Innumeracy: Mathematical Illiteracy and Its Consequences
by John Allen Paulos
Average Customer Review:
Paperback (18 August, 2001)
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Editorial Review

This is the book that made "innumeracy" a household word, at least in some households. Paulos admits that "at least part of the motivation for any book is anger, and this book is no exception. I'm distressed by a society which depends so completely on mathematics and science and yet seems to indifferent to the innumeracy and scientific illiteracy of so many of its citizens."

But that is not all that drives him. The difference between our pretensions and reality is absurd and humorous, and the numerate can see this better than those who don't speak math. "I think there's something of the divine in these feelings of our absurdity, and they should be cherished, not avoided."

Paulos is not entirely successful at balancing anger and absurdity, but he tries. His diatribes against astrology, bad math education, Freud, and willful ignorance are leavened with jokes, mathematical or the sort (he claims) favored by the numerate.

It remains to be seen if Innumeracy will indeed be able, as Hofstadter hoped, to "help launch a revolution in math education that would do for innumeracy what Sabin and Salk did for polio"--but many of the improvements Paulos suggested have come to pass within 10 years. Only time will tell if the generation raised on these new principles is more resistant to innumeracy--and need only worry about being incomputable. --Mary Ellen Curtin ... Read more

Reviews (59)

innumeracy
John Allen Paulos's book Innumeracy turned out to be a lot more interesting than I had expected.The issues he speaks of are still relevant today.His reasons for writing this book were obvious.He seems to be fed up with all of the mathematical illiteracy in our world.Throughout the book he gives several examples of common consequences of this innumeracy.
Paulos begins with a simple explanation of some cases in which we are innumerate.He states that most of the time it is very simple math that people make mistakes on.He then moves on to probability and coincidence.He speaks of a coin toss game, and chance encounters.When reading his work it seems very obvious that there is nothing that happens by chance.When he works out the math for estimating how many people in a given room are Capricorns, it really makes you think about how silly you are for getting excited about such a coincidence.Several other examples of coincidence were mentioned in this chapter that we never think twice about.Paulos then turns his attention to pseudoscience.He really seems to be annoyed by this subject.He mentions several different types of the pseudoscience like, astrology, healers, predictive dreams, ect.. My favorite part was when he explains predictive dreams.We never really think about how high the chances are that we will have such a dream simply because we like to think that there is some mysterious power we have.Reading this book has definitely brought me back down to earth and made me a little more conscious of just believing any statistic that I hear, or believing in a healer or psychic.In this section he also talks about the scams in blackjack, false positives in medical diagnosis, and UFO's.The rest of the book is about all of the rest of his observations of how much innumeracy is in our society.Everyday we see demonstrations of what Paulos is saying, but we never really think about how to prove statistics, or coincidences.
Overall Paulos's premises are true.He makes very valid points about how completely innumerate the majority of our world is.However, he seems a little pessimistic at times.Surely some of his claims are a little far fetched, but that is expected from someone who knows numbers as well as he does.
Paulos expresses his arguments clearly and proves that what he is saying is true with the mathematical equations to back it up.His claims are consistent, and the argument was complete. Every bit of the book had relevant evidence taken into account.
The only problem with the book is that is was not totally fair.He really did not give too much credit to the opposing views and arguments.The argument at times was a little far fetched.He suggests that most people don't understand mathematics, or how to feel about statistics.He thinks that the majority of people just believe statistics to be the absolute truth.He underestimates the intelligence in the world a lot throughout his book.
Again I think that this book was very well written.The layperson can get some enjoyment out of it, and it is a quick read.I would recommend the book to someone who as an open mind, and wants to know more about statistics, probability, and why our world is set up for innumerate people.

If Only Everyone Would Know This Stuff...
This is a great book. Quick read. Funny at times. Interesting in all cases. Personally, I always considered myself much more comfortable with numbers than most people, while at the same time understanding that I still only understood a very small part of mathematical knowledge available. Reading this book, I realized that although I didn't fall into all the math-traps other people seem to fall into, I still were way off when it came to understanding certain every day numbers.

I would recommend this book to anyone. It is not hard to read as one would expect a math book to be.

A must read for the numerate and innumerate alike
This book offers valuable common sense advice that can be used in a broad array of every day situations. The narrative is very readable and easily accessible to all, only requiring an occasional minimum of mathematical reasoning.

For those who are already familiar with the concepts, it is a refreshing summary of the pitfalls of the innumerate. And for those of you who have always considered mathematics to be 'one of your worst subjects', then this book may very well give you a new perpective and teach you something to boot.

I found it to be refreshing and entertaining read and recommend it to all.

... Read more

Isbn: 0809058405
Subjects:  1. General    2. Mathematics    3. Popular works    4. Science/Mathematics    5. Teaching Methods & Materials - Social Science    6. Education / Teaching Methods & Materials / Social Science   

The Language of Mathematics: Making the Invisible Visible
by Keith J. Devlin, Keith Devlin
Average Customer Review:
Paperback (01 March, 2000)
list price: $14.95 -- our price: $14.95
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Editorial Review

Keith Devlin is trying to be the Carl Sagan of mathematics, and he is succeeding. He writes: "Though the structures and patterns of mathematics reflect the structure of, and resonate in, the human mind every bit as much as do the structures and patterns of music, human beings have developed no mathematical equivalent of a pair of ears. Mathematics can be seen only with the eyes of the mind." All of his books are attempts to get around this problem, to "try to communicate to others some sense of what it is we experience--some sense of the simplicity, the precision, the purity, and the elegance that give the patterns of mathematics their aesthetic value."

