Book Description

"Deals in a very entertaining way with problems in normal life related to mathematics, luck, coincidence, gambling." – The Independent (London)

Why do your chances of winning the lottery increase if you buy your ticket on Friday? Why do traffic lights always seem to be red when youre in a hurry? Is bad luck just chance, or can it be explained?

The intriguing answers to these and other questions about the curiosities of everyday life can be found in this delightfully irreverent and highly informative book. Why Do Buses Come in Threes? explains how math and the laws of probability are constantly at work in our lives, affecting everything we do, from getting a date to catching a bus to cooking dinner. With great humor and a genuine love for the subject, Rob Eastaway and Jeremy Wyndham present solutions to such conundrums as how fast one should run in the rain to stay dry and who was the greatest sportsman of all time.Discover the mathematical explanations for the strange coincidence of two.

Presidents dying on July 4, the uncanny "accuracy" of horoscopes, and other not-so-coincidental coincidences. Eastaway and Wyndham also reveal how television ratings work, which numbers are more likely to be big winners in the lottery, and why bad things, just like buses, always seem to happen in threes.

Whether you have a degree in astrophysics or havent touched a math problem since high school, this book sends you on a fascinating journey through the logic of life where Newtons laws explain bar fights, exploding rabbit populations, and why showers always run either too hot or too cold. Why Do Buses Come in Threes? is a delightfully entertaining ride that reveals the relevance of math in absolutely everything we do. ... Read more

Reviews (5)

Superb book for non mathemeticians
This book is a superb sampler of interesting aspects of math. I found it very similiar to "A mathemetician reads the newspaper" by Paulos (also a great book). People who like Paulos will like this book a lot.

Parts that I particularly loved were the coverage of sections not treated in other, similiar texts. How fast to run in the rain to stay the driest, how to cut oddly shaped cakes into equal parts, etc.

Parts that I found the least exciting were the re-treatments of the stuff of standard layman's math books- does the world need another description of the travelling salesman problem, or Fibonacci sequences throughout nature? (though these descriptions are better than most that Ive read)

Overall, this book was very enjoyable. If you've read no "math and the world books" you will think it is 5 stars, and if you've read many of them you will think 4 stars (or just skip those chapters)

Good idea, but not well executed.
When I saw this book, I thought it was a great idea for a book. I bought it without even opening it or reading the back cover!

However, the book fell short of my expectations. Some of the topics covered didn't warrant inclusion, and some of the topics could have been covered in much more detail. (Also, a minor nit is that some British words used would not be known to the average American reader, although most of the Britishisms would be.)

It is worth reading, however, if you think that you would enjoy it based on the subtitle, "the hidden mathematics of everyday life". It touches on a great number of topics, and has a good balance of hand-waving and formulas.

Great picture of the diversity of mathematics!
This book contains a great mixture of examples of applications of math to different areas. My favorites was learning why coins that are not round have an odd number of edges! Their example is the British 50 pence piece, which has seven rounded sides.

I think this book gives a great introduction to what mathematics is all about, and will be of interest to both mathematicians and non-mathematicians. Just read it!

how come buns come in dozens but weiners come in eights?
this is an entertaining look at math and how it permeates our lives and pervades nature. the authors cover a variety of topics ranging from explaining coincidences to why we always get stuck in traffic jams. the best chapter is ch.1, titled Why can't I find a four leaf clover? they explain how Fibonacci's series turn up so often in plants (the number of petals, for example, is always a, or a multiple of, a fibonacci number), as well as the golden ratio, pi, and why cells in beehives are shaped like hexagons. the pervasiveness of hidden mathematics in nature can make one wonder whether there's an intelligence behind it all.

the book also contains a number of mathematical formulas. i remember reading somewhere that for every equation given in a book, sales drop by 5000 (or some number like that). Hopefully that won't happen here.

A fun and interesting look at mathematics.
I am a math major at The College of New Jersey and this book was intriguing and amazing. It answers most questions about everyday life in simple terms and easy definitions. There are also plenty humorous examples. ... Read more

Book Description

Group theory deals with symmetry, in the most abstract form possible. It is a core part of the undergraduate math curriculum, and forms part of the training of theoretical physicists and chemical crystallographers. Group theory has tended to be very dry—until now. David Joyner uses mathematical toys (primarily the Rubik’s Cube and its more modern cousins, the Megaminx, the Pyraminx, and so on) as well as other mathematical examples (e.g., bell ringing) to breathe new life into a time-honored subject.

"Why," asks the author, "should two such different topics, mechanical puzzles and abstract group theory, be related? This book takes the reader on an intellectual trip to answer this curiosity." Adventures in Group Theory will not only appeal to all math enthusiasts and interested general readers but will also find use in the classroom as a wonderful supplementary text in any abstract algebra or group theory course. ... Read more

Reviews (3)

Riddled with errors, but ---
I have never seen so many typos, omissions, and errors in a published book. Many of the examples are poorly introduced, theorems are mentioned that don't exist in the book, etc. Other than Rubik's cube, most of the other puzzles are presented in a completely incomprehensible manner. It's very annoying, in a book that's otherwise just what I want. It does give a good quick and dirty intro to the group theory needed, however.

In depth group theory via games and puzzles
I am old enough to remember the original appearance of the Rubik's cube puzzle. I examined it a few times while in a store, but never put any effort into it. Later, I looked at some of the literature that explained how "easy" it was to solve the puzzle. The solution involves the use of some advanced topics in group theory, so it is a puzzle with a mathematical twist. However, that is not the only application of group theory, there are many ways in which it can be used. Joyner shows us many of them, and provides the foundation before he tackles the problems.
This is an excellent book that can be used to either refresh your understanding of group theory or teach it to advanced undergraduates. The objects being manipulated are easy to understand, sometimes easy to build or acquire and the explanations are easy to follow. They are also different from those found in the standard group theory text. Puzzles are an area that fascinates many people, so it is often an advantage to present mathematical instruction in the form of a puzzle rather than in the standard sequence of background notation, theorem and then proof.
Finally, the author is to be commended for donating all of the profits from the book to the Earth Island Institute. It is a non-profit organization dedicated to environmental projects throughout the world. Therefore, not only can a purchase of this book do your mathematical skills some good, it can also improve the quality of life for everyone on the planet.

Published in the recreational mathematics newsletter, reprinted with permission.

