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NP refers to the problems to which we would like to find the best solutions. And Fortnow takes it from there, sketching the history of the P vs NP pursuit since it was first formulated in the s up until the present. If we can know for sure that all problems ultimately have fast solutions, then it's only a matter of time before we discover them. And solve all our problems. He thinks that there is no possible ultimate beautiful world, but that we will have to strive to find "good enough" solutions to those hard problems. And yes, he does talk about what those hard problems are in theoretical computer science and how they affect our everyday lives.

Cryptography is perhaps the most well-known application area for those hard problems. Fortnow doesn't think we are anywhere near to solving P vs NP, that we may even be hundreds of years away.

Ketan Mulmuley, On P vs NP, Geometric Complexity Theory, and the Riemann Hypothesis III

Or that we may never solve it. Overall a fine book. Comparable in level to a physics book by say, Sean Carroll or Lee Smolin.

In other words, you will have to challenge your mind a little to grasp every example and problem description. I would recommend the book for any academic library collection collects popular science. In particular, since there seems to be fewer popular computer science books than other fields, Fortnow's book fills a gap. I would normally not suggest this type of book for smallish public libraries, but again it does fill that gap.

In this Book

As for school libraries, mathematically gifted students at the high school level would find a lot to love about this book. But for the layman wanting to get a detailed explanation of the problem and it's developments so far, it's a great account. Sep 04, Ami Iida rated it really liked it Shelves: math. View all 3 comments. Apr 26, Robert Martin rated it liked it. The chapters on cryptography, while interesting, seem to be really out of place. Nov 18, Arquero rated it liked it. Jul 02, Dana Robinson rated it it was amazing.

The Golden Ticket: P, NP, and the Search for the Impossible - Lance Fortnow - Google книги

Probably not that accessible to non-CS folks, but a very good overview. May 12, Akarsh Seggemu rated it really liked it. Lance Fortnow, has explained the concepts of what is P and NP in this book like a novel. If you watched the film Charlie and the Chocolate Factory; you will enjoy reading this book. Dec 22, Edward B. This book is an attempt at a "popular" non-technical explanation of the P-vs-NP problem.

Fortnow doesn't even give a rigorous definition of the problem - which is fine, because a rough one is good enough for the purposes of the book.

Plus, you halve your audience with every mathematical formula included in a book. Source: apocryphal; I read it once somewhere, attributed to some publisher or other. I came in with a basic understanding of the problem. I don't think I came to any new insights. An This book is an attempt at a "popular" non-technical explanation of the P-vs-NP problem. And I really don't think that someone who had never heard of P-vs-NP before would walk away with more than the very vaguest of notions.

Still, there were quite a few interesting details, metaphors, etc. And it was a surprising quick read. Mar 18, Roger B rated it really liked it Shelves: math. Oct 18, Brett Thomasson rated it really liked it Shelves: non-fiction , full-review-available , math , science. Very broadly speaking, there are two kinds of math problems in the world: Ones which can easily be solved by a computer and one whose solutions can be easily checked by a computer.

The set of solvable equations is called P. The set of checkable equations is called NP. An Very broadly speaking, there are two kinds of math problems in the world: Ones which can easily be solved by a computer and one whose solutions can be easily checked by a computer. Georgia Tech Computer Science professor Lance Fortnow has spent much of his career considering this problem and writes about some of the history of its investigation in 's The Golden Ticket: P, NP and the Search for the Impossible.

It would also make some things significantly more difficult, such as online security. Current online security relies on equations that can't be easily solved because of the number of digits they use and immense number of possible number combinations. He offers some thoughts on what the development of quantum computing, which is projected to be immensely faster than current computing, might mean about getting a definitive answer either way. He keeps the formula and equation use to a minimum, saving much of it for appendices for the readers interested in that part of the story.

The Golden Ticket is a great introduction to a math problem that few people know about and even fewer understand, and a good way to try to start thinking about it and its implications. Although Fortnow doesn't delve much into the philosophical implications of the P, NP problem, he provides enough of the basic tools for the curious to begin that part of the journey themselves.

Original available here. May 19, Patrick Stein rated it liked it Shelves: math. Added: I finished this book last night. The book has some interesting discussion of different NP problems. And some brief naming of key figures in developing the field. However, the book was really short and yet there is still lots of it that had no place. There is a big discussion of Quantum Computing at the end.

QC is interesting and all. But, the discussion starts by saying we already know that QC won't be able to do NP-Complete problems in P unless we can also do them traditionally in P. So, why then discuss QC for thirty or forty pages? Yes, it is interesting how one might convey a qubit to someone else or teleport something from Chicago to Singapore, but neither of those involve anything in NP. What I was expecting from this book was a good lay of the land as to where the problem stands which the book did decently on , anecdotes and bios of key folks who extended the field which the book did incredibly little of So, get on the hump.

As I was reading, I frequently had to look things up including the definitions of P, NP, and NP-complete in order to understand what the author was getting at. I did not like the frequent use of made up scenarios to illustrate what the author was attempting to explain.

I would expect that an experienced science communicator with a deep understanding of the topic could have provided more realistic situations then a make-believe world called Frenemy. The writing was not always clear enough for me to follow the author's train of thought to a conclusion. He would be talking about something and then all the sudden talking about something else which may or may not have been connected, but I couldn't figure it out.

I was very interested in this topic and really wanted a more in depth understanding of it. I did not get that from this book.

See a Problem?

I only finished reading it so that I could discuss with my book group. Jul 16, Freeman Crouch rated it really liked it. Computer Science doesn't have a lot of great pop science writers. The issues are abstractions of abstractions of abstractions, and the jargon is sometimes difficult, even when the issues are pretty simple. It is a question about what problems are inherently hard to compute.


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I think most of my teenaged students who basically are somewhat interested in computing would get through this and enjoy it. Full diclosure: I am a high school CS teacher.

The Golden Ticket: P, NP, and the Search for the Impossible

How he manages to expunge professorisms from his writing so well I have no idea. He tells stories about the present and historic researchers and speculative stories about what a world where NP-hard problems could be solved in polynomial time.

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If you liked "A Brief History of Time" or other science writing for intelligent lay audiences this might grab you.