Life by the Numbers, Devlin's companion book to the PBS series of the same name, is heavily illustrated and soothingly low on equations. But as he says, wanting mathematics without abstract notation "is rather like saying that Shakespeare would be much easier to understand if it were written in simpler language."

The Language of Mathematics is Devlin's second iteration of the approach he used in Mathematics: The Science of Patterns. It covers all the same ground (and uses many of the same words) as the latter, but with fewer glossy pictures, sidebars, and references. Devlin has also added chapters on statistics and on mathematical patterns in nature. --Mary Ellen Curtin ... Read more

Reviews (11)

Perceiving patterns.
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.]

Breathtaking
This book is an incredible account into the ideas of mathematics. Devlin presents simple and extremely abstract ideas into a language that just about anyone can understand. Although some previous knowledge of the fields investigated does help, this book serves as a great introduction into such things as perspective geometry, non-Euclidean geometry, network theory, topology and quantum mechanincs. It also provides some great insights into the history and uses of number theory, algebra, geometry and calculus. I've have never read a mathematical/scientific work that was written with such passion and was a complete page turner (I read it straight over the course of 3 days). I am still amazed on how such a work can be under $50 because it is worth much more than that.

Clear and engaging
Keith Devlin is one of the best popular mathematics writers around, and this is one of his best works.The eight chapters cover number theory, set theory, calculus, group theory, topology, probability and the application of mathematics to the physical world.The discussion in each chapter, couched generally in English, not mathematics, is so clear that a math-phobic can understand it.By the end of each chapter a great deal of fascinating mathematics has been described, and in some cases the formal basis is sketched--but the emphasis is always on narration, and a lay reader who doesn't even want to understand mathematics can still read this and get a sense of the dramatic history of mathematics.

Devlin states at the end that he decided to exclude many areas of mathematics in order to focus more effectively on what he did cover. As a result there is little or no coverage of chaos theory, game theory, catastrophe theory, or a long list of other topics.The fact is there will always be holes in a book this size--mathematics has expanded so much in the last hundred years that even a book ten times this size could barely survey it.The decision to focus was a good one, and the subjects chosen are good: the truly exciting stories are here: Archimedes, Fermat, Gauss, Galois, Riemann, Wiles, and many more.

Potential purchasers should note, by the way, that this book was reworked from Devlin's "Mathematics: The Science Of Patterns".In Devlin's words (not from either book): "The Language of Mathematics is a restructuring of Science of Patterns that omits most of the color illustrations (a minus) but has two new chapters covering topics not in Science of Patterns (a plus). If you want lots of color, go for patterns; Language of Mathematics covers more ground."I've read both, and I have to say they're both worth getting.The two new chapters in this book are the ones on probability and the applications of mathematics in science; they're well done and interesting.However, the pictures in Science of Patterns are very high quality.

They're both fine books, and I can strongly recommend each of them.If you have to get one, I'd say get Science of Patterns.Even though Language of Mathematics does have some colour plates, Science of Patterns is really a gorgeous book to read with many good illustrations.I ended up buying both, and you may end up doing that too. ... Read more

Isbn: 0716739674
Subjects:  1. General    2. Mathematics    3. Mathematics (General)    4. Popular works    5. Science/Mathematics    6. Applied mathematics    7. Philosophy of mathematics   

Mathematics: From the Birth of Numbers
by Jan Gullberg
Average Customer Review:
Hardcover (01 October, 1997)
list price: $50.00 -- our price: $31.50
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Editorial Review

What does mathematics mean? Is it numbers or arithmetic, proofs or equations? Jan Gullberg starts his massive historical overview with some insight into why human beings find it necessary to "reckon," or count, and what math means to us. From there to the last chapter, on differential equations, is a very long, but surprisingly engrossing journey. Mathematics covers how symbolic logic fits into cultures around the world, and gives fascinating biographical tidbits on mathematicians from Archimedes to Wiles. It's a big book, copiously illustrated with goofy little line drawings and cartoon reprints. But the real appeal (at least for math buffs) lies in the scads of problems--with solutions--illustrating the concepts. It really invites readers to sit down with a cup of tea, pencil and paper, and (ahem) a calculator and start solving. Remember the first time you "got it" in math class? With Mathematics you can recapture that bliss, and maybe learn something new, too. Everyone from schoolkids to professors (and maybe even die-hard mathphobes) can find something useful, informative, or entertaining here.--Therese Littleton ... Read more

Reviews (51)

Numbers, numbers, everywhere...
Jan Gullberg describes his impulse to write this book as deriving from conversations with his son, who was studying engineering.Gullberg himself was not a mathematician, but rather a surgeon of international standing; mathematics became a hobby of his, an intellectual pursuit with practical applications that he could share with his son.This thick book (nearly 1100 pages) has over a thousand drawings, which were prepared by Gullberg's son, Par.