For the love of Puzzles...
I just got this book yesterday and I have not read it fully, but I had to write a quick review to say how excited I am about this book. The Rubik's Cube craze hit when I was young. I loved solving the cube and have loved puzzles ever since. I did start trying to describe a solution mathematically when I was at college, but got side tracked and bogged down in some of the math. So this book was a great find for me. I am going to enjoy reading this book and following the mathematical proof. Even though there does seem to be a lot of equations and for the casual reader this might put them off, but from my first browse of the book the math isn't too complex and should be something that anyone who has taken some introductory math courses at the college level should be able to follow.

If you love puzzles and especially the Rubik's cube and math doesn't frighten you then I highly recommend this book. ... Read more

Book Description

A colorful tour through the intriguing world of mathematics

The world of modern mathematics abounds with fascinating, unusual ideas–ideas and concepts even seasoned mathematicians often wonder about. Mathematical Journeys takes you on a grand tour of the best of modern math–its most elegant solutions, most clever discoveries, most mind-bending propositions, and most impressive personalities.

Writing with a light touch while showing the real mathematics, author Peter Schumer introduces you to the history of mathematics, number theory, combinatorics, geometry, graph theory, and "recreational mathematics." Requiring only high school math and a healthy curiosity, Mathematical Journeys helps you explore all those aspects of math that mathematicians themselves find most delightful. You’ll discover brilliant, sometimes quirky and humorous tidbits like how to compute the digits of pi, the Josephus problem, mathematical amusements such as Nim and Wythoff’s game, pizza slicing, and clever twists on rolling dice. For a glimpse of the minds that gave birth to the math, read the profiles of such great thinkers as Paul Erdös and Leonhard Euler.

Each chapter of the book focuses on some interesting piece of mathematics, giving the history and requisite math background, the solution of a problem or two, and some indication of natural generalizations and related areas of study. Whether you’re a math novice curious to learn what your calculus class left out or a math lover ready for the green chicken contest (What’s that? Read the book!), Mathematical Journeys will give you a true taste of what mathematicians themselves find most exciting about math. ... Read more

Reviews (1)

The grandeur and historical context of mathematics
Mathematics is more than just a large set of problems. Perhaps more than any other thing, it is about ideas, often from a seed planted by a basic human physical need, but in most cases, the original germ appeared in the mind of a human. Two basic principles make the ideas of mathematics different from the abstractions in other areas. The first is that those of mathematics can be resolved. And once they are resolved, the issue is settled forever. As I often tell my math students, the only way this result can ever be rendered false is by somehow modifying the definitions of the terms. The second is that the results of mathematics almost always prove to be useful. It is said that Albert Einstein was continuously incredulous at how the mathematics he needed for relativity already existed, but was considered little more than a curiosity.
In this book Schumer captures a great deal of the grandeur of mathematics as well as the historical context when some of the great mathematical ideas germinated and grew to maturity. My favorite chapter was the one about Paul Erdös, a man with a great sense of humor, incredible mathematical talent, an odd sense of humility and whose impact on the mathematical world is probably greater than that of anyone else, including Euclid. While there is no question that the codification of geometry done by Euclid has had a profound effect for millennia, Erdös was personally involved in many careers. Those touched by his genius continue to spread the mathematical seeds imparted by his many symbiotic relationships.
Other topics include the green chicken problem solving contest, the Josephus problem, basic games such as Nim and Wythoff's game; Mersenne primes and number theory; Fermat primes, magic and Latin squares; the consequences of rolling unusual dice, a history of the computation of pi, primality testing and Pascal's triangle. Schumer writes with a great deal of wit, precision and humor, yet employs very little excess verbiage. The highest level of mathematics needed to understand the descriptions is that of number theory and combinatorics. A set of problems is given at the end of each chapter and solutions are included in an appendix.
This is a book that could be used as a text for a course in the history of mathematics. With such a broad range of topics, it would allow any instructor to demonstrate the breadth of mathematics as well as give some background on the personalities that helped form it into what we have today. It can also be read just for enjoyment, and if you were to use it as a textbook, some of the people, instructor included, would find that it serves you well in both capacities.

Published in the recreational mathematics e-mail newsletter, reprinted with permission. ... Read more

Book Description

How many people do you need in a room before there'll be a birthday in common? Why is 70 weird, and what can we do about it? How can 56 people eat 1 pizza? In 100 bite-size chapters of no more than three pages each, Adam Spencer gives each number, 1 to 100, its place in the limelight. For example, take 65. It's the constant of a 5 x 5 "magic square" -- a square that contains the numbers 1 to 25, where all the rows and columns and each diagonal add up to 65. Elizabeth Taylor had 65 costume changes in Cleopatra. And sharks can travel up to 65 kilometers per hour (about 40 mph). After reading Adam Spencer's Book of Numbers, readers will never look at numbers the same way again. ... Read more

Book Description

Reviews (1)

More gems from a master
Lewis Carroll was of course one of the greatest and most influential children's writers who ever lived. He was also a mathematics lecturer at Oxford who wrote excellent books on logic. It has been said that these were two halves of a split personality, but this book is proof that they were not. Here are some wonderful puzzles that unite the children's writer and the mathematician, and will appeal to everyone who has the slightest trace of mathematical ability. Edward Wakeling, a noted authority on Lewis Carroll and himself a mathematician, has done a good job assembling this book. ... Read more

Book Description

The Inquisitive Problem Solver is a collection of mathematical miniatures composed to stimulate and entertain. On a deeper level, these little puzzles, accessible to a general audience, provide a setting rich in mathematical themes. One of the larger purposes of the book is to show how everyday situations can lead an inquisitive problem solver to profound and far-reaching mathematical principles. Discussions accompanying the problems reinforce important techniques in discrete mathematics, and the solutions - which require verbal arguments - show that proofs and careful reasoning are at the core of doing mathematics. In addition, anyone reading this book will learn that asking good questions is just as important to the progress of mathematics as answering questions. The book contains more than a dozen open problems for further research by amateurs or professionals. This treasury of problems will serve as a resource for anyone seeking to improve their problem-solving knowledge and know-how. ... Read more

Reviews (1)

Interesting but demanding
I bought this book to spend some of my free time after dinner. With its impressive collection of mathematical riddles this book is intellectually stimulating. One has to recognize, however, that from a certain point some of the problems are reserved to the truly "aficionados" of mathematics. Educators in the field of mathematics my find this book particularly interesting. ... Read more

