunctionology have complete solutions. • Burton's Elementary Number Theory has “Hints”, and “Answers” to selected exercises (i.e. those where the answer was a number, not a proof — these are not much work for an author…
on “Books I Recommend” ↗…form into the equation to find out the C_i and a_i using the initial conditions. It's exactly like solving a differential equation. Another path is to look at formal power series, and a good book is Generatingfunctionology. Knuth Oren and Patashnik's Concrete Mathematics covers the basics very well and goes into much more detail on finite difference calculus.
on “A Fairly Fast Fibonacci Function” ↗Combinatorial Problems and Exercises by Lovasz I don't know much in the way of more advanced expository combinatorics books, other than the more narrow Generatingfunctionology (Wilf) and the already mentioned Enumerative Combinatorics (Stanley).
on “I'm writing a book about algorithms and Lisp” ↗Nothing to add to this except to say that Generatingfunctionology is an awesome book. Although I haven't read it, another in the same space is A=B, also co-authored by Wilf (https://www.math.upenn.edu/~wilf/AeqB.html) (another co-author is Zeilberger, whose name anyone…
on “Fast Fibonacci numbers using Monoids” ↗I think the mistake in your thinking is that infinity is a value or reachable destination. It's a concept and it behaves differently than a number. Also go read Generatingfunctionology and Concrete Mathematics
on “0.999...= 1” ↗…https://www2.math.upenn.edu/~wilf/website/MAASpeech In fact everything by Wilf that I've read is lovely: the paper "Recounting the rationals" (https://www2.math.upenn.edu/~wilf/website/recounting.pdf with Neil Calkin), and the book generatingfunctionology https://www2.math.upenn.edu/~wilf/DownldGF.html
on “Knuth changes his mind on Bernoulli number B_1” ↗Most of the higher level math text books I've read present theorems and their proofs , but not much on strategies for actually solving problems (a notable exception: Wilf's Generatingfunctionology), so this seems like it should become a very nice resource. As one would expect from a brand new site, it's rather short on content. The content that's there right now, though is pretty good.
on “Mathematical trick wiki Terrence Tao blogged about is now live - Tricki” ↗As mentioned in another subthread, Pugh's Real Mathematical Analysis is great, and better motivated than baby Rudin. Wilf - Generatingfunctionology (CRC 3rd ed.; free 2nd ed. pdf[1]) Lovasz - Combinatorial Problems and Exercises (AMS Chelsea) The classic probability book is Feller (2 vol), but it's absurdly priced. There's also Sidney Resnick's…
on “Ask HN: Math books like SICP?” ↗Obligatory mention of Wilf's "generatingfunctionology" that is also an excellent book [1]. [1] https://www.math.upenn.edu/~wilf/gfologyLinked2.pdf
on “Combinatorial Algorithms (1978) [pdf]” ↗Great idea to compile this list. One of my favourite mathematics books that is available for free download is GeneratingFunctionology - https://www.math.upenn.edu/~wilf/DownldGF.html Well-written and incredibly rewarding.
on “Free and Open-Source Mathematics Textbooks” ↗Beware - one step more and you get into the region of generating functions. I recommend a book Herbert Wilf with a wonderful name of Generatingfunctionology (https://www2.math.upenn.edu/~wilf/gfology2.pdf).
on “Convolutions, Polynomials and Flipped Kernels” ↗And, if you want to know more about generating functions, you can check out the book "generatingfunctionology" by the recently late Herbert Wilf gratis at http://www.math.upenn.edu/~wilf/DownldGF.html
on “Fibonacci series and Dynamic programming” ↗…summed this series(valid for x < 1): 1 + x + x^2 ... = 1/(1-x) Plug in x = 2 to get: 1 + 2 + 4 + 8 ... = -1 There's a million of these series in your dusty old Calculus textbook. Or you could look in 'generatingfunctionology' to find others. Complex analysis makes it more interesting, because the additional Cauchy-Riemann constraints make the solution unique. And so people are more willing to say that the unique solution…
on “Does 1+2+3+... Really Equal -1/12?” ↗This appears to be the book, on Scribd: http://www.scribd.com/doc/7846856/Generatingfunctionology-H-...
on “Generating functions and counting” ↗