This book can be classified in many ways.In one sense, it is a giant book of mathematics trivia - almost every major and minor aspect of mathematics is represented here in some fashion, from the explanation of cardinal and ordinal numbers to the analytic geometry, calculus, probability and statistics, and symbolic logic.These are arranged in a fairly standard progression, one that most people who have studied mathematics in school will recognise, at least up to the point that they studied.

Another classification of the book can be that of a mathematics encyclopedia.The table of contents, supplemented with the name index and the subject index in the back of the book, makes this a ready reference for short descriptions.

There are fun pieces here - for example, Gullberg derives approximate values for pi in two different scriptural texts (a passage from Kings and a passage from Nehemiah); there are mathematical jokes (yes, there are such things) and puzzles, some of which have only been recently solved (Fermat's last theorem, for example).There are historical pieces and purely mathematical pieces here, and in general the reader will learn about mathematics even when one doesn't understand fully the information being presented.

This is the one drawback of the book - it is not a mathematics textbook.It does not set problems to be solved, but rather presents the theory and ideas, which, if one is not already familiar with them, one will have difficulty learning them for the first time here.There are some pieces that will seem familiar from prior schooling, and no doubt a number of things that will simply make logical sense, but for those who have not had differential or integral calculus, for example, the explanations here will likely make sense in the general philosophy behind the ideas (the two are essentially opposite forms of the same problems) but the actual mathematical operations will not be so comprehensible.

This is not to say that the mathematically illiterate need be intimidated by this book - the good thing about this text is that it does have something for everyone regardless of mathematical proficiency, and can enlighten and entertain people from those who live for numbers to those who run from them at top speed.

Its a good "general intrest" math book, but nothing more.
I purchased this book while in high school, and I felt it was an intresting book as a general refrence and trivia about mathematics history. I attempted (as I remember) to read the book cover to cover but only got about half way through. It did serve as an occasional (but mostly never) reference in some of my early college math courses like differential equations and multi-variable calculus.

However, with respect to coverage of more intresting (perhaps more 'modern' mathematics), there is virtually none (lest we call elementary linear algebra 'modern'). I do not think it would be appropriate as a refrence for any college courses beyond the aformentioned introductary levels, but again, it serves its purpose more for the pre-college/general audience individaul. I do not agree that if you have had no exposure to calculus that this book would be all to terribly difficult.

The first half of the book can be understood with knowledge up to school trig/analysis course.Of course, you will probably not learn the material either, but it is indeed possible (at least in my opinion) that the general 'gist' of the material can be comprehended with school knowledge of mathematics.

Overall, I would have preferred that they would have covered logic/proofs and axiomitized systems more in the book as these aspects have much more to do with the development of math (and especially the modern incarnations of algerba and analysis), further the true beauty in mathematics lies in the logic and proofs. Instead the author dives into topics such as a survey of specific types of trigonometeric mappings (I felt the sections on trig and conics were a bit excessive relative to other topics in mathematics that were just brushed upon or ignored entirely).

Yet, for the price, and for the expected audience, the book defintilly more then gives the reader his/her moneys worth. It is indeed full of many illustrations and background history on the various topics of school mathematics and should serve the reader well as a way to enligthen themselves of the topic of mathematics.

Impressive Overview of Mathematics
Let's put this book into perspective.At 1040ish pages, it
manages to cover the birth of numbers, algebra, geometry,
probability, differential and integral calculus including
multi-variables, trigonometry, matrices,
complex numbers, logarithms, numerical analysis, first and
second order differential equations... it goes on from there,
touching on a number of other topics. How many
textbooks is that from high school and college?

Wow.Gulberg does it with style.Brief historical anecdotes,
references to the appropriate mathematicians, proofs that are
easy to follow and understand (I found one error), clear
examples in many cases.I read this book and felt like I came
away not only with an excellent review of the key components of
these areas of math, but a better understanding of the whys
and the hows and the whatfors of applications and proofs and
where it all came from.

Maybe this book tested the limits of Dr Gulberg's mathematical
knowledge, as one reviewer suggested.Maybe not.The man was
busy doing surgery, too, and he's done a magnificent job of
putting together a book consisting of concepts that some people
never understand.

No, this book doesn't include a lot of graduate school math.
But as a review of about 14 years worth of math for me, I was
thankful I didn't have to read 10,000 pages, but only 1/10th
that much.

I think it will serve me well as a reference for when my children
are working on their homework, and it certainly has been
an entertaining review for me.

Kudos, Doc. ... Read more

Isbn: 039304002X
Subjects:  1. History    2. History & Philosophy    3. Mathematics    4. Science/Mathematics    5. Study & Teaching    6. History of mathematics    7. History of science   

What Counts : How Every Brain is Hardwired for Math
by Brian Butterworth
Average Customer Review:
Hardcover (27 August, 1999)
list price: $26.00
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Editorial Review

At first glance, neuropsychologist Brian Butterworth'sWhat Counts: How Every Brain Is Hardwired for Math might infuriate mathphobes who insist that they just can't get a handle on numbers. Could it be true that natural selection produced brains preprogrammed with multiplication tables? Read a few pages, though, and you'll see that Professor Butterworth has more than a little sympathy for the arithmetically challenged, and indeed confesses that he too has a hard time with figures. His thesis isn't that we are born doing math, but that we are born with a faculty for learning math, much like our ability to learn language. He goes on to argue that unique individual differences in this faculty combine with our educational experiences to make us either lightning calculators or klutzes who can't figure tips.