Book Description

Are you "proud" to admit that you never liked math? Were never good in math?Are you struggling to pique your students' interest in math? Are you bored by the routine, mechanical aspects of teaching to the test in mathematics? This book offers a plethora of ideas to enrich your instruction and helps you to explore the intrinsic beauty of math. Through dozens of examples from arithmetic, algebra, geometry, and probability, Alfred S. Posamentier reveals the amazing symmetries, patterns, processes, paradoxes, and surprises that await students and teachers who look beyond the rote to discover wonders that have fascinated generations of great thinkers. Using the guided examples, help students explore the many marvels of math, including

* The Amazing Number 1,089. Follow the instructions to reverse three-digit numbers, subtract them, and continue until everyone winds up with . . . 1,089! * The Pigeonhole Principle. All students know that guesstimating works sometimes, but now they can use this strategy to solve problems.* The Beautiful Magic Square. Challenge students to create their own magic squares and then discover the properties of Dürer's Magic Square.

The author presents examples to entice students (and teachers) to study mathematics-to make mathematics a popular subject, not one to dread or avoid. ... Read more

Book Description

This entertaining book of mathematical days exercises the brain with confounding puzzles, intriguing math problems, and, of course, detailed solutions to all the conundrums. Readers will enjoy 366 days' worth of stimulating math. ... Read more

Reviews (6)

I'm looking forward to a second edition
This book does a good job of keeping to ol' noodle from turning into mush. But....

Just a few days ago I was somewhat frustrated by it. When checking my answers I was led to believe that I was wrong, but after checking and rechecking and writing a program treverse the curve (Dec 21) I found that the book was incorrect on this one(don't let that stop you from working it though). Maybe I am wrong.

Another frustration was that yesterday's question (Dec 28) was a little off from the answer, it asks for area but supplies 1st of the 3 consecutive integers. The second issue has me working the problems in the fullest detail so that if another aspect of the problem is answered I'll still have the saticfaction of seeing that I had the correct answer.

I'm not knocking the book. These issues kinda' keep me on my toes. The book is great otherwise. I look forward to the next problem(day) and sometimes discover that I have completely forgotten how to answer some questions. I would quickly buy a new version of this book.

Clearly Theoni Pappas' best book / Good book regardless
Theoni Pappas seems to have a mixed reputation (at least, if we go by Amazon reviews). Some people like her art deco approach to popularizing math and like the fact that it is aimed toward kids, parents, and self-learner adults who only have a vague recollection of high school math. Others diss her books as being too simplistic, too easy, too derivative, etc.

Whichever side of that argument you fall into, I think any reasonable person that is interested in math should agree (after perusing *Math-A-Day*) that this is clearly her best book and a good popular math book by any standard.

As others have pointed out, this book is organized as mathematical vignettes for 366 days of the year (which includes leap years). Each of these math capsules includes a brainteaser-type question that requires at most high school level math knowledge, some math trivia, and a math-related quote. From what I can tell skimming through it, the problems seem to be a nice mix of relatively accessible questions that aren't too hard all the way up to fairly challenging problems requiring a lot of sophistication (although, like I said, not much knowledge).

The problems and their solutions (included in the end of the book), as well as the math trivia, should be of interest to all ages and of particular interest to those with an interest in learning as much about math as possible. This is a great book and is definitely not for juvenile primates or for drunken neighbors as suggested elsewhere. Learning about interesting mathematical trivia -- like Mayan mathematics -- should be of great interest to any genuine math lover and other clever, intelligent people.

In short, whether you like Pappas' other books or you'd like to lump them, THIS book, *Math-A-Day*, is definitely an interesting book and worthy of the attention of math lovers.

cute
I picked this up when headed for N.Y. from L.A. About half of the puzzles would be stimulating to a juvenile orangoutang while of the dole roughly half required information not generally available in economy class whilst the rest stimulated my drunken seat mate to use his paper bag above Denver.

Not a 'bad' book nor an evil one, a mathematical 'sugar on maple syrup'. Grand if one is 'stuck' somewhere and finds the Mayan counting system 'essential'.

Great Job
I bought this book just three days ago and I am hooked. The book has a variety of puzzles and problems that will keep you turning the pages consistently. I have bought many math puzzles books, and have been disappointed, but this book is up there with The Moscow Puzzles. Great job, Mrs. Pappas.

great collection of puzzles and historical facts
I'm generally very critical about current math and puzzle books. I don't want to brag, but at last count, I owned some 150 math/puzzle books. In other words, I think can say that I've pretty much seen them all...

Well, this book is one of my favorites! Yes this book has some old chestnuts, but the majority of the problems are quite original and only difficult enough to be entertaining. It's also full of interesting historical facts, all related to math of course.

Up until now, I've generally stayed away from Pappas books. I find them a bit too elementary, but this one, I'll keep.

Thanks Theoni for a fine book. ... Read more

Book Description

On May 11, 1997, as millions worldwide watched a stunning victory unfold on television, a machine shocked the chess world by defeating the defending world champion, Garry Kasparov. Written by the man who started the adventure, Behind Deep Blue reveals the inside story of what happened behind the scenes at the two historic Deep Blue vs. Kasparov matches. This is also the story behind the quest to create the mother of all chess machines. The book unveils how a modest student project eventually produced a multimillion dollar supercomputer, from the development of the scientific ideas through technical setbacks, rivalry in the race to develop the ultimate chess machine, and wild controversies to the final triumph over the world's greatest human player.

In nontechnical, conversational prose, Feng-hsiung Hsu, the system architect of Deep Blue, tells us how he and a small team of fellow researchers forged ahead at IBM with a project they'd begun as students at Carnegie Mellon in the mid-1980s: the search for one of the oldest holy grails in artificial intelligence--a machine that could beat any human chess player in a bona fide match. Back in 1949 science had conceived the foundations of modern chess computers but not until almost fifty years later--until Deep Blue--would the quest be realized.

Hsu refutes Kasparov's controversial claim that only human intervention could have allowed Deep Blue to make its decisive, "uncomputerlike" moves. In riveting detail he describes the heightening tension in this war of brains and nerves, the "smoldering fire" in Kasparov's eyes. Behind Deep Blue is not just another tale of man versus machine. This fascinating book tells us how man as genius was given an ultimate, unforgettable run for his mind, no, not by the genius of a computer, but of man as toolmaker.

