Elegant, yet highly mathematical, look at the life of Alan Turing
595713
Leavitt freely admits that there is abundant documentation on the life and work of Alan Turing. I've read several of these works, and I can tell you this one is nothing like the rest. Leavitt has mastered the art of transforming Alan's complicated work into a form that truly captivates you. I had expected more on Turing's personal life, but Leavitt really concentrates his energy on revealing the inner workings of Turing through his professional and academic work. He offers perspectives that many others have totally missed. Some might challenge some of Leavitt's "reading between the lines," but most will enjoy the fresh view.
3469038
Based on the true story of Alan Turing and his computing machine that enabled the Allies to break the Germans' famous Enigma code machine, this film has it all: wartime drama, personality clashes, personal triumph and heartache, as well as a great script and brilliant performances by Benedict Cumberbatch and Keira Knightley.  A great film.
58747
Benedict Cumberbatch and the rest of the cast are brilliant in this movie based on the true story of Alan Turing, the father of modern day computing.  The team at Bletchley Park helped to shorten WWII by 2 years, and saved over 14 million lives according to estimates.  The heart-wrenching conclusion is both unbeleivable and eye-opening.  The sound track for this movie is so good.
3521756
Although calculus has been around for hundreds of years, still few outside of students, mathematicians and physicists really know what it is or what it does.  At last, as we peer backward in time, Oscar E. Fernandez reveals its hidden secrets in our daily lives.  He does this with dazzling analogies drawn from discussions within delightful chapter titles.  From parabolic arcs to why blood vessels branch off at certain angles in his new book, Everyday Calculus.

We are invited to understand nature through the myriad expressions mathematics provides.  The principals, however, we are all familiar with, such as rates of change, the nature of the derivative, and continuity are impregnated in everything we see and do.  They are the master plan of nature.  And most familiar, the area under the curve, better known as Riemann sums.  And if you work this all backwards, you get the antiderivative, better known as the definite integral, the Fundamental Theorem of Calculus.

In all, its a delightful read.  It will make you laugh and capture your imagination in this man-made, logical structure that can predict the future.  How?  It makes use of recurring functions, patterns and logical patterns that carpet our depth of understanding, both in scientific pursuits as well as worldly renditions of what is all around us.  It is a unique time for us as humans to be so privileged so as to witness the development of this very human, man-made language that has supported our conjecture and help build on tomorrow.

With a simple illustration of how Induction Powers the world, Fernandez demonstrates in very readable terms how our understanding and nature tames the wild, electrical beast that makes our world run.  Mathematics is the cornerstone of every technological foundation and rendition of scientific nurturance.  I applaud the efforts Fernandez for taking this bold step to clarify the logical position of mathematical concepts

In Touch Limits in ways most of us thought only mathematicians and physicists would comprehend.  Now, Fernandez makes such elusive concepts clear with vivid illustrations.  Its only a matter of time before the populous at large will feel as comfortable discussing mathematical concepts as they discuss Einsteins relatively theory today.  We are hence moving in the right direction.

Everyday Calculus is a triumph in the pursuit of the lofty goal of comprehending the world.  Fernandez has touched upon a sensitive nerve, not just because mathematics makes most people cringe, but because the subject has allowed the passage of great things from some of the greatest minds ever to wander within the twentieth century.

