Most people either misunderstand what math is all about, or see it as a collection of rather disjointed areas collected together under a single name. Devlin does an admirable job of re-educating us all, and showing how the different areas of mathematics are linked together, often in rather surprising ways.

This book is simply brilliant. The amount of information Devlin has managed to cram between two covers is amazing. Having spent years studying this stuff, it's rather depressing to see that most of the important things I've learned can fit into a 350 page book, but then this is surely a testament to Devlin's skill.

Although this book makes no formal educational expectations of the reader, I feel that a true beginner would have trouble following a lot of parts, although they would still get the general idea. This would be better then nothing, but I think that this book would be best appreciated by those with some formal math background. I would be curious to see what a high school student would make of this, since I really wish I'd had this book back then. When you see the beautiful ways that mathematics connects the most seemingly disparate ideas, you can't help but want to learn more!

Devlin: "The particular topics I have chosen are all central themes within mathematics... But the fact is, I could have chosen any collection of seven or eight general areas and told the same story; That mathematics is the science of patterns, and those patterns can be found anywhere you care to look for them, in the physical universe, in the living world, or even in our own minds. And that mathematics serves us by making the invisible visible."
At this writing it has been more than a few years since my last class in mathematics. But I liked math as a student and still do, even at the point that notation and degree of abstraction begins to hurt my head, so to speak, I still like it. There is a solidity and a beauty in mathematics that eclipses the empirical sciences. It is not only the practical applicability, logical purity, and beauty of mathematics that interest me, it is also its very immateriality. As Devlin states, "music exists not on the printed page, but in our minds. The same is true for mathematics; the symbols on a page are just a representation of the mathematics."
This is a wonderful book. Before 1900, mathematics could be wholly categorized within about a dozen subjects. While advances are still being made in some of these older disciplines -- Devlin discusses how developments in number theory are being applied to encryption for such purposes as banking security -- there are now at least 60-70 somewhat distinct disciplines of mathematics. The author reveals the logical foundations, history, and current applications of number theory, mathematical logic, the calculus, relativistic geometry, topology, and probability. Applications of mathematics to such seemingly far-flung fields as linguistics, electrodynamics, and astrophysics are briefly but aptly considered. He introduces us to the patterns and progressions of perceptive minds, from the Pythagoreans, Platonists, and Peripatetics, to Pascal and Penrose, with glances at Galileo, Gauss and Godel. [Okay, enough alliteration ... just having a little fun with patterns; and patterns, as Devlin instructs, is precisely what mathematics is all about.]

I've always had a like-hate relationship with math; I didn't do well in it in college, but I've long been fascinated by physics. There are many books for the lay person about the cutting edge in physics; books like that are harder to find in the world of mathematics.

But Keith Devlin has done it. He surely captured me near the beginning when he described mathematics as the study of patterns; a wonderful description that starts to get at why mathematics seems to be the language underlying the physical universe.

This was not an easy book for a slightly math-averse person, but Devlin's explanations were always clear, and more importantly, always gave a sense of context of what he was discussing.

I did not like math as a subject when I was a student. And there is allot of talk today about math phobia and how we might have not been taught math properly. Well that is why I am trying to teach myself math but differently and I also am a behavior therapist treating math phobia in children (jasona@barak-online.net- author - BEING IN CONTROL Natural Techniques for Increasing Your Potential and Creativity for Success in School). This book helped me understand math concepts through the science of patterns. For once I enjoyed math as a topic. Great history, pictures and everyday concepts that are relevant to a non math major. I was able to understand most of the book without problems and this book helped me go on to read other type books like it on math.

The book is fun to read ,very informative and very clear.
It doesnt matter if you know some university mathematics or not ,anyhow you will find this book a pleasure to read ,and if you dont know nothing about mathematics it will change your perspective on the world. I suggest you will get a copy and read it.Excellent book!.