... Read more

Reviews (17)

Good, but not great.
This is the story of the history behind the development of IBM's "Deep Blue" computer and its 1997 match against Garry Kasparov. We start in the mid-1980s with some of the happenings at Carnegie Mellon University (CMU) and how the author got drawn into this saga. After describing his thought process on why the design behind the top chess computer at CMU did not make sense, and how he developed his own chip, the author describes the initial successes and failures of that machine (ChipTest). This is the best part of the book as we are priviliged to much detail about the development and the author's as well the reader's anticipation level is kept high. The rest of the book is somewhat downhill as we are not privy to additional interesting details behind the transition from ChipTest to Deep Thought. Also, when ChipTest was being developed the author didn't have anything to lose--once the author had ChipTest the stakes were higher--and the narration takes on a bit of a defensive tone (not outright defensive, but we can read it between the lines).

Anyway, my interest in chess is revived thanks to reading this book--I am playing again with friends and have also lined up a couple of books on improving my game in my Amazon[.com] shopping cart.

Best book I read all year - very inspiring and insightful
The Deep Blue-Kasparov matches were what pushed me from being someone who knows how to play chess, into a serious tournament chess player 5 years ago. I found the matches to be fascinating, as did the media who put the results of the matches on the front pages of newspapers such as USA Today. I also happen to be a computer science major, who works full time as a software engineer. This book for me was the perfect blend of my two main interests in life - chess and computers.

Hsu tells a very fascinating story. It is not just about chess and computers however. It is the story of a young immigrant who comes to the US to study, and ends up doing something that is of a major historical significance in the minds of many people.

This book was a real page turner. I did not want to put it down. I thought the path leading Hsu to work on chess programs was fascinating. He made a suggestion to the leading computer chess professor who did not like it. This inspired him to implement the idea. It was a case of several things coming together, which ended up leading to the creation of a great computer project.

Hsu's story of hard work was very inspiring. I liked how he did not consider the match to be "man vs machine", but man as a toolmaker vs man as a performer. If you found the Deep Blue matches interesting, you will certainly enjoy this book.

Intriguing story told with lots of heart
For a book on the arcane and technical worlds of computer science and chess, this story is highly readable and entertaining, and often quite funny and deeply poignant. The development of a history-making machine was, in the end, a very human adventure.

Story of Man vs Machine
Loved this book which details an engineer's dream to create the best chess computer in the world. Appreciated the technical explanation as well as the stories of bugs encountered during the development. Could have been 5 stars if not for the writing style which I found to be quite bland.

Slightly Disappointing
I was slightly disappointed with this book, but since much of the material is only available from the author, it was worth reading. Having played tournament chess, having written chess software (non-commercial), and especially having been one of a thousand or so at the final games where Kasparov lost, I had high expectations for this book. Perhaps too high. That might explain why I was disappointed.

As the author points out, it is not a book on chess analysis and that seems obvious. However, even the analysis from a software standpoint is weak -- it merely seems to be a hardware let's-build-it-one-thousand-times faster. Come to think of it, the author DID state that he was writing the book that way, so I shouldn't be too surprised.

I was delighted that the author liked "Surely You're Joking, Mr. Feynman" (a fantastic book) and that further heightened my expectations. Unfortunately, the book lacked the creativity and humor of anything like that.

It was not a "bad" book, just not quite what I expected. That does not discredit the great work done or what might come in the future as a result of it. For that, the accolades are already present. ... Read more

Amazon.com

Bring more joy to your favorite math-head with Five More Golden Rules from science writer and national treasure John L. Casti.Though a quick glance through the book will cause an intense fight-or-flight response in the numerophobic, Casti's writing is lovely and lucid as ever, explaining not just equations and theorems but their significance in our lives. Having discovered in Five Golden Rules that he couldn't restrict himself to just five important 20th-century mathematical theories, this follow-up explores the intricacies of knot theory, functional analysis, control theory, chaotic systems, and information theory.Each of the five lively chapters introduces its subject with a seemingly unrelated anecdote that is (of course) informed by the theory in question.Then it's headlong into the wonderful details of postulation and demonstration that make math so much fun.Unlike a textbook, Five More Golden Rules meanders and breaks away from its proofs to discover relations between the symbols and the real world, from the stock market to the coastline of Norway.Besides giving the reader a break, this makes the abstract, almost ethereal concepts concrete and provides a definite advantage to the interested student.Perhaps textbook publishers should take note of this technique; until they do, we'll have to curl up with Casti's Five More Golden Rules if we want to have fun with our higher math. --Rob Lightner ... Read more

Reviews (6)

MEANT for non-mathematicians???
I'm math and computer science student. I have studied linear algebra and know lots about linear spaces, n-dimensional vectors, matrices and other stuff. Still I sometimes found it hard to get out proof or just idea of those formulas. Why do you need formula, if you can't understant its essence. Then there are lots of calculus expressions. I DON'T think it's for everyone!

BUT, I found the book SPLENDID just because of those subjects covered - and covered quite generally without too deep details (although sometimes I wanted more).

I certainly don't agree with those folks who say that there is no explanation on subject's importance. There is ENOUGH! Then I ask you: "Why did you buy that book? Just randomly?" If you have little gray cells in your box then you'll understand why something is or isn't important. I DON'T have need for lengthy texts of explanations why this and not other subject. That is boring!

Where is the value added?
In this book, John Casti takes an academic's eye toward 5 interesting areas of mathematics. Unfortunately, his treatment of the material reminds me of sitting in all too many classrooms in graduate school, with a professor rambling and scribbling on the board without ever bothering to indicate why it even mattered. Like all too many of my professors, he leaves the truly interesting material (the impact) to the reader's imagination. Casti really missed the mark here. He had the opportunity not just to present mathematical proofs, but to show why this is really interesting stuff. Instead, the material is presented no differently than how it would appear in a graduate level textbook. So, why not stick with those graduate level textbooks? Where is his value added as an author?

nice sequel for math major not the layperson
In Five Golden Rules John Casti wrote a wonderful book about important theorems in mathematics that were discovered in the 20th Century. The style and description was such that a layperson could understand, enjoy and appreciate the results. All the theorems were discovered before 1950 and they all dealt with topics in applied mathematics and particularly game theory and operations research.