Butterworth's style is perfect for his subject, seamlessly weaving scholarly analysis with down-to-earth humor and practical examples that will satisfy the researcher and the lay reader alike. Drawing on archaeology, anthropology, linguistics, and his own neuropsychology, he makes his case like a masterful attorney while remaining careful to leave room for scientific falsification. The history of counting is engrossing and will be new to many readers, as it has been a rather arcane field until recently--but it's just one of the many new vistas opened for the readers of What Counts. --Rob Lightner ... Read more

Reviews (4)

save your money
What an awful book! I started with great expectations, and got steadily more disappointed and finallly just disgusted. I have never read a book on a supposedly technical subject so disjoint and disorganized. I cannot recall the author ever finishing a concept, dotting his is, or completing a promised list of topics. In many places, he makes statements such as "There are two important topics regarding.......and he gives you number one, but try and find number two. And so on throughout the book. In the middle of a technical topic, he will wander off onto pages and pages of interesting examples of ????what ? I could not figure out. Save your time and energy and money. This is an awful book.

A Challenge to a Popular Myth
"What Counts" is a necessary rebuttal to the idea of mathematical giftedness or genius in general which pervades our culture and manifests itself in Hollywood movies like "Good Will Hunting"and, more tragically, in our system of education.The author confrontsboth of these issues in detail.

For example, on Hollywood's prodigy WillHunting he challenges anyone to come up with a real life example of thischaracter which would be a counter example to his premise which states thathigher mathematical learning/ability is a result of zeal, hard work (10years for truly great achievements), and exposure to the necessary culture,i.e. teachers and books.

As Butterworth explains, Will Hunting seeminglyhas no zeal for anything but girls and spends most of his time in bars yethe knows all about and comprehends arcane mathematical concepts and myriadother subjects.

Mathematicians may like to hang on to the idea of theirown giftedness for the sake of their egos and most people who see"Good Will Hunting" think the character is believable so thisbook is a definite challenge to a popular myth.

Except for the chaptersdealing strictly with mathematics which are not necessary (and hence thelack of 5 stars) this book may inspire people to work hard instead ofmaking excuses.

Look for more on this subject from author/mathematicianKeith Devlin with his book (coming out in August) "The Math Gene: WhyEverybody Has It, but Most People Don't Use It."

Interesting but flawed
I'm going to assume anyone reading this has already read the other reviews in amazon.com.This leaves me free to comment on problems with the book rather than provide a synopsis.

The first two sentences in the preface to "What Counts" explain the basic fact, I am not particularly good at maths or calculation."

Butterworth proves this often enough for it to be a very good reason why he shouldn't have written of flaws, only someone who has no feel for mathematics could write a book containing many typos of the form a^2 + b^2 = (a - b)(a + b).

o He's discovered a new and amazing correspondence with any subset that is neither the whole set nor the empty set." Imagine, there's a one-to-one correspondence between the integers and the set {0,1}.Well, no there isn't.

o He's made the equally exciting discovery that the rationals between 0 and 1 are uncountable.It is revealed on page 339 that the points on the real line are uncountable "because there is points." Since the argument applies to the rationals, they too must be uncountable. Sigh.

Here are some specifics to illustrate other problems in "What Counts".

o The discussion of cognitive archaeology is highly speculative and frequently unconvincing.For example, he speculates that counting lunar phases is important to women so they'll know when their baby is due.This isn't of value without a citation of "primitive" peoples who do this.

o Butterworth seems to believe that math is the same as arithmetic, though of course he does know better.The book is almost exclusively about our "natural ability" to add, subtract, multiply, and divide. Geometry, the other "basic" mathematics, is almost completely ignored.The omission is a major deficiency.

o He also has a very strong opinion that there is no such thing as a mathematical gift.Rather, it's a manifestation of interest, good teaching, and hard work.The argument is made quite intensely, but not convincingly, and probably would almost universally be disputed by mathematicians (which doesn't prove it wrong, of course).What is convincing and should have been the point of the discussion is that we could be doing a much, much better job of teaching mathematics.(The previous reviewer has correctly pointed out the value of Butterworth's critique.)

o The appendix contains a less-than-satisfying discussion of Godel's Incompleteness Theorem, which has no apparent purpose other than to dazzle and confuse the naive reader.

There's quite a bit more that's objectionable, but the point should have been made adequately with this list.

On the other hand, the quote from Oliver Sacks on the dust jacket about how the book "solicits the reader's own thoughts" is correct.I came away from the book with ideas for dozens of experiments and possible research areas.Of course, since my background is mathematics and not a cognitive neuropsychology, I can't comment the non-mathematical assertions but can only hope them to be accurate.

The book is valuable as it has nuggets of great interest and the subject matter is fascinating. There aren't many popular books covering this material, so I'm giving it 3 stars.Good editing and minor collaboration with someone who is "good at maths" could turn it into a 5 star book ... Read more

Isbn: 0684854171
Subjects:  1. Arithmetic    2. General    3. Mathematical ability    4. Mathematics    5. Neuropsychology    6. Number concept    7. Philosophy & Social Aspects    8. Psychological aspects    9. Psychology    10. Science    11. Science/Mathematics    12. Psychology & Psychiatry / General   

The Kingdom of Infinite Number: A Field Guide
by Bryan Bunch
Average Customer Review:
Hardcover (10 January, 2000)
list price: $23.95 -- our price: $23.95
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Reviews (7)

If You Hate Math, This May Be The Book For You
I think this book has something for just about everyone.It's a great read, and it's not dumbed down.

