Analytic Combinatorics Philippe Flajolet Robert Sedgewick 9780511801655 Books
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Analytic Combinatorics is a self-contained treatment of the mathematics underlying the analysis of discrete structures, which has emerged over the past several decades as an essential tool in the understanding of properties of computer programs and scientific models with applications in physics, biology and chemistry. Thorough treatment of a large number of classical applications is an essential aspect of the presentation. Written by the leaders in the field of analytic combinatorics, this text is certain to become the definitive reference on the topic. The text is complemented with exercises, examples, appendices and notes to aid understanding therefore, it can be used as the basis for an advanced undergraduate or a graduate course on the subject, or for self-study.
Analytic Combinatorics Philippe Flajolet Robert Sedgewick 9780511801655 Books
Flajolet and his group at INRIA (B. Salvy, P. Zimmermann, many others) have created the field of "analytic combinatorics", and this book has everything you might possibly want to know about the subject (since the selection of topics is very thoughtful, it does not have that much you would NOT want to know). The only reason to possibly not get this book (assuming you are interested in the subject) is that the PDF is available free on Flajolet's web page, but the book for is quite convenient and quite reasonably priced.Product details
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Tags : Buy Analytic Combinatorics on Amazon.com ✓ FREE SHIPPING on qualified orders,Philippe Flajolet, Robert Sedgewick,Analytic Combinatorics,Cambridge University Press,0511801653,Combinatorics & graph theory,MATHEMATICS Discrete Mathematics,Mathematical theory of computation
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Analytic Combinatorics Philippe Flajolet Robert Sedgewick 9780511801655 Books Reviews
Wow!!! I would have thought the plans to build Combinaoric transformer robots would be classified but here is all the theory on . Whoa?!? My wife got me this as a 25th anniversary present and I thought that's not so romantic but I couldn't have been more wrong. We've both read this book cover to cover a few times and it is hot stuff. I hope you live someplace cold because you will not want to go out until spring after you get this pot boiler cooking.
Sort of the hidden underbelly of combinatorial mathematics is the relationship to
fractals and this book actually seems to admit it exists.
Some of the different types of generating function are hard to follow
and a reference to Roman's Umbral calculus or Sheffer sequences
would be useful as well, but a lot of very useful information
is here and they do mention Dr. Sloane's EIS.
Not since I got a look at the classic Riordan text have I seen
a book that packs this kind of impact on the field
of combinatorial mathematics.
This book is one for students who are serious about learning
the developing science of combinatorial analysis.
I just wish I could afford it
and not have to check it out of the library to be able to read it!
The connection of Bernoulli functions to bosons
and Euler functions to leptons isn't touched on,
but it is the reason that combinatorial analysis is important to physics.
So you can't give the book 5 stars even as good as what is presented is.
This book covers a LOT of ground FAST. You can think of it as the third volume in the following sequence
(1) Algorithms; Sedgewick and Wayne. Appropriate for an upper level undergrad/grad text book for a university algorithms course.
(2) Analysis of Algorithms; Sedgewick and Flajolet. Much more detailed treatment of algorithms, and using the Generating Function approach to Algorithm Analysis.
(3) Analytic Combinatorics S&J. Advanced aspects of the above.
Here is the setup For some category of computer science or combinatorical object, let A[n] denote how many distinct examples there are of size n. Then the complex function f(z) = sum(A[n] z^n) is the "Generating function" for A[n].
The S&J methodology is (1) generate an equation for f(z) directly from the combinatorical object. (2) Use this equation to solve for f(z), or at least obtain info about it. (3) Use classical complex analysis (singularity analysis and saddle point methods) to obtain excellent estimates of A[n].
I am confident this will get easy once I work out about 100 examples!
Flajolet and his group at INRIA (B. Salvy, P. Zimmermann, many others) have created the field of "analytic combinatorics", and this book has everything you might possibly want to know about the subject (since the selection of topics is very thoughtful, it does not have that much you would NOT want to know). The only reason to possibly not get this book (assuming you are interested in the subject) is that the PDF is available free on Flajolet's web page, but the book for is quite convenient and quite reasonably priced.
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