Oscar Fernandez is as bold as Alfred S. Posementier in his quest to deliver mathematical thinking as natures gift to the thinking person.  In years past, the chorus of theorems has remained unsung until a few brave souls have taken to the pen and ascribed the edict of logic and charisma wrapped together in a neat, logical and coherent package, just as Euclid would have dreamed so.  As children of the greatest mathematical thought, remain in the humble crowds.
768602
The Math Gene is a wonderful insight into mathematics and how humans may have evolved the ability for mathematical thought. Dr Devlin gives a powerful argument for his theory in three parts.  He begins with an explanation of the nature of mathematics, and dispells many misconceptions about math held by people outside of the mathematics community. He then spends the bulk of his text describing the nature and evolution of language and communication in humans and their differences with animals in that respect. He explains what pressures in the environment would be necessary to cause an evolutionary change in language and thought in a way that is understandable by a layperson and plausable to someone with a strong scientific background.  He ends his book with a comparison of the mind's mathematical and language processes, why language (particularly gossip) must have preceded mathematical thought, and why mathematical thought is a direct product of any consciousness capable of language.
I thoroughly enjoyed this book, and have recommended it to friends and colleages alike.  I would also recommend another one of Devlin's books, The Language of Mathematics, for a glimpse into the diverse and beautiful world of math any person could understand and appreciate.
1282526
Readers who are considering a computer science career should find this manuscript enlightening, entertaining and a boost to vocabularity with the likes of : machine ecology, accretion, bug tracking, version control, kluge, fractal, edge cases, entanglement,  spaghetti, code sorcerie, engineering hygiene, zeroth, sibitizing, and most compelling honorificabilitudinitatibus (page 53).
"We are in a new era, one in which we are building systems... can't be grasped in their totality.  They are simply too complex".
Microsoft Office alone has been estimated to be in the tens of millions of lines of computer code.
The road system in the U.S. has 300,000 intersections, with traffic signals, and is the substrate for the constantly churning turmoil of transportation.
"We have entered the age of entanglement.  Each expert knows a piece of the puzzle but the big picture is too big to comprehend".
The United States Code is a collection of federal laws that elaborates on the U.S. Constitution (originally a few pages) that now denotes 500 pages just to the postal service section.
In the financial world no single person understands the interconnected systems and few completely understands a single one.
Remember the Wright brothers?  Including the pilot their 1903 invention weighed in at 750 pounds.  A Boeing 747 has 147,000 pounds of aluminum, six million parts, and 173 miles of wiring.
How much more progress can civilization endure?
1370672
This is one of these books that changes your intellectual perspective.  An excellent introduction to Complexity Theory, still in its infancy with a lot of debates because it is a work in progress.
Complexity theory is perhaps the antithesis of reductionism and a complement of the most successful scientific philosophy that, however, leaves out such complex phenomena  as the emergency of life and intelligence, the weather, ant colonies, the immunologic system, biological metabolism,  brain functioning, self- referential systems, non linear phenomena,  game theory, the economy, artificial intelligence, etc.  Complexity theorists are trying to find common patterns in these different fields and take cues from dynamical systems, cellular automata, random Boolean networks, chaos theory, information theory, biological systems and others. The author defines a complex system as one that exhibits non trivial emergent and self-organizing behavior.
It seems that some of these systems have a balanced combination of randomness and determinism very well exemplified in ant colonies and immunological systems. Stuart Kaufmann says that life happens "at the edge of chaos".
The skill of the author to explain difficult questions in an easy language is demonstrated in  the description of the mechanics of DNA and the explanation of what is a fractal dimension, for example.
Other interesting topics covered are genetic algorithms (which have great practical applications and solve problems in  a rather mysterious way which is difficult to understand), cellular automata (a class of non Von Neumann computers), a software program to make analogies in a microworld defined by Douglas Hofstadter (author of the Pulitzer Prize winner "Gdel, Escher, Bach: an Eternal Golden Braid"), an excellent discussion of the best strategy in games derived from the "Prisoner's Dilemma", Small World and Scale Free Networks (the internet being one example), power laws, etc.
To sum up, if you are not an expert in Complexity, but are curious to learn about all these topics I would strongly recommend reading this book.
110305
Behind Deep Blue was written by the man who lead the research and development team which created the chess computer that beat the World Chess Champion, Gary Kasparov. Hsu tells a lot of fascinating stories about his involvement with IBM, academia and the world of computer-vs-computer chess tournaments. It never got too bogged down in computer or chess jargon.