Numbers for Everyone!
Not since the great Indian mathematician Srinivasi Ramanujan has anyone gotten so involved in the personality of numbers to the extent as which Bryan Bunch has, and the reader is far better off for it. The classic story about Ramanujan and the personality of numbers is the tale about the number 1729. When he was ill in a hospital in England he was paid a visit by his friend and colleague G. H. Hardy, who had been given a ride in a taxicab bearing that number. Upon greeting Ramanujan, Hardy remarked that 1729 seemed like an exceedingly dull number and he hoped that this would not be taken as a bad omen. Ramanujan immediately answered: "No, no, my friend, on the contrary; it is a very interesting number. It is the smallest number that can be formed by adding two cubes together in two different ways!"

Such is the involvement of author Bryan Bunch with the personaliy of numbers. His tales of whole numbers from one to googolplex, fractions, algebraic, transcendental and imaginary numbers is sure to entertain and inform any reader with an interest in the world of numbers. His work is such that there is no such thing as an uninteresting number. To prove that there can be no such thing as an uninteresting number, consder the following: 'One' is interesting because it is considered neither prime nor composite; 'two' is ineresting because it is the only even prime number; 'three' is the smallest odd prime number; 'four' is the smallest even number to be a square; 'five'is a Fermat prime; 'six' is the smallest perfect number;...until the first 'uninteresting' number is reached. The fact that it is the first uninteresting number immediately makes it interesting!

Despite a few minor errors and the November 14 discovery of the primality of 2^13446917-1 (replacing 2^6972593-1 as the largest known prime number), I still believe that this book would be of great interest to any reader with an interest in numbers.

1729 = 1^3 + 12^3 = 9^3 + 10^3, in case you are interested in the Ramanujan story.

Numbers for Everyone!
Not since the great Indian mathematician Srinivasi Ramanujan has anyone gotten so involved in the personality of numbers to the extent as which Bryan Bunch has, and the reader is far better off for it. The classic story about Ramanujan and the personality of numbers is the tale about the number 1729. When he was ill in a hospital in England he was paid a visit by his friend and colleague G. H. Hardy, who had been given a ride in a taxicab bearing that number. Upon greeting Ramanujan, Hardy remarked that 1729 seemed like an exceedingly dull number and he hoped that this would not be taken as a bad omen. Ramanujan immediately answered: "No, no, my friend, on the contrary; it is a very interesting number. It is the smallest number that can be formed by adding two cubes together in two different ways!"

Such is the involvement of author Bryan Bunch with the personaliy of numbers. His tales of whole numbers from one to googolplex, fractions, algebraic, transcendental and imaginary numbers is sure to entertain and inform any reader with an interest in the world of numbers. His work is such that there is no such thing as an uninteresting number. To prove that there can be no such thing as an uninteresting number, consder the following: 'One' is interesting because it is considered neither prime nor composite; 'two' is ineresting because it is the only even prime number; 'three' is the smallest odd prime number; 'four' is the smallest even number to be a square; 'five'is a Fermat prime; 'six' is the smallest perfect number;...until the first 'uninteresting' number is reached. The fact that it is the first uninteresting number immediately makes it interesting!

Despite a few minor errors and the November 14 discovery of the primality of 2^13446917-1 (replacing 2^6972593-1 as the largest known prime number), I still believe that this book would be of great interest to any reader with an interest in numbers.

1729 = 1^3 + 12^3 = 9^3 + 10^3, in case you are interested in the Ramanujan story. ... Read more

Isbn: 0716733889
Sales Rank: 670846
Subjects:  1. Arithmetic    2. Mathematics    3. Number Theory    4. Number concept    5. Numbers    6. Numeration    7. Science/Mathematics    8. Theory Of Numbers    9. Mathematics / Number Theory   

Precalculus : A Self-Teaching Guide (Wiley Self-Teaching Guides)
by SteveSlavin, GinnyCrisonino
Average Customer Review:
Paperback (29 December, 2000)
list price: $17.95 -- our price: $12.21
(price subject to change: see help)
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Reviews (10)

Errata-fest
Breifly - there are errata in even the 'Basics' section at the beginning of the book, which is the elementary algebra review.

The cover of the book boasts, "Over two million copies sold".Well, if that's the case, then there has been over $35.9 million dollars wasted by trusting consumers (at $17.95 retail). I invite the lazy editor of this book to check my math.

Read this book if you want to do poorly in math
I was bothered by the review written by Antonios Giannakas. Mr. Giannakas calls himself a mathematician, I am not convinced he ever read the book. If I (an undergrad.) can find numerous mistakes in this math text, a MATHEMATICIAN should be appalled by the amount of incorrect information in this book. It is hard to believe this book was ever published in the first place. STAY AWAY FROM THIS BOOK!