This marvelous book to explains to non-mathematicians the joy, beauty and power of mathematics. Each topic is presented in an original manner with alot of colorful illustrations to delight the eye and mind. Devlin shows how mathematical thinking is critical to our exploration of the world around us. This is one my top ten of all time list

This book is a comprehensive in-detail overview of a wide rage of mathematical subjects, from Fermat's Last Theorem to topology. If you are considering a mathematical career, this book is a great buy.

The phrase "Golden Age" is most often used to refer to an era when the dominant players exhibited characteristics that are later called "amateurish." For example, the fifties are often called the golden age of American television and the thirties and forties the golden age of science fiction. However, like most such glittery phrases, it can be redefined to suit ones purposes, and that is what Devlin does here. He takes as his era of consideration the years since 1960.
Some of the topics are those that have been resolved in this time span, such as the four-color problem, the classification of simple groups, Hilbert's Tenth Problem, and the Continuum Hypothesis. Others are some that have been created by the advent of computers, such as fractals, chaos, and the efficiency of algorithms. Finally, there are those where only significant progress has been made, such as Fermat's Last Theorem, factoring large numbers, and Knot Theory. All are dealt with in a manner that will allow the non-technical person to understand them. The writing is clear, concise, and direct.
With over half of the material dealing directly with work done on computers, it is clear that the author's use of the phrase is correct. However, this era will go down in history as the original golden age of the use of computers in mathematics and not as a new golden age of mathematics alone.
Strongly recommended as a primer on major mathematical accomplishments since 1960, this book can be enjoyed by amateurs and professionals alike.

Published in Journal of Recreational Mathematics, reprinted with permission

This is the best popular math book I've ever read. The first edition of this book was responsible for rekindling my interest in pure mathematics after a long layoff (which has persisted to this day). The author covers some topics that are typically covered in popular math books (such as chaos theory and the difficulty of factoring large prime numbers). Fortunately, most of the book is devoted to topics that are rarely dealt with in such books, such as the classification of finite simple groups, the class number problem, and the Riemann hypothesis. The new edition also contains an expanded section on Fermat's last theorem (which has been proved since the first edition came out). What I like about Devlin's style is that he goes into the math to a much more significant extent than most popular science writers and yet still keeps everything easy to understand for anyone with (say) an understanding of basic calculus. The only (minor) criticism I have of the book is that Devlin often gets tantalizingly close to a major result and then begs off with the statement "the full result can only be understood by specialists". Most of the time, this makes little difference, but with the class number problem (which, among other things, explains why exp(sqrt(163)*Pi) is almost an integer), he leads you along a fascinating journey and then doesn't explain the original motivating problem (why exp(sqrt(163)*Pi) is almost an integer). However, this is a minor nit and doesn't significantly detract from a fascinating book.

Dear friends,

Apologise bad English. "An Electronic Companion to Calculus" is very nice book. It covers matter of calculus first year technical university course. It is written with clear and fluent style, with many good examples. For us it can be used as the excellent textbook of the special English.
However, our University Library can buy books abroad only 2002 and later (lack of resources). I intend buy it privately.

Best regards

RNDr. Ctibor Henzl, Ph.D.
VŠB - TU Ostrava, Faculty of Electrical Engineering and Computer Science
Department of Theoretical Electrical Engineering

17. listopadu 15, Ostrava - Poruba, 708 33, CZECH REPUBLIC

As a teacher of large calculus classes, I know that my students are unable to get much tutorial help. Devlin's Calculus Companion is like having your own tutor--you get instant feedback, hints, and an explanation of why your answer is correct of incorrect.

Life by the Numbers has a simple thesis to prove: that math is anywhere and everywhere; but instead of asserting the pervading ubiquity of mathematics whether you like it or not, the book convinces you that you *will* like it, period.

The book is richly illustrated and jargon-free, true to its promise on clarity and easy-of-reading especially for the non-professional readers. It is not so much of a wild speculation however to suggest that even a professional (specialist) mathematician will get a worthy entertainment reading this book, considering the wide spectrum of human interests where mathematics is unexpectedly to lurk that Devlin adventurously explores.