Perhaps he found the list of five golden rules too restrictive and thus comes the sequel "Five More Golden Rules". Again, it would be hard to argue the choices. Casti goes into the details of the theorems and the theory related to them much like he did in the first book. However, in this book, he has chosen topics from very abstract areas of mathematics. I have a masters degree in mathematics and a Ph.D. in statistics and yet I had no familiarity with knot theory. So I learned a lot from chapter 1 but found it to be difficult reading, more like a mathematics textbook than a popular book for the scientist and layman.

This feeling continued as I read the other four chapters even though I was treading on territory that was very familiar to me (e.g. the Kalman filter of control theory). It was reassuring to me to see that this impression was also shared by the three customers that had already written reviews on the book.

I recommend this book wholeheartedly for mathematicians and other with strong math training. The Hahn-Banach theorem was the most important theorem that I learned about when I took my functional analysis course at the University of Maryland some 26 years ago. But I have not had much use for it since and I completely forgot what it said. Casti provides me with a nice reminder and shows how this result is a generalization of very practical results that relate to quantum mechanics and other results in physics.

The latter part of the 20th Century saw a great deal of activity in nonlinear dynamics. This is connected by Casti to the Hopf Bifurcation theorem. That chapter deals with many topics that grasped the attention of applied mathematicians, including chaos and catastrophy theory, strange attractors and the beautiful geometry of fractals. This material is not for a layperson. On the other hand, the introduction to the chapter, covering what a dynamical system is, provides a wonderful analogy to a treasure hunt in Central Park that can be appreciated by everyone.

The Kalman filter provides an example of how linearization of real dynamic systems allows one to write a prediction equation for the state at the next time point recursively as a function of the current state and the new measurements. This recursive formulation leads to the same solution that Wiener had found much earlier, but because of the recursion, it is much more suitable for real time computer applications. This was essential to controlling space vehicles and is the important result that made the trip to the moon possible. Casti covers the theory of Kalman filtering very well but emphasizes many of the interesting abstract concepts rather than the more concrete aspects of the solution.

The finally chapter on the Shannon Coding Theorem takes us into the realm of information theory. Casti provides the key references. Electronic communication in the 20th century has benefitted from the efficient coding of information that makes transmissions faster easier and error free. This is very important work with unforeseen applications. Casti points to applications in genetics.

Another interesting feature of the book is the connection made between the knot theory associated with Alexander's polynomials and DNA sequencing, a subject to be further explored in the 21st Century.

Beauty that is not made accessible to the layperson
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«The linear dynamical system (**) is completely reachable if and only if the block matrix C contains n linearly independant vectors, that is, rank C = N»

If you don't feel completely at ease with this sentence, do not read this book. Every page contains mathematical propositions of such level, and such level of mathematical fluency is required in order to fully appreciate the content of John Casti's book. The content is interesting but the reading is made rendered somewhat tedious by this high density of maths. I have a degree in engineering, and I often fast forwarded trough the equations in an effort to not lose sight of the big picture Casti want to show the reader.

At the end you will be smarter, but it will not have been a relaxed reading. If you are looking for food for toughts, I would recommand, among others, «Paradigms Lost : Tackling the Unanswered Mysteries of Modern Science», by the same author.

More Difficult than Five Golden Rules
The prospective reader is warned that this book requires considerably more mathematical background than Five Golden Rules, a fact that is not made clear on the book jacket nor in the nonexistent forward or table of contents. In addition, Casti seems to have found it necessary to leave many more points incompletely explained than in Five Golden Rules; though perhaps this was unavoidable given the more difficult subject matter. I am puzzled about what audience Casti thought would read the book. ... Read more

Book Description

Robert Kaplan's The Nothing That Is: A Natural History of Zero was an international best-seller, translated into eight languages. The Times called it 'elegant, discursive, and littered with quotes and allusions from Aquinas via Gershwin to Woolf' and The Philadelphia Inquirer praised it as 'absolutely scintillating.' In this delightful new book, Robert Kaplan, writing together with his wife Ellen Kaplan, once again takes us on a witty, literate, and accessible tour of the world of mathematics. Where The Nothing That Is looked at math through the lens of zero, The Art of the Infinite takes infinity, in its countless guises, as a touchstone for understanding mathematical thinking. Tracing a path from Pythagoras, whose great Theorem led inexorably to a discovery that his followers tried in vain to keep secret (the existence of irrational numbers); through Descartes and Leibniz; to the brilliant, haunted Georg Cantor, who proved that infinity can come in different sizes, the Kaplans show how the attempt to grasp the ungraspable embodies the essence of mathematics. The Kaplans guide us through the 'Republic of Numbers,' where we meet both its upstanding citizens and more shadowy dwellers; and we travel across the plane of geometry into the unlikely realm where parallel lines meet. Along the way, deft character studies of great mathematicians (and equally colorful lesser ones) illustrate the opposed yet intertwined modes of mathematical thinking: the intutionist notion that we discover mathematical truth as it exists, and the formalist belief that math is true because we invent consistent rules for it. 'Less than All,' wrote William Blake, 'cannot satisfy Man.' The Art of the Infinite shows us some of the ways that Man has grappled with All, and reveals mathematics as one of the most exhilarating expressions of the human imagination. ... Read more

Reviews (6)

As complex as math can be.
As if math wasn't complex and confusing enough, a book with equally confusing english was written about it. With out bragging, I am fluent in mathmatics; I understand it as if it were my primary language. What I am not fluent in is English, and unfortunately this book was written only for the English elite. 1/4th of the time I understood half of the poetic correlations between mathmatics and philosophy described in this book, which, consequently happens to be 3/4ths of the context. Basically, if you understand mathematics as well as I do, but do not understand poetry and philosiphy well, do not read this book, you're well off where you are. If you do understand English, extreemly well, and want to know more about mathematics, read the book. But if you could care less about mathematics, or english, then don't even read this review.

Is the Prose Delightfully or Excessively Rich?
As you can read from other reviews, this book rates 5 stars for its excellent description and illustration of many fascinating topics in mathematics. Not all readers, in contrast, will appreciate the authors' most unusual prose style. At times they can't seem to write a sentence without a metaphor, and often a startling or even madcap one. Allusions, philosophical insights, snatches of poetry and unusual quotations, verbs that wriggle or hop--they are all crammed together. So at times the mathematics seems a good deal easier to handle than the prose.