-a mathematician

Full of mistakes
I am only into Chapter 3 and have found numerous mistakes.Including mistakes in important formulas such as the Quadratic Formula.I do not recommend this book to anyone who already has problems with math! ... Read more

Isbn: 0471378232
Sales Rank: 261486
Subjects:  1. Algebra    2. Calculus    3. Exponential functions    4. Linear programming    5. Mathematics    6. Pre-Calculus    7. Recreations & Games    8. Science/Mathematics    9. Study Guides    10. Trigonometry    11. Calculus & mathematical analysis    12. Mathematics / Recreations & Games   

Calculus Made Easy
by Silvanus P. Thompson, Martin Gardner
Average Customer Review:
Hardcover (08 September, 1998)
list price: $21.95 -- our price: $14.93
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Reviews (61)

One of the best math book
This is a book I definitely would keep for a long time, even until I go to college. I'm HS junior and taking AP calculus, with only algebra 2 as preparation from last year. I found this book is very easy to understood even for a self-taught person like me. I would recommend this book for every body who is taking calculus with or w/o proper preparation.The sample question covered broad type of calculus question you might face in the exam. I actually borrowed this book from my school library,and found it's worth to have it one at home. Now I'm gonna purchase it.

You won't really understand Calculus without this book!
Most calculus courses are taught to college freshman by graduate students who really didn't understand the course when they were freshman being taught by graduate students who didn't understand it when they were taught, etc, etc.Once you realize that most college instructors aren't proficient in the course to teach it, then you start to realize that if you're ever going to truly understand calculus, then you better find an alternative source of knowledge.And this book is exactly that source.

Read this book before you enter one of those imposing lecture halls (or at least the appropriate chapter of this book).Then and only then will you begin to at least recognize what the instructor is saying.And hopefully you will recognize when they're saying something that is not quite right.

Calculus is not hard; it's just not easy. This book probably should have been titled Calculus Made Understandable, or Caculus Made Fun, but it wasn't.So read the book and do the problems.It will open up a whole world of enjoyment that will last a lifetime.

Remember this very important point.Math was never learned in a lecture hall --- it's only truly learned in a study hall or library doing problems over and over and over.

Calculus made Easy
I am now finished with Calculus II and I still don't understand the content of thisbook. It is extremely complicated and poorly written. It makes it seem that Calculus is so easy, but it's just easier studying the old fasioned way, doing homework problems.I really don't recommend this book, at least for undergrads. ... Read more

Isbn: 0312185480
Sales Rank: 15298
Subjects:  1. Calculus    2. Mathematics    3. Science/Mathematics    4. Study Aids / Study Guides   

Calculus for Cats
by Kenn Amdahl, Jim, Ph.D. Loats
Average Customer Review:
Paperback (07 September, 2001)
list price: $14.95 -- our price: $12.71
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Reviews (4)

Helps me keep up with my son!
In my continuing quest to always be the source of all information for my son, Calculus For Cats has saved me! As his math skills continued, I was starting to pay for sleeping through Calculus in High School. But Ken Amdahl saved me. This is a perfect book for anyone wanting to learn the concepts of Calculus ... even if you hate math and cats!

The cats have succeeded
According to the authors, cats want to keep people confused about calculus, and I think that cats helped to write this book. Actually, I have been reading a lot of math and science concept books, trying to find any that really clarify the ideas, processes, and applications; technique is best learned with a good textbook. I did not find the analogies in Calculus for Cats to be particularly engaging or enlightening, but this short book does act as a primer of sorts. I would have enjoyed this book more if the authors had focused on interesting real-world examples rather than on mouse-catching examples.

Made me want to sign up for Calculus!
This book was amazing.It took something that we, from the outside of the math world, find enormously complex and confusing and through imagery and the imagination of the authors, made it understandable and accessible.I recommend it highly, especially to anyone who is about to take calculus for the first time.If you read this, you will be able to conceptualize what you are learning about....essential to truly understanding mathematics. ... Read more

Isbn: 096278155X
Sales Rank: 138122
Subjects:  1. Calculus    2. Mathematics    3. Science/Mathematics   

The Art and Craft of Problem Solving
by PaulZeitz
Average Customer Review:
Hardcover (09 February, 1999)
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Reviews (14)

Essential for budding (and experienced) problem-solvers
I join the ranks of previous reviewers here who honestly feel that having read this book in high school would have almost certainly changed my life.I, too, did very well in high school math competitions, but the maturity I am gleaning from this gem may have vaulted me into a different league.

It contains hundreds of problems from various levels of competition, from AIME problems all the way through some of the toughest Putnam problems (which, if you know anything about the Putnam, are about as hard as competition problems come).But the biggest help are the vital insights and exciting ways of looking at these problems.Don't take my word for it--many past IMO contestants have suggested this book too.

Particularly helpful is the way the author divides the book into sections based on often-used concepts and techniques.For example, you will see applications of the pigeonhole principle from the most basic (e.g. "In a drawer with socks of 2 colors, show that after picking any 3 socks, we must have a pair of same-colored socks.") through some rather difficult ones (1994 Putnam A4, an Erdos problem, and more).

The same goes for a multitude of others--the invariants section includes both the classic chocolate bar-cutting problem and Conway's rather difficult checker problem.Then, not only does he solve the latter beautifully, but incorporates nontrivial questions that ensure the reader has completely understood the solution (e.g., "Could we have replaced lambda with an arbitrary integer?Why not?").