I recently purchased a videotape of the Star Wars™ movie, 'The Phantom Menace.' It is difficult to believe that a more convincing point of evidence for the power of applied mathematics will exist for some time. The scenes where the generated creatures are in motion have a degree of reality that is astounding. As Devlin spends a great deal of time explaining in this book, what you see is a complex series of numbers translated by a computer into pictures on a screen.
Other topics concerning image generation by computer involve the visualization of scientific data. People working in this area are often a combination of graphics artist and computer scientist. With such enormous amounts of data being collected, interpreting it and filtering out the points of interest has become a horrifically difficult task. The only way that it can be done is to find ways to filter the data as much as possible and then display it in a visual manner where the key points are easily discernible. No quote better describes the situation than that uttered by R. W. Hamming, 'The purpose of computing is insight, not numbers.'
The physics of sports is also described in some detail. No matter how well trained their bodies are, athletes are still bound by the laws of physics, so at some point their training must incorporate these laws. A simple question such as whether to jump higher or spin faster when figure skating can determine the difference between a medal winning performance and simply watching it happen on television.
This book is a tour de force in how many applications there are for mathematics, with many that appeal to young people. An appreciation for the value of mathematics is the first step towards a desire to study it, and this book will no doubt spark the appreciation.

Published in Journal of Recreational Mathematics, reprinted with permission.

It's not easy to write a good textbook in Math. Only few people are gifted in that ability. K. Devlin is one of them.
The subject is not easy, but the auther leads you step by step to a full understanding of the constructible universe and the results related to it.
You will find very clear proofs in it, a reasonable ordering of the material, and all the other things that you look for in a good Math book.
Despite the high price, I reccomend buying it.

... but keep it in mind for that teenage nerd in your life.

To help you evaluate my evaluation, let me note up front that I have three long-ago years of graduate math courses under my belt, which made me familiar with four of the seven problems discussed here. I got bored with much of the account of those four, had fun with the discussion of the sixth problem (the Birch and Swinnerton-Dyer Conjecture, which has to do with rational points on elliptic curves), and obtained a vague picture of the remaining two.

My three-star rating is bound to be misleading. Keith Devlin has an enormous gift for mathematical explanation, but as he himself recognizes, in attempting to explain to the proverbial man on the street the seven Millenium Problems (for solving each of which the Clay Mathematical Institute, hoping to spur mathematical research in the 21st century somewhat as David Hilbert did with his famous set of 23 problems in the century just past, has put up a cool million American dollars), he has bitten off more than anyone could possibly chew. I don't mean to suggest it could have been done any better.

If you hanker to tackle the problems and win one of those millions for yourself, start hankering for some other pipe dream. These problems are tough. If you want to thoroughly understand what they consist of, you will need to go to the official technical description of the problems in the book jointly prepared by the Clay institute and the American Mathematical Society. If you want a light overview of them, there's no such thing, but this book is as good a compromise between ease and clarity as you will get. If you just want a feel for where mathematics in general stands at this point in history, the backward glance at Hilbert's problems given in "The Honors Class" is a better place to start.

The challenge for Devlin (aside from gearing up to understand the two most abstruse problems himself) was to describe the problems without assuming any knowledge on the reader's part beyond high school algebra. So he has a humongous amount of ground to cover. With sprightly historical notes, he zips through complex numbers, complex functions, infinite sums and products, special relativity, quantum field theory, symmetry groups - and that's just the first two, easiest chapters. He does a particularly fine job, I felt, with the fifth chapter, on Poincare's conjecture. The mathematics needed for a precise statement of the conjecture is fairly daunting, but his informal description conveys the heart of it vividly and accurately.