I was at first tempted just to dismiss this style as mere overwriting, but as I read further I started to see that it nicely fit the remarkable turns of thoughts of the master mathematicians as they tested their brains on the challenges of number and space. The more-than-quirky prose, including its philosophical and quasi-religious asides, definitely adds to the interest and instructiveness of the book, I finally decided.

This book is, as you can imagine, far more absorbing than the school math most of us were subjected to. Five stars.

The proof of a.0 = 0 is incomplete.
In the proof on page 40 of a.0 = 0,

Line 1: a.0 = a(1-1)
Line 2:.......= a - a
Line 3:.......= 0

since (1-1) is shorthand for 1+(-1), distributivity only yields

a(1-1) = a[1+(-1)] = a.1+a(-1)

so that going from Line 1 to Line 2 implicitly assumes that a(-1) is equal to -a, which has not been previously established from the axioms.

Great Math..... Obscure Prose
The mathematics in this book is clear and absolutely delightful - reminiscent of high school math. The derivations, proofs, figures and equations are all very clear and the words immediately associated with them are very useful complements. The problem arises when we are in-between the mathematical expositions, i.e., where historical and miscellaneous other snipets are presented; these would normally be pleasant diversions and would make the book even more interesting. But here, this is not the case. The prose is rather obscure, complex and cryptic and tends towards the quasi-poetic, quasi-philosophical and quasi-parabolic all at once. This is most unfortunate for a math book where simplicity and clarity of expression are paramount. Had the historical and other digressions been written clearly and in plain English, then this book, in my opinion, would have easily been 5-star material. But as it is, the math is worth an easy 5 stars, the prose an unfortanate 1 star for an average of 3 stars.

To Infinity, And Beyond!
We all take our pleasures where we find them, and everyone is different, with different sources to draw upon. It will seem peculiar to many people that others could take pleasure in mathematics. Children usually learn to be bored or frightened by math, but there isn't any reason for this, other than incompetent teaching. As an attempt at remedy, husband and wife team Robert and Ellen Kaplan in 1994 began the Math Circle, Saturday morning sessions for kids who just wanted to find out more about mathematics. (The sessions were changed to Sunday morning when soccer practice interfered). Some kids (especially those who were pushed into the classes by their parents) dropped out, but some have come back, year after year, and the Kaplans have found that posing questions, inviting conjectures, asking for examples, and even suggesting ways towards proofs can be something children can enjoy. Mathematicians have been telling us for centuries about the beauty of the objects and systems that they have explored. The Math Circle seems to have taught math in a way to at least some kids who have caught the spirit of the quest for mathematical beauty. In _The Art of the Infinite: The Pleasures of Mathematics_ (Oxford University Press), the Kaplans have put some of those lessons into book form, concentrating on infinities of various kinds. This is a book for adults, or kids who hanker to think about math like adults ought to, but it is full of a sense of play.

As you might expect, things start simple and get very complicated, and this is true right off in the first chapter, considering more and more complicated numbers. The Natural Numbers are introduced with patterns, as if you had stones to position on a table. 1, 3, 6, and 10 stones make pleasing equilateral triangles, and 1, 4, 9, and 16 make pleasing squares. We move from these to zero and negative numbers: "Certainly zero and the negatives have all the marks of human artifice: deftness, ambiguity, understatement." Are these numbers invented or discovered? The profundity of this question is plumbed throughout the book. Rationals, irrationals, and finally the complex numbers are all included. As the numbers mount up, the irregularity and regularity of the primes is considered, one of the most fruitful arenas of number theory. Euclid had to make an assumption about the infinite, his famous fifth postulate; but it is only an assumption; assuming that parallel lines meet eventually produces also a worthy geometry that tells us much about how the Einsteinian universe works. But there is no need to look into these strange worlds to find wonders; before leaving Euclid's terra firma, we are reintroduced to the triangle, and are presented with some astonishing revelations of secret points within and around the simple three sides that will remind you that no matter how simple things look, or even how simple things are, everything is more complicated than you can imagine.

And if you want your infinities more complicated still, the final chapter has to do with Cantor's work. Common sense tells us there must be half as many even numbers as there are whole numbers, but Cantor showed that the infinity of both was equal. He showed that the infinite number of points in a line as long as your finger was equal to the infinite number in a line as long as from here to the Sun. In fact, the number of points on a line is equal to the number of points in a plane. And yet, some infinities are bigger than others. This is strange territory indeed, and requires some concentration to understand and enjoy, even with the Kaplan's literate, witty, and clear explanations. This is a fine introduction to different aspects of serious mathematics; true to its subtitle, it is a book full of pleasures. ... Read more

Reviews (1)

Written as accessibly as possible
Designing Experiments & Games Of Chance: The Unconventional Science Of Blaise Pascal by William R. Shea (Galileo Professor of History of Science at the University of Padua) is an informed and informative survey and analysis of the life's work of the talented mathematician, physicist, and religious philosopher Blaise Pascal. Investigating Pascal's ingenious mathematical experiments, his philosophies of experimental science, his pioneering work concerning theories of probability, and more, Designing Experiments & Games Of Chance is an introduction into the lasting wisdom of a great thinker. Written as accessibly as possible for readers of all background with a basic grounding in math, Designing Experiments & Games Of Chance is a work of impressive scholarship and a welcome addition to academic Science History reference collections. ... Read more

Book Description

Twelfth edition of classic work offers scores of stimulating, mind-expanding games and puzzles: arithmetical and geometrical problems, chessboard recreations, magic squares, map-coloring problems, cryptography and cryptanalysis, much more. "A must to add to your mathematics library" — The Mathematics Teacher. Index. References for Further Study. 150 black-and-white line illustrations.
... Read more

Reviews (2)

Must have for any recreational mathematician.
This is a timeless classic and a primary reference
for recreational mathematicians. And the price
is unbeatable.

A Classic Compendium...
This is a classic collection of mathematical recreations. Originally written by W.W. Rouse Ball around 1900, this edition has been updated by the great geometer H.S.M. Coxeter. It is a comprehensive first source for information about magic squares, Platonic and Archimedian solids, "Knight's Tours" and other chessboard recreations, and just about any other variety of math-related puzzle you could name.

For a mathematician, Coxeter is an excellent writer, and the book is quite accessible, even to relative math novices. Fans of Martin Gardner's books, of his "Scientific American" Mathematical Games columns, will want to own this. And because it's published by Dover, the price is right, too. ... Read more

Book Description

Can you solve history’s most mind-boggling puzzles?