You don't have to be a math competition buff to gain from this book, however.If you're simply interested in mathematical puzzles and problems, and are looking to expand your repertoire, this book will help you.Anyone with a good dose of intelligence and motivation will benefit.

For an additional problem book, check out Mathematical Olympiad Challenges by Andreescu and Gelca.For purely Putnam treatment, there are several volumes written by Kedlaya.And if you're a CS student, looking for honing those CS math skills to be razor sharp, you should definitely look into Concrete Mathematics by Graham, Knuth, and Patashnik.

Happy solving.

The Book I wish I had in High School
When I was in high school, I placed second in the Alabama State Mathematics Contest and won many others. However, I might could have been competitive with the IMO style problems had I had this book and would be much better off today had I seen this book earlier.

This book is for the exceptionally brilliant and the mentally tough.It is absolutely necessary to approach this book in a different way from a standard math textbook. You MUST attempt the examples BEFORE looking at the example solutions, NO MATTER HOW DIFFICULT OR FRUSTRATING. You may be bamboozled by the problems, but even trying to understand the problems before looking at the solutions and thinking about how a solution might proceed will pay huge dividends in the long run.

For example, in the first chapter Zeitz presents an example asking the reader to prove that the product of four consecutive integers cannot be a perfect square. The solution involves some clever algebraic trickery not visible to the inexperienced, but persistence and getting your hands dirty is key.

If you persist in spite of the considerable difficulty, you will find that you get better very, very quickly. You will also notice that it isn't just contest problems it helps you solve. I have found that I have solved my homework sets in the Berkeley graduate engineering program much more easily since working these problems. You will start to see creative and clever solutions where they exist in everything problem oriented.

PATIENCE PATIENCE PATIENCE!

Brilliant
As a high school student that is essentially bored with the regular, ho-hum classes that my school offers, this book is perfect.It gives a problem-solving foundation for math enthusiasts desiring to compete nationally in contests like the AMC, AIME, and USAMO.The problems are excellent and cover a wide range of difficulty (past ASHMEs, USAMOs, and, finally, IMOs); and the solutions are well-written, logical, and intelligible.In short, if you are looking to "get better" at problem solving, this is the book for you.

Note: I also bought Problem-Solving Strategies by Arthur Engle.Those, perhaps more advanced, problem-solvers that want even more of a challenge should purchase this book as well (as both books give very challenging problems, but Engel's is undoubtedly more advanced). ... Read more

Isbn: 0471135712
Sales Rank: 15371
Subjects:  1. General    2. Logic    3. Mathematical Analysis    4. Mathematics    5. Mathematics (General)    6. Problem solving    7. Science/Mathematics    8. Applied mathematics    9. Mathematics / Logic   

Number Theory for Computing
by Song Y. Yan
Average Customer Review:
Hardcover (01 May, 2000)
list price: $54.95
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Reviews (1)

A gifted writer opens many doors for the student
I just picked this monograph up at the Crypto-2000 conference at UCSB. Itis an unassuming, straight forward walk through the elements ofcomputational number theory. The author claims all that is required is highschool math; however, once cracking the book open the reader finds that thematerial is more directed at the advanced undergraduate, or even thegraduate math student, computer scientist, or to he/she who wants asingular experience in good mathematics. For example, there are side barsthat touch on some of the very brightest of the number theory elite;providing much needed insight as to their motivations and pursuits ofattack. Many a complicated concept is rendered harmless and fashionedreadily available for the learned reader. It is the kind of book that youcan not put down. I passed it around to a few of my colleaques; the bookquickly became a pleasent read for them followed up by a request to forwardthe ISBN number to their email accounts. The author knows the crafts ofboth writing well and displaying the beauty of number theory. Lastly, thetechnical content is not watered down, the author maintains academicdiscipline while making anecdotal information available via side-bars.Otherwise, the inspired reader would have to track down a text on thehistory of mathematics to sort out the 'story' behind the insights. Insteadit is "all" there for you to consider or mark for a later read. ... Read more

Isbn: 3540654720
Sales Rank: 1463441
Subjects:  1. Applied    2. Computer Books: General    3. Computer Engineering    4. Mathematics    5. Number Theory    6. Theory Of Numbers   

The Colossal Book of Mathematics: Classic Puzzles, Paradoxes, and Problems
by Martin Gardner
Average Customer Review:
Hardcover (10 September, 2001)
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Reviews (8)

A book about the unexpected and the beautiful in math.
Yes, as several reviewers pointed out, the title is a bit misleading.But in my opinion it shortchanges the book!This is a book about unexpected and beautiful mathematical realities, and can be read (almost) like a novel.One pauses, of course to think, but without any pain.The clarity of the presentation makes the contents accessible to anyone.The footnoting and bibliographical information make further research easy.The illustrations are exact and plentiful.It's even beautifully laid out and printed, (I refer to the hardcover edition).An absolute classic.Give a copy to a bright young mind to counteract the horrible effects of the average math "education" prevalent in our public and private schools.If you own 100 books on math, this could still easily become your favorite.

Interesting Read
I have never read any books on "recreational mathematics" so didn't know quite what to expect from this book--in general I found it entertaining and interesting, with a broad range of topics, including physics, statistics, logical paradoxes, higher dimensions, etc.You don't really have to be a math person to enjoy this book; almost anyone interested in stimulating topics should find at least parts of it interesting.