All the above is subject to a major caveat. The real agenda for this volume is narrower than educating the general public. The main thing the Clay Institute wanted its prize offer to accomplish was to stir interest in math among students. Considered in those terms, I'd give it five stars, because the people who are going to lap the book up with relish are mathematically gifted high school students. If bits of each chapter go over their heads, it will only serve to whet their appetites. Because it's so ideally suited for them, I'd like to see (and I'm sure the Clay Institute would like to see) Devlin's opus in every high school library in the country.

Is the solution of any mathematics problem worth one million dollars? Yes, in fact there are seven such problems. In 1999, Landon Clay established the Clay Mathematical Foundation and in 2000, the Clay Foundation announced seven separate prizes of one million U. S. dollars for the solution of each of seven mathematics problems. In keeping with the famous list of unsolved problems enunciated by David Hilbert at the turn of the previous century, this list can be considered the problems for the new century, which also happens to be a new millennium.
Make no mistake, these problems are very hard. Even with all his mathematical expertise. Devlin readily admits that he really does not understand them all and had a very difficult time writing about them at a level so that a general audience could understand the basics of the problems. The seven problems are

· The Riemann hypothesis
· Yang-Mills Theory and the Mass Gap Hypothesis
· The P vs. NP Problem
· The Navier-Stokes Equations
· The Poincare Conjecture
· The Birch and Swinnerton-Dyer Conjecture
· The Hodge Conjecture

and the Riemann hypothesis is distinguished in that it is the only one that was also on Hilbert's list at the turn of the previous century. In his descriptions of the last two problems, it is clear that Devlin is struggling to understand the fundamentals of the problems.
Nevertheless, he does manage to inform the reader about what the problems are about, as well as a taste of how difficult they are. Like the problems David Hilbert stated in 1900, this collection of problems forms a marker by which the mathematical progress of this century will be measured. For that reason, all mathematicians should learn something about them, and this book is an ideal initial step.

Published in Recreational Mathematics e-mail newsletter, reprinted with permission.

In this book the author makes a sincere attempt to describe to a popular audience the content behind seven mathematical problems that were chosen by a private foundation called "The Clay Institute" as being deep enough to warrant a prize of $1,000,000 for their solution. The goal is realized in some parts of the book, but falls short in others, but it still is of value to those who are curious about the history and content behind these problems. The author is aware of the difficulty in describing the content of the problems to readers without substantial mathematical preparation, and he does a good job in general.

One can of course think of many other problems that fit the stature of the millennium problems, such as the invariant subspace conjecture, or developing a complete mathematical model of the cell, but these seven will no doubt spark the curiosity of a few young persons as they further their studies in mathematics. Some of the millennium problems, such as the Riemann hypothesis, the NP problem, the Poincare conjecture, and the Navier-Stokes equations, require only an undergraduate education. The others definitely require more background, just to understand even the statement of the problem. All of the them are fascinating, and will no doubt stimulate some incredibly interesting mathematical constructions.

Personal note for anyone interested (from someone who has worked on one of these problems for several years): For those readers who are thinking about attacking one of these problems, it is important to be really interested in solving it, for your own satisfaction, and not to be concerned about the financial reward or what the solution will bring you in terms of professional advancement. Large blocks of time will be needed to think about the problem, and therefore you will have to be concerned with your livelihood in the interim. Being a single person will definitely relieve you of the financial burden of having to support a family, but on the other hand a family will bring you personal warmth as you take the roller coaster ride of confidence and depression that goes with this kind of research. A traditional tenure-track position might be difficult to justify, since you will not be publishing and therefore your chances of obtaining tenure will be greatly diminished. It might also be wise in whatever job you work in to keep your ambitions to yourself, as colleagues and other mathematicians will typically not be encouraging in your decision to work on the problem. Therefore, you will definitely find yourself working on two problems in your life: the millennium problem and a constrained optimization problem, the latter being how to live your life in the interim, and whose solution possibly ranks in similar complexity. Your research in the millennium problem will probably take years, and as you see more lines appear on your face and your colleagues take the normal professional route, you might have doubts about your decisions. The more time spent on it without resolution of course will close the doors on a standard career in academia, and you will approach a critical point where there is no turning back. It is at this time that you will realize that it is you that has taken charge of yourself, your goals, and your attitudes about mathematics and life...and this of course is the best possible life anyone can have.