Ever since the Sphinx asked his legendary riddle of Oedipus, paradoxes, conundrums, and puzzles of all kinds have kept humankind perplexed and amused. Why is this so? What do puzzles reveal about the human mind?Do they have implications for the study of mathematics?

The Liar Paradox and the Towers of Hanoi answers these questions, taking you on an interactive tour of the world’s most enduringly intriguing brain twisters–ingenious puzzles that have played a pivotal role in shaping mathematical history. Marcel Danesi introduces you to ten masterpieces, explaining the math behind them and including exercises and answers–as well as the chance to try your hand at similar puzzles. As you navigate the maze of labyrinths, bridges, maps, and baffling problems, you’ll see how certain ideas in mathematics originated in the form of puzzles, from optical illusions to sequences to impossibility theory. From die-hard puzzle mavens to math aficionados, this kaleidoscope of conundrums is sure to enlighten, entertain, and impress. ... Read more

Book Description

Inspiring popular video games like Tetris while contributing to the study of combinatorial geometry and tiling theory, polyominoes have continued to spark interest ever since their inventor, Solomon Golomb, introduced them to puzzle enthusiasts several decades ago. In this fully revised and expanded edition of his landmark book, the author takes a new generation of readers on a mathematical journey into the world of the deceptively simple polyomino. Golomb incorporates important, recent developments, and poses problems, inviting the reader to play with and develop an understanding of the extraordinary properties of polyominoes. ... Read more

Reviews (2)

Ultimate book on polyominoes by the inventor.
Polyominoes is an entire sub-domain of geometrical puzzles and
this book is the epitomie of the subject. Packed full of
results and puzzles old and new. An extensive bibliography
is provided. Another one for the bookshelf of all mathematical puzzlers.

Even better the second time through
One of the most eagerly anticipated second editions in the history of mathematics, the wait was worth it. Literally defining a whole new area of recreational mathematics, the problems and proof techniques introduced in the first edition have kept an entire generation of mathematical thinkers busy. Although easily understood, some of the problems have defied solution for decades after the publication of the first edition in 1965. It now appears that all of the problems listed as unsolved in the first edition have been resolved, the last succumbing in 1993. As befits the enormous interest in these problems, three people announced solutions simultaneously, this reviewer being one of them.
While there is not a lot of material that was not part of the first book, it still stirs the mathematical heart. For these problems and proofs are timeless things of beauty. Even a child can understand how to put polyominoes together - my two-year-old daughter is an existence proof of that. And the proofs are sometimes so clever in their simplicity that one is tempted to use the phrase attributed to Paul Erdos, "That one is from God's little book." Who among us fails to appreciate some of the proofs of placing pentominoes on a checkerboard that relies on nothing more than the number of spaces colored black versus red. Even the proofs of the problems that took decades to resolve can be understood by those with only a rudimentary knowledge of mathematics. Sometimes, if you can count to 60, you can understand the proof.
Truly a jewel in the crown of mathematical royalty, this book deserves to be a runaway bestseller.

Published in Journal of Recreational Mathematics, reprinted with permission ... Read more

Book Description

Each summer six math whizzes selected from nearly a half-million American teens compete against the world"s best problem solvers at the International Mathematical Olympiad. Steve Olson followed the six 2001 contestants from the intense tryouts to the Olympiad"s nail-biting final rounds to discover not only what drives these extraordinary kids but what makes them both unique and typical. In the process he provides fascinating insights into the science of intelligence and learning and, finally, the nature of genius.
Brilliant, but defying all the math-nerd stereotypes, these teens want to excel in whatever piques their curiosity, and they are curious about almost everything — music, games, politics, sports, literature. One team member is ardent about both water polo and creative writing.Another plays four musical instruments. For fun and entertainment during breaks, the Olympians invent games of mind-boggling difficulty. Though driven by the glory of winning this ultimate math contest, they are in many ways not so different from other teenagers, finding pure joy in indulging their personal passions.
Beyond the the Olympiad, Olson sheds light on many questions, from why Americans feel so queasy about math, to why so few girls compete in the subject, to whether or not talent is innate. Inside the cavernous gym where the competition takes place, Count Down uncovers a fascinating subculture and its engaging, driven inhabitants. ... Read more

Reviews (12)

enjoyable read = f(interesting, riveting, informative)
I once worked with a man who could look at a sheet of numbers and find an error within a few seconds. He said he could visualize the numbers and their patterns in his head. He was the adult version of the nearly 500,000 kids who annually tryout for the Math Olympiad. In 2002, SPELLBOUND, an extremely entertaining film hit the festival circuit, and followed eight boys and girls from regional spelling bees to the national spelling bee competition in Washington. In this book, Steve Olson changes the medium from film to paper, and the competition from spelling bees to mathematics, and the result is an entertaining, alluring, and riveting read about young men (of 119 U.S. team members, only 1 was female), math reasoning, and math problems in an international competition in Northern Virginia (don't worry, the six math solutions are in an appendix). Olson, who has written about genomics, genetics, and the state of science education in American schools, also adds covincing arguments in the book about the education systems' onerous failures to teach math properly, and he is uniquely qualified to discuss whether these kids are products of math nurturing or genetic nature. The key players in this book are the six immigrant-heavy members of the U.S. 2001 team: Oaz Nir (a poet who had already won a gold medal and is now at Duke); Gabriel Carroll (who also had won a gold medalist at a past competition and is now at Harvard); Tiankai Liu (still in high school); Ian Le (now at Harvard); David Shin (now at MIT); and Reid Barton (who had won 3 gold medals at past cometitions, now at MIT). Other key players in the book are the team's coach, Titu Andreescu, and Melanie Wood, the team guide. The book provided nto only an enjoyable read, but some very good insights into creative problem solving methods when time is crucial.

Applaudable Book
This book is an exceptional book. Being a serious follower of solving Maths Olympiad Problems since my college, I compare it with two of my batchmates who had won gold and silver medal respectively in the IMO in 1991. The book is a superb journey into the competition the 6 kids who have vied for Glory. The book has different angles to it. It gives information on the Maths Olympiad (for parents who have dreams of sending their kids to attaining glory), it tells about team work, problem solving skills, the fundamental change we need in our american math curricula. Congrats Steve on a job well-done. If there would be more than 5 stars I would have gladly given that for this book.

