Complexity of a Simple Man
359063
Candid, broad reaching and insightful. Reveals the intelligence, complexity, wisdom and faith of a Pope whose everyday interactions demonstrate a remarkable childlike simplicity and joy. It takes a lot of prayer, honesty, hard work and love to become that simple. This is a great interview and a great read.
2061622
It is a book that the most part of him is written in a naive form(not in formal logic).
You need a basic knowledge of Set Theory(like Halmos Book).
Very interesting and the book started from the root of the problem.
Very Good
878431
In or around 1637, Pierre de Fermat wrote in the margin of a maths book notes describing what became known as Fermatean Triples. He claimed to have found an equation that was hard to solve. "I have a truly marvellous demonstration of this proposition which this margin is too narrow to contain". That one sentence was to tease mathematicians for centuries. The proposition, known as Fermat's Last Theorem, is simple to describe such that even a child can understand it: that there was no solution to the equation "a**n + b**n = c**n" (where '**' is 'to the power of', a, b, and c are whole numbers greater than 1, and 'n' is greater than 2).

Written like a detective story where the answer is known, this book is easy to follow, and leads readers through a maze of ideas, concepts and subtleties that would be a disaster in the hands of a lesser writer. This is absorbing narrative, leading up to the lecture where Andrew Wiles presented his proof of the non-solution of the equation. However, the proof presented on 23rd June 1993 was the beginning of a nightmare for Wiles, as a serious logic error was subsequently discovered that took an all-consuming 15 months to rescue.

The story of how a very gifted mathematician devoted himself for seven secretive years to a question that others had given up on is only half the tale that Singh tells. It is a journey through some of the history of mathematics, with the solution to the amateur mathematician Fermat's problem being an accidental occurrence. Along the way there are very good insights into the differences between mathematical proofs and scientific proofs; the former must be indisputable, whereas scientific proofs are only ever probabilistically true, and do change as knowledge increases.

There is no need for a great interest in or knowledge of mathematics to enjoy the story, which itself draws the reader onwards. I know nothing of the similarities between modular equations and elliptical equations, tied up within what became known as the Taniyama - Shimura conjecture, yet can appreciate the means by which Wiles was able to prove Fermat's theorem by establishing the mathematical truth of the latter.

Simon Singh started by investigating the story of Andrew Wiles and Fermat for a British television program. This book that he subsequently produced set new levels for the history of science as a popular writing genre. At the end, Singh goes further, and raises questions as to whether the discovery was worth it. If Wiles had not been able to rescue his proof, it is suggested that the effort would not have been in vain, as there were significant advances in mathematic knowledge obtained in the trying. Singh also discusses other difficult areas, and muses on whether some of these will be unprovable, or insoluble. Fermat's Last Theorem, having frustrated the best mathematical brains for over 350 years, is now established, and is not one of the 'unknowable truths of mathematics'!

In concluding, it is fitting to use the words with which Andrew Wiles concluded his 1993 lecture: "I think I'll stop here".
592065
long, complicated, slow, but worth it. This book require a lot of patience since it's not easy reading that you can get done in a day or two. The book is very detail which i like. You need to read at least 50 pages to really get into this, once you past this point then it'll get interesting. Hope to nee his other novels soon, especially "half a confession".
3820528
This slim monograph on Fast Sequential Monte Carlo (SMC) methods is an advanced topic in mathematics, so an undergraduate education in probability and statistics is a prerequisite and many readers will want to start reading at the appendices where some of the prerequisite material to read the body of the book is briefly reviewed, such as the satisfiability problem (SAT), vertex colouring, the knapsack problem etc. Of the five issues, outlined by Knuth, of concern in combinatorics the books examines;
1) the existence of arrangements that meet some stated conditions,
3) the enumeration of those possible arrangements and
5) the optimal arrangement given some cost function of those arrangement.

As an example of one of the problems the book looks at using SMC methods, consider the knapsack problem which can be stated as: How can I fill a knapsack of a given capacity with some set of objects of varying values and sizes? The first thing to determine is are any of the objects small enough to fit in the knapsack - ie the existence of an arrangement. The book skips the construction of a solution, to counting the possible ways to fill the knapsack with those objects. The authors then don't address the issue of determining a way of computing each of those solution systematical but then move onto the problem optimizing the filling of the knapsack give some objective function such as the filling with the most value. This crux of the book is the examination of stochastic techniques that avoid the need to construct and generate the full solution space, but that can quickly estimate the number of solutions and the likelihood that a particular solution is optimal when the number of possible solutions becomes very large. For example, one of the key algorithms discussed in the book is stochastic enumeration that can be used to approximate the nonstationary Markov chain committor function for a SAT problem.