Mathematics and mathematicians can be the objects of public interest, if there are individuals capable of explaining those items in a form that the intelligent reader can follow. Keith Devlin is such a person and the editors of the British paper, The Manchester Guardian, were intelligent enough to understand that. The result is a mathematically simple-minded yet enjoyable collection of 143 brief vignettes covering mathematics and computer science.
Generally, only one and one-half pages in length, most articles earn the accolade, "touche." As many writers point out, the short piece is often the hardest to write, as every word must count. Devlin succeeds in the most difficult of arenas, in that enough background must be given so that the naïve reader can understand the topic and the point is resolved with sufficient clarity. And all this is done with a minimum of formulas. While sophisticated mathematicians and computer scientists will find the material limp, this work is capable of standing on its own as a piece of entertainment.
An existence proof that mathematics and computer science can be made understandable to an intelligent public that is interested, this book should be an element of every public library.

Published in Journal of Recreational Mathematics, reprinted with permission.

Anyone seeking a deeper understanding of the foundations of the mathematics will benefit from reading this excellent book.
Despite considerably abstract (almost no concrete examples), this book was carefully conceived to guide the reader through some of the most exciting contemporary ideas on set theory. If I had to name a minus about this book, I would mention the lack of solutions to the problems posted by the author. This makes the book a little less suitable for self-study.

Nevertheless, this book was written with care and love for the subject.

In Keith Devlin's business-oriented book, Infosense, he describes how to make sense of the constant flow of information. By describing how information differentiates between knowledge and data, he attempts to show how businesses and individuals can benefit from information management. Devlin goes into detail to explain important terms associated with information and its incorporation with communication. He especially focuses on the distinction between information, knowledge, and data. Although it may seem that Devlin is benefiting his audience of mainly executives and managers, he is actually confusing other individuals who may read his work.

If Devlin's intent is to explain how businesses and individuals can benefit from information management, then there needs to be a clear-cut definition of information. He does not ever do this in Infosense. In pages 12-16, Devlin writes a section titled "What is Information?" yet never tells us his definition of it. This can create confusion in any reader's head that is trying to grasp his concepts. In addition, Devlin ends up sounding very repetitious by continually discussing the same topics over and over. Although he does this in portions of his book, he introduces an idea of "situation theory" on page 6 and refers back to it often without fully explaining it. It seems that Devlin is attempting to be technical, but finishes being repetitive and sometimes vague.

In parts of Infosense, it is obvious that Devlin is a mathematician. Throughout various parts of the book, he uses diagrams and examples that become extremely confusing to someone without his background. He uses algebra problems with variables on page 68 to aid in the explanation. To an executive this may even be a challenge to comprehend. At a point in the book, Devlin turns the topic of discussion from differences of information, knowledge, and data to being a good manager. The areas discussed go from description to explanation of "how-to." These subjects of how to run meetings and have an effective conversation are part of the communication process, but can be talked about more fully in a complete other book or incorporated into Infosense more smoothly. Devlin's work should have been more carefully planned out.

Although there are many elements that create uncertainty, some aspects of Infosense may be beneficial to those trying to advance their career. As far as a reading level, it is not difficult. There is not a challenging vocabulary and there is use of a simple sentence structure. Clever anecdotes to enhance the need for information in the communication process are used in the book. Such as the one about the miscommunication causing a plane crash on page 9, these are the most interesting parts of the book. There is a summary at the end of each chapter which precisely says all that is stated in that chapter. Some things are said much more exactly in the summary than in the chapter. Throughout the chapters there seems to be extra rubbish that is unnecessary for the explanations. The chapter summaries narrowed down what needed to be said in the first place.