Okay
Having competed in some of the competitions mentioned, I guess I expected more from this book. If you are looking for the level of "Poker Nation" for Poker or "Word Freak" for Scrabble, you are likely to be disappointed. Enough research and personality to garner a quick reading.

Thoughtful and insightful glimpse of math and so much more
This beautifully written narrative goes well beyond its ostensible topic -- the little known world of middle school math competitions and some of the people who inhabit that world.

In addition to painting vivid portraits of six students who perform extraordinarily well in this highly competitive realm (while remaining remarkably well rounded), author Steve Olson reminds us of the sheer beauty and elegance of mathematics. For those who enjoy mathematics, Olson does an exceptional job of explaining competition math problems and solutions, while providing insights into why each is particularly challenging. And for those who are intrigued by wider and more abstract issues, Olson uses the details of each student's life to pose and probe intriguing social and cognitive questions, such as the nature of creativity and of genius, the pros and cons of competition, and the possible role of gender and ethnicity in influencing how kids approach and solve mathematical problems under pressure.

All in all, it is a wonderfully insightful and thoughtful book.

Much More than a 'Math Book'
Steve Olson was a National Book Award finalist for his previous book, "Mapping Human History," which examined what discoveries in genetics and related fields are teaching us about the course of human migration around the world. That book was about much more than migration, however; what made it so interesting was how it prodded us to rethink our notions of racial, religious, national and other differences. It showed how, in general, these differences are simultaneously more trivial and more complex than many of us imagined.

Now, in "Count Down," Olson turns his attention to mathematics. Yet, as before, his book is much more than it seems -- in this case, much more than a "math book." Once again, Olson examines far broader questions, such as the nature of creativity and genius. He builds his narrative around several teenagers in a single mathematics competition, but that is largely a device to look beyond equations and algorithms to deeper matters about what makes us human.

I thought this was a splendid book -- readable, provocative, even heart-warming. I'm already looking forward to seeing what topic Olson decides to tackle next. ... Read more

Book Description

Math is not the dry subject you think it is. It is in fact all around us, in the shapes of everyday things and in the patterns of nature. Stewart presents a beautifully illustrated view of the magical nature of the hidden math all around us. Whether studying a spider's web or a zebra's stripes or ocean waves, Stewart displays the math behind nature's patterned beauty.

Oh, and about that snowflake? Every snowflake is a perfect hexagon, and as most children can tell you...no two are exactly alike.

The stripes of a zebra...the complexities of a spider's web...the waves of the ocean...and the shape of a snowflake. These and other natural patterns have been recognized by scientists for centuries. What do they have in common? They can all be accounted for mathematically.

In What Shape is a Snowflake? internationally acclaimed mathematician Ian Stewart shows how life on earth develops not simply from genetic processes, but also from the principles of mathematics. Starting with the simplest symmetrical patterns, each chapter looks at a different kind of patterning system and the key scientific issues that underlie it.Patterns can embrace chaos, fractals, dislocations, even statistical regularities, and are found in many things that at first seem irregular or featureless. A constant wind blowing over a flat expanse of sand, for example, will develop ripples, which eventually lead to sand dunes that are often arranged in long parallel rows or other geometric forms. And the smooth surface of a growing organism will develop beautiful patterns of spots, stripes and colors.

Beautifully illustrated, What Shape is a Snowflake? is an illuminating and engaging vision of how the apparently cold laws of mathematics find organic expression in the beauty of nature. ... Read more

Reviews (2)

Mathematics deserves four colour
I must admit I was looking for more detail from this book than it contains. I was looking for more detail on hexagonal systems.
Instead there is less detail and less formal mathematics. I found it to be rather similar to other publications by Ian Stewart, such as the book Fearful Symetry which contains many of the same ideas.

Despite my personal desires I am glad to see that Ian has finally been granted lots and lots of expensive four colour illustrations with which to explain how interesting mathmatics really is.

I immediately found a use for it in the workshops I run for children. It is the best illustrated book Mr Stewart has yet produced.

A Universe Full of Mathematics
In _What Shape is a Snowflake? Magical Numbers in Nature_ (W. H. Freeman), Ian Stewart has managed to write a wonderfully comprehensive and colorful mathematical tour of the universe from top to bottom without putting a single equation into his book. In fact, there aren't really many numbers. He gets to show what happens when a mathematician looks at the infinite aspects of the world. He writes, "I am a mathematician. I experience these wonders through a mind that has spent a lifetime learning how to detect patterns, how to understand patterns, how to find new patterns... I stand on the shoulders (and lean on the elbows) of giants, on five thousand years of mathematical history that has been groping toward such understanding. I see what all humans see, and in a few respects perhaps I see more. I see clues to rules, laws, regularities."

The snowflake is key to his tour, and there is plenty to learn specifically from it, but since Stewart is keen to draw on patterns all over the place, the range of his book is amazing. In well connected chapters, looking closely at snowflakes takes him to the leafy patterns of frost on the window, the organization of leaves around spirals and Fibonacci numbers, the spiral of the nautilus shell, the stripes and amazing triangle patterns on other sea shells, the patterns of stripes on zebras and fish, the grooves in sand dunes and the lines of dunes themselves, the lines a sidewinder leaves in the sand, the synchrony of a millipede's legs and a horse's at different gaits, the oscillations of the legs of robots, the ups and downs of animal populations, the chaotic variations of weather and of the planets in the solar system, and the shape of the universe. It is clear that Stewart sees connections everywhere, and is only using the snowflake as an excuse to look at the foundations of physical laws, the nature of time, space, and matter, and why patterns in one field give clues to patterns in something entirely different. "I'm going on a journey in search of the snowflake's secret," he says, "and, with it, the deeper secrets of our astonishing universe. And you're coming with me." It's a beguiling invitation from a masterful guide.

Naturally a tour of this type, with all it encompasses, is not going to be long on detail, and anyway, one would have to start getting into equations for that. There is a useful list for further reading at the back of the book, for those who insist on stronger doses of such stuff. Stewart's book, however, is an exhilarating, accessible, vividly illustrated voyage through classic and current mathematical ideas. By the end of it, a reader will understand that the snowflake's shape is determined by phase transition, bifurcation, symmetry-breaking, chaos, fractals, and other complexities. Oh, and the book does eventually reveal what shape a snowflake is. ... Read more