I think the book would benefit from online support materials like data sets for readers to play with, test and deepen understanding.  The bibliography is good but many of the references will be difficult/expensive to get hold of outside of an academic institution.
3309129
It is sort of difficult to read, but computer programming is not simple. The program itself is wonderful, go python :)
4765215
Well there are parts that are straightforward and easy to ponder. However there are other authors that are less straightforward or one could say confusing and difficult to wade through.
508601
This was an amazing book about a very complex man. A man, for good or bad, lived life his way, by his rules. There was not a dry or boring spot to be found. My interest was held throughout. This was a thoroughly engaging and enjoyable book.
4027141
I enjoyed this book very much - it is fresh in expression and introducing complex ideas - even humourous at times! And yet for all that there is a sense of some lack of achievement also, although this may not be a failing of Mr Wilson.
As a mathematics student - and I have studied quite a lot of mathematics - it seems to me that proofs came in three kinds. There are the mind opening 'obvious' ones that are so stand-alone that once you read them there is nothing to learn. The blinkers have been lifted from the eyes and the world is a different place. Then there are the proofs that take such a lot of work to assimilate and for a long time you just don't see it. Perhaps you never really do, but you do come to accept it because the mathematics community is convinced. Then there are the proofs that even the mathematics community struggle with. The four-colour problem's proof is one of these. Consequently there is left a nagging doubt, which I gather is quite widespread amongst people far wiser and knowledgeable than me - than Mr Wilson also I suspect.
The curious thing is that a conjecture like the four-colour mapping, or Fermat's last theorem, or the conjecture that all even numbers can be made up of the sum of two prime numbers, is so powerful AND there are no counter examples available to challenge the conjecture. So why can they not be proved by some elegant insight such as Fermat claimed for his last theorem but never showed the world before his immanent death in a duel? Why can the four-colour problem only be proved by such inelegant computer-assisted means as this book describes? Perhaps Mr Wilson's greatest achievement is in exposing the doubts and dissatisfactions of the current proof of the four-colour problem despite the appearance that it may well be adequate (this goes for the proof of Fermat's last theorem too).
498343
There are few books which can even come close to the lucidity and simplicity with which Ivan Niven explains the basics of combinations and permutations. He even puts forth difficult topics like Generating Polynomials in the most simple and understandable fashion. No doubt this is a prescribed book at Harvard!!  It has personally helped me in preparing and coming out successful for admission to the Indian Institute of Technology institutes,which is one of the toughest examinations in the world .  The book is suitable for anyone who wants to understand the maths involved in making a choice. This will be of great help for High School students, Under Graduates,Graduates and teachers of Mathematics. A gem from Ivan Niven.
2708393
I find myself agreeing with all the comments made so far.

It's not too common to find a book that is able to describe in simple terms, such a large and  diverse range of mathematical tools.

The author uses a framework - to tie together tools used in  describing and handling deterministic, semi deterministic, and stochastic systems.  For an example of Deterministic, try ODE's (ordinary differential equations), for semi deterministic - try Periodic but noisy wave-forms (some stock prices), and finally Stochastic - Random looking waveforms that have underlying patterns that can be described using  either using Chaotic indicators (Hurst, Liapunov ) or probability type descriptors.

This book is the kind of thing you needed to help steer you through those dry mathematical books that are divorced from reality - A sort of classification system for deciphering what kind of gunpowder was used in those display's of intellectual fireworks from the tops of ivory towers.  Kinda "So thats what all that maths means, but in plain english".

A depth of understanding, for practical application, without intellectual egotism and opaqueness.  (But then maybe I'm just a bit thick ... :)

I'd tend to call this book as an equivalent to the Rosetta Stone for the maths of dynamical systems.

You may not use it directly - but you will benefit and grow in understanding from its' plain and simple  sign posts along your journey.

It has its place on my book shelf.
3597342
The problems in it are not very hard, but extensive and fundemantal.
It teaches you how to think out a solution.

Recommend
2382704
Life Itself is somewhat a seminal work of modern complexity research. The author makes a convincing case that life itself is quite complex. So complex, in fact, that it would be hard to ever understand it  by using only the narrow lenses that "hard sciences" like physics and chemistry provide.

While still relevant, it is nice that you can purchase used copies of the book that are in great condition for a fraction of the $90 price of a new copy.
4319871
Michael Drosnin's THE BIBLE CODE illustrates well a real-life application of a mathematical idea which is at once simple and complex. The central notion presented is that the Torah (Old Testament) is riddled with  predictions of the future encoded as equidistant letter sequences.  Approximately 100 examples of this are given in the book.
Unfortunately,  the mathematical problem upon which the book depends is given short shrift.  Drosnin quotes a Harvard mathematician, an NSA cryptanalyst, among others,  who seem to think that the phenomenon observed is unique and inexplicable.  But this is clearly wrong.  The same phenomenon *can* and has been observed  in other works, such as  Melville's MOBY DICK.  The more words you string  together, the greater the likelihood of finding words that match or  describe events.
The book works well as non-fiction/fiction, is easy to  read and quite compelling in it's way.
1934723
I purchased this based on simplicity and price as a gift for my brother-in-law in his early 30s. It did not look impressive coming out of the box, however once I began to try putting the pieces back in the square the challenge began. It is essentially a puzzle, with several ways to put the puzzle together so it creates a square. It is small, so it travels well and comes in quite handly during those inevitable moments of boredom.
1866005
For the majority of people, advanced physics is something understood only by a select few, something that requires years of post-graduate work to grasp. In this book, Stephen Hawking attempts to take these extremely complicated and unfathomable theories and present them in a manner that is both understandable and entertaining. For the most part, he is successful.

Hawking starts by recounting the development of the understanding of our world through the eyes of physics. This helps show how the many perceptions of our universe that we now take for granted often took many years to be understood and accepted. This allows the reader to see that there are many things that could change still about our current perception of the universe.

Having done this, Hawking delves into more complicated concepts, such as the theory of relativity, the Big Bang, black holes, and the end of the universe. He talks to the reader in language they can understand, yet he never "speaks down" to the reader. Hawking also considers the role of God in a universe governed by physics in a way that I believe would not offend the believer.

In all, Hawking manages to condense a lot of complicated material into a short, simple book. I believe the reader will acquire a better picture of the mind of the astrophysicist, but I don't the relevance of these intangible concepts will be readily grasped. Upon finishing the book, I was left wondering what many of these difficult theories actually mean to us as a whole.
3846234
Purportedly a simplified rewrite of his earlier work, but parts of it are quite challenging from a conceptual point of view. I have gone back and re-read several sections in an attempt to get my head around it.