Overall, Keith Devlin's Infosense is a book that could have effectively explained the theory of information, but did not. Devlin wrote the book for executives and managers of big businesses to advance their careers. As far as helping them think more abstractly and mathematically about information, Infosense is a worthy source. However, if you are looking for precise answers of what information is, then this is not the place to look. Devlin discusses knowledge extensively, but this book does not leave you knowledgeable. No sense is made of Keith Devlin's Infosense.

Keith Devlin's InfoSense is an interesting book that tries to explain and define terms such as: information, data, knowledge, constraints and conversation.

In the first few chapters, Devlin defines such terms mentioned above from different points of view. He tries to explain to the common reader his own definition of Information. However, he does not give his precise definition at once and expand from it.

He gives different meanings throughout the first seven chapters, that the reader has to go back to the previous chapters and try to unify all the definitions and make an understanding for his/her own. Although he states on pg. 24 that defining Information is hard to define, yet he continues to give us more definitions. He also gives the "Information Equation" which it is interesting, but does not explain it enough for the common reader. Throughout his book, Devlin also mentions "Situation Theory." Yet, he does not give a clear explanation of it until page 39. By doing this, the reader has to go back and apply the meaning to the previous references.

Starting on chapter 7, Devlin's book shifts to explain "conversation" and its properties. From this point on I find the book more interesting when it comes to the business world. This is the reason I give the book 4 stars. His understanding of conversation is thorough and the examples are great. Devlin's analysis of conversation and communication as a whole helps me to improve my communication skills at work as well as in other situations.

I would recommend this book for everybody. I personally believe it truly depends on the audience. I found the book far from being boring or "mind boggling". I was a bit lost towards the beginning but caught up what Devlin was getting at through reading the chapters that followed. Its pretty good for business oriented people. As a college student I would say its above average. The chapters are short and have useful summaries. Well atleast to me it shows the author took the readers into consideration while writing 'Infosense'.

As a mathemetician, Devlin used equations to distinguish between information, data and knowledge. He wants his readers to understand knowledge and information based on a scientific logical foundation. The author provides equations such as "Information = Data + Meaning" (p.14) and "Knowledge = Internalized information + ability to utilize the information."(p.15). In essence information only turns into knowledge when we attach meaning to it. Anyone can obtain information but comprehending it makes it meaningful.

Devlin and his colleagues have used Situation theory, which they have procured mathematically and come up with interesting strategies to increase productivity and improvement within a group. He mentions that the ideal group size is two or three and with the addition of more group members the likelihood of confusion increases. I think this is obvious. This reminds me of a newspaper article I recently read. It was in the Baltimore Sun, and the article discussed the enormous class size of the University of Maryland. Imagine you are a student in a class of 450(or so). It is pretty obvious that it would be easier for Western Maryland College students (in a class of 30 or less) to deal with the information (class lectures) when you communicate back and forth with the professor and your classmates. We in a small group of people are more likely to attach meaning to the data and gain knowledge faster than would UMD students.

Incidentally my College Park friends disagree with me on this argue that it all depends on the professor capability to manage the class. They are mistaken ofcourse, because our chances of confusion and misunderstandings multiply far faster than our brainpower. But,I have no doubt Devlin is right on the right track with this idea. Furthermore, Devlin has also discussed that "information immersion" can make communication more efficient by increasing the overlap between team member's individual contexts. Also, he has used good examples to point out the situation theory view of information and how it can prevent complexities. The airline disasters and the poorly designed ATM are examples of this.

Also, like others I found the tiles of the chapters intriguing. I think the author is very good at specifying examples. In page 161 he discusses IBM's computer Deep blue, which beat world champion Garry Kasparov in 1997. Devlin explains that while computers process information human expertise involves knowledge.

As I mentioned before this book is highly recommended for the average businessperson because of the practical information that Devlin provides in this book. He has discussed Microsoft's electronic knowledge guide (SPUD) and People and information finder (PIF) which could better help manage organizations. Hence, to turn this fruitful information into knowledge a business person would have to apply it.