Some interesting things concerning the identity of Deep Blue (or computers in general) emerge from Hsu's story. Hsu speaks of his computers' identities in ways which facilitate his sportsmanship. So for instance, almost every time one of Hsu's computers loses a game it is retrospectively explained by reminding the reader that the computer had been regrettably forced to play when it still needed a few more weeks of software or hardware tweaking.  It never lost because it was an inferior machine - it lost because its superiority could not manifest because its update/debugging had been interrupted by the tournament schedule.  As the book makes clear, Hsu's computers were continuously undergoing relentless tweaking, providing Hsu with this excuse every single time one lost. This may be par for the course when diagnosing machines - since any sub-desired performance which can be corrected can, therefore, be "explained" as the unfortunate consequence of the machine's present uncorrected state. For humans it's different. When I lose a foot-race I can't say, "Well the only reason I lost is because this race was scheduled a few years before my training made me fast enough to win it."

Another fascinating element of the book is Hsu's recounting of Deep Blue's now-famous rejection of 36. Qb6 in game two against Kasparov in the 1997 match. Kasparov broadly hinted that the computer's decision not to move that way was a human decision - implying that the IBM team had cheated. Hsu's defense of Deep Blue is convincing. But there is raised an interesting point regarding computer intelligence. If Deep Blue did in fact choose to avoid 36. Qb6 without human intervention then Kasparov's heartfelt identification of the move as cheating has Deep Blue passing a simple version of a Turing Test.
4824274
The theory of computation represents a fascinating landscape that intersects computer science and mathematics and can be roughly divided into three overlapping areas: automata and formal languages, computability theory, and computational complexity. And there is enough interesting knowledge about each area to fill three books, each twice the size of this one. And because of this I find it remarkable that the author has succeeded in filling a slim volume with the essential theory and results from each area, in a style that not only seems very accessible and intuitive, but also demonstrates important relationships between the three areas. For example, most books on computability theory do not discuss automata outside of Turing machines, but in his book Sipser elegantly proves that the equivalence problem is decidable for deterministic finite automata, but undecidable for pushdown automata.

Not only does the author have very good coverage of the three areas, but he also is able to strike a nice balance between mathematical rigor and intuitive understanding. His "proof idea" proof preambles greatly helped my students better understand the main ideas behind each result. In terms of coverage I found only a handful of introductory topics that were neglected: Greibach Normal Form, Rice and Rice-Shapiro Theorems, algebraic aspects of formal languages, Turing degrees, and perhaps context sensitive languages. With that said, remember that this book is just a semester-long introduction to a vast landscape. I recommend the following books for more depth: Peter Linz, "Introduction to Formal Languages and Automata"; Nigel Cutland, "Introduction to Computability Theory"; Christos Papadimitriou, "Computational Complexity".

Another strength of the book is how the author distinguishes exercises and problems: "exercises" are similar to the worked out examples, and can be solved by following one of the presented examples, algorithms or theorems, while "problems" require significant expository writing and deeper insight. Most undergraduates should be able to handle the exercises, but will find the problems very challenging if not impossible, due to the fact that students at this level are mostly familiar with problems that can be solved in a few steps by following some algorithm. So these problems have the capability of developing student intellect, but if assigned in too large a quantity can break the spirit of the developing student. Have care!

I congratulate Dr. Sipser on this fine book. May it inspire millions of readers to question the meaning of computation and explore its possibilities and limitations.
52743
The author seeks to describe the events that led to the proof of Fermat's theorem and succeeds amply. Not only is the book informative, its very very enjoyable. The book does not require a math background.  In fact the author takes care to properly introduce any math term or concept he uses.
Fermat was a great mathematician. In one of his notebooks he stated an equation and mentioned that the margin was too short for the proof of the statement. Later mathematicians found it impossible to prove this math statement. So hard was the problem that it became one of the most popular problems in mathematics and remained unsolved for centuries! Recently, a math professor from Princeton proved this theorem after a marathon effort.
The book introduces the reader to a lot of key mathematicians and interesting anecdotes associated with them. The best aspect of the book is that it presents events spanning centuries, in a manner that fits them together as parts of a solution to a single problem. Its not a sequential narration of events, instead its a coherent presentation of what was done over the years and how it contributed to the final assault.
4025217
There is at least one other book about Paul Erdos called The Man Who Loved Only Numbers and that one is pretty good, but this is even better.  The author does an excellent job of capturing the personality of this brilliant but really very peculiar mathematician.  He even makes a believable stab at explaining some of the mathematics to the general reader.
4365211
"Programming in Haskell" is among the most elegant computer language books I've read, and it will go on my shelf next to The Little Schemer and Godel, Escher, Bach.