The book consists of numerous short articles with bibliographies for each.If one article bores you, move on to the next...I found the articles on statistics, logical paradoxes, a 2D Universe (Planiverse) and others very interesting and enjoyable.It is important to understand that this book is not a puzzle book per se; although almost every articles includes some task for hard-core readers to perform ("Prove that...", or "How many..."), it is really intended as reading material.

A few negatives:the articles almost all seem to have been written in the 1950s or 1960s (!); each article has an addendum which attempts to bring it up to date.Although this didn't matter that much to me, since I have never read anything on recreational mathematics, I doubt that much of the material would be new for anyone that reads the topic regularly.Similarly, it would have been more interesting to discover what topics are currently "hot" in this field.Also, the author spends too much time for my taste on trivial mathematical games such as folding paper into different shapes rather than on really thought-provoking mathematical topics (purely a personal preference, I suppose).

The imporatance of Mathematics
Martin Gardner is the grand old man of popular mathematics.He especially likes the math behind puzzles, riddles and logical conundrums.Logic and mathematics is the source of his thinking on the Skepticism he professes in his writings on pseudoscience, religion, the paranormal, UFO's, and other outlands of science and rational thinking.

This book is a collection of his best columns from Scientific American magazine.It was of the good reasons to read the magazine.Like many other things in the last few years, that publication jumped the shark at some point.Gardner was one of the reasons to still read it for a while there.

Gardner, however, is not just interested in the mathematics.The men, and history of the questions is also important to him.That is because it forms a context to the questions and the discovery of the answers.Context is very important to the author.Without it, you really don't know where you are.

If you like the writing of such good folks like Douglas Hofstadter, Jeremy Bernstein, Eli Maor, John Allen Paulos, Richard Feynman, Stephen Jay Gould, Isaac Asimov, Carl Sagan, Arthur C. Clarke or Ed Regis, than you will probably like the writing of Gardner.

Mathematics is something that people don't read a lot. At least not recreationally. Normally because they don't understand that it forms the basis of real logical thought.A real understanding of the modern world requires one of the understand science.And science that isn't, at least in part, based on mathematics isn't real science.It is something more of our leaders should take a real interest in.How can we expect our leaders to make good decisions on cloning or when-life-begins if they have no real understanding of science and mathematics?

Which is why Martin Gardner should be considered a national treasure. ... Read more

Isbn: 0393020231
Sales Rank: 127115
Subjects:  1. Games    2. Games/Puzzles    3. Logic & Brain Teasers    4. Mathematical Recreations    5. Mathematics    6. Recreations & Games   

The Concise Oxford Dictionary of Mathematics (Oxford Paperback Reference)
by Christopher Clapham
Average Customer Review:
Paperback (01 March, 1996)
list price: $14.95
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Reviews (1)

There's a better one
I find this reference book a little disappointing. While not a bad book, it's not comprehensive enough and explanations are (in many cases) too concise. If you don't already know the meaning of the term you're looking up, chances are you won't understand it after reading the item. I also purchased the Harper Collins Dictionary of Mathematics, and here are the good news - it's much better than the Oxford. Much more comprehensive and more readable. It's not perfect either, but if you're going to have only one of these, I recommend the Harper Collins. ... Read more

Isbn: 0192800418
Sales Rank: 634275
Subjects:  1. Dictionaries    2. General    3. Mathematics    4. Mathematics (General)    5. Reference    6. Science    7. Science/Mathematics   

Handbook of Mathematics and Computational Science
by J. Harris, Horst Stocker, John W. Harris
Average Customer Review:
Hardcover (17 July, 1998)
list price: $39.95 -- our price: $34.96
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Reviews (7)

Useful but limited and *no bibliographies*!
This handbook covers a range of undergraduate applied mathematics.Besides standard topics: geometry, indefinite and definite integrals, linear algebra, complex variables, etc.; it also covers some discrete math: Boolean algebra as applied to digital circuit design, graphs, etc.; and a bit of programming (including written-out programs implementing some algorithms).But its coverage is just too idiosyncratic to rely on.Its treatment of digital logic is surprisingly long, and its treatment of matrices surprisingly short.Why does it mention the rather specialized topics of fuzzy logic and neural networks?Why doesn't it mention wavelets?Why doesn't it include any material and algorithms on strings (regular expression matching, for example)?

But the worst feature of this book is that it doesn't provide bibliographies for the topic it covers.If you need more detailed treatment of matrices or graphs, where should you go for a fuller treatment?It doesn't help at all.

Very comprehensive reference.
This book is great for students and professionals alike.

The Swiss Army Knife of math books
The best way I can describe this book is that it is as close to a swiss army knife you are going to find in a mathematics book. It has everything from high school math to math for advanced undergraduates and possibly early graduate school in engineering, physical sciences, economics, and mathematics. It also has a few helpful sections on programming in Fortran, C, Pascal, and C++ (although I wouldn't rely on this book to learn those languages). It is a great reference book for scientists and engineers. ... Read more

Isbn: 0387947469
Sales Rank: 49795
Subjects:  1. Advanced    2. Applied    3. Computer Science    4. Computer Science (General)    5. General    6. Handbooks, manuals, etc    7. Mathematics    8. Mathematics (General)    9. Science    10. Science/Mathematics    11. Mathematics / General