I'm coming from the typical experienced C/C++/Java/Python background, with some past toying with Scheme.

The text presented an enlightening and well explained new concept in typed functional programming on nearly every page, with Haskell used as an excellent medium.

My only regret is that now I realize just how impoverished C/C++ and my other day-to-day languages are - although the functional approach is infecting my style even there.
2104252
Alan Turing, one of the fathers of modern Computers.  This movie is about his collaborators and his invention, which helped Britain and the Allies break the code that The Germans used with the "Enigma" machine for most of WW II.  Excellent movie, proving that ALL Govts sometimes act foolishly...Unfortunately, this time, it was Britain's turn.
2691480
There's a lot to whet the mathematical appetite in this book.  There is also a bit to frustrate and, in places, annoy that appetite.  Overall, MT is a very interesting book.  For the most part, it is accessible to any reader.  In it's closing section -- on Goedel's theorem, decidability, the halting problem, information and related matter -- things get pretty abstruse fast.  If you're not already familiar with these topics, it requires an act of considerable concentration to navigate the formalism of these sections.  But doing so rewards the effort.  I can't say I got (or bothered to labor over) all the details, but I did get the big picture.  And it's a pretty breathtaking view.  MT is a book I think I'll return to down the road, having done some additional reading on these topics, to ponder some more.  A very thought-provoking read for sure.
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).
3841257
Elements of the Theory of Computation, by Lewis and Papadimitriou, is something of a classic in the theory of computation. Of the many books I have used to teach the theory of computation, this is the one I have been most satisfied with.  It covers all of the fundamental concepts one would expect in such a book (more on this below) but offers a bit more mathematical rigor than most other books I've seen on this topic.  It also covers one topic that is rarely even mentioned in other textbooks: the composition of Turing machines.
The book begins with a brief introduction to the relevant discrete mathematics (such as set theory and cardinality) and proof techniques, then introduces the concepts of finite automata, regular expressions, and regular languages, describing their interrelationships. It proceeds to context-free languages, pushdown automata, parse trees, pumping lemmas, Turing machines, undecidability, computational complexity, and the theory of NP-completeness.  (These are all standard topics.) Along the way, Lewis and Papadimitriou also introduce random access Turing machines and recursive functions,  and do a nice job of explaining the halting problem and how this translates into undecidable problems involving grammars, various questions about Turing machines, and even two-dimensional tiling problems. All of these topics are covered with an appropriate mix of formalism and intuition.
Perhaps the feature I like best is the discussion of composing simple Turing machines to obtain more complex and interesting machines.  The authors even introduce a convenient graphical notation for combining Turing machines and spell out specific rules for composition. While most authors are forced to immediately employ heuristics in reasoning about complex Turing machines (lest the notation become overwhelming), Lewis and Papadimitriou are able to keep the discussion more formal and structured by virtue of their Turing machine "schema".  I believe this makes their arguments more rigorous and even easier to follow.
This is clearly one of the best books on the theory of computation. However, be aware that there have been very significant changes from the first edition, which was lengthier and more thorough.  I confess that I actually prefer the first edition, as it contains nice sections on logic and predicate calculus (which have been removed from the 2nd edition), and is a bit more formal (albeit with some fairly awful notation). The 2nd edition is definitely crisper, with much cleaner notation; it is clearly more student-friendly, which was presumably the aim of the new edition.
If you wish to teach an introduction to theoretical computer science, or wish to learn it on your own, this would be a fine book to use. It's hard to go wrong with this classic.
1293757
Roger Penrose, a renowned mathematician and physicist, has put together a highly readable account of some of the most significant and yet perplexing ideas of modern mathematics and physics.  His writing is more detailed and more understandable than the popularizations of his colleague, Stephen Hawking.  This book renewed my interest in modern science.