The Joy of Mathematics
by Theoni Pappas
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Paperback (01 June, 1989)
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Reviews (7)

These are vignettes, designed to inspire further exploration
The widely divergent reviews reflect a lack of understanding of the purpose of this book. It is meant to touch on many mathematical ideas, not to go into depth on any one idea. My son read this at age 8, then at 10, and again at 12 - getting something more out of it every time. Many of the ideas intrigued and inspired him to seek out more information on his own, to research and understand more deeply. For that purpose, it deserves the highest rating.

I did not give 5 stars because there are some instances where I did find errors, these do not detract from the purpose of the book, but they are annoying to those of us who try to delve deeper. What I consistently found myself doing is researching from the internet and other print resources. But the idea originated from the overview in the book.

Many recreational mathematics books are inaccessible to beginners or math phobes. This book allows you to sample many, many ideas without feeling overwhelmed by details you may not understand. If you want details, you go explore the world opened up by the book.

Too cursory for much use, very often misleading.
Sorry to say but this book is a dud.While the concept of presenting interesting mathematical facts is great the presentation is so brief, so wrought with errors, and so incomplete that the work is not worth perusing.

Some of the "chapters" have answers at the back of the book and some do not.It appears that the author could not make up her mind wether this was to be a "math tricks" book or a "popular mathematics" presentation substantiated by theory.

There are many other excellent books that are more fulfilling.Journey Through Genius comes to mind.

All in all a disappointing work.

A pathetic little book that could have been good
This book could have been good if the author had done a careful job of writing the text, and perhaps if the illustrations were original, and above all if the author had understood the material she was writing about.Sadly these are often not the case with this book.

Rather, this book gives every sign of being essentially copied from bits of many dozens of other books.All the illustrations appear to be low-quality xerographic copies from other books (clearly used without any permissions).

But worst of all, the book is chock full of misstatements,misconceptions, and sentences that don't convey any meaning.

This book gives the non-expert reader the impression that he or she is learning something, but a great deal of the time this is just the illusion of learning.

I will list a few of the errors and illusory learning that I can readily find:
________
p. 6:The illustration of the cycloid curve should show it to be in a vertical direction where one arch meets another; instead it is at 45 degrees to the vertical.
________
p. 7:It is stated that when marbles are released in a cycloid-shaped container, they will reach the bottom at the same time.This phenomenon occurs for a bowl whose cross-section is an *inverted* cycloid, but that is omitted.
________
p. 13:Both the "impossible tribar" and "Hyzer's optical illusion" are NOT mathematically impossible, contrary to what is written.(They can be constructed in 3 dimensions.)Twistors are mentioned but not defined, even in a rough, metaphoric way -- just not at all.
________
p. 18:It is mentioned that pi cannot be the solution of an algebraic equation with integral coefficients, but there is no discussion in the book of what such an equation is.
__________
p. 19:Also, it is stated that the probability of two randomly chosen integers' being relatively prime is 6/pi.Not only should the correct number be 6/(pi * pi), but the idea of randomly choosing an integer is left completely undiscussed, although there is no known way to do this.
________
p. 38:The Platonic solids (aka regular polyhedra) are discussed here, but although they are defined twice, neither definition is correct.(The author neglects to mention that the faces of such a solid must be *regular* polygons.)
________
p. 45:The Klein bottle is discussed and illustrated here, but there is no mention that a genuine Klein bottle cannot be constructed in ordinary 3-dimensional space.(The familiar model of a Klein bottle depicted here is a self-intersecting version of the real Klein bottle, which does not intersect itself.This is much like the fact that a picture of a knot drawn in the plane must appear as if the knot intersects itself, though it does not do so in space.)
________
p. 46:The illustration at bottom purports to show what the model of the Klein bottle would look like if it were sliced in half.The halves are erroneously shown as identical, but they should be mirror images of each other.
________
p. 78:The title of this page is "Fractals -- real or imaginary?"
This is an entirely misguided question that will only confuse the reader.All mathematical concepts are real within mathematics, and do not exist (except as approximations) in the real world.

It's a worthwhile topic in the philosophy of mathematics, and could well have been introduced in this book, but it has nothing whatsoever to do with fractals per se.
________
p. 91:Here the author attempts to describe a model ofhyperbolic geometry (in a circular disk) devised by Henri Poincaré.However, she gets it exactly backwards, saying that objects get smaller as they approach the boundary of the disk.
(She may have been well-aware of how this model works, but her prose is at best completely ambiguous.)
________
p. 96:Here it is stated that it has been proved that knots cannot exist in more than 3 dimensions.Apparently the author is unfamiliar with an extensive and thriving field of higher-dimensional knots.(For example, a sphere can be knotted in 4-dimensional space.)
________
There are many, many more such gaffes, but I fear I have gone on too long.I just wanted to make it crystal-clear that this book is riddled with erroneous and vacuous statements. ... Read more

Isbn: 0933174659
Sales Rank: 105292
Subjects:  1. General    2. Mathematics    3. Mathematics (General)    4. Popular works    5. Science/Mathematics   

More Joy of Mathematics: Exploring Mathematics All Around You
by Theoni Pappas
Average Customer Review:
Paperback (01 April, 1991)
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Reviews (2)

Countless, clear examples of the math world around you
Many have sadly been led to believe that math is a cold, lifeless subject limited only to homework assignments and balancing your checkbook.Nothing could be further from the truth, and Pappas books show this.Her "More Joy of Mathematics" shows a vast amount of instances of where math shows up, some math history, and a few visual brain teasers.How are exponents involved in the forging that creates a powerful Samuri sword?How do the properties of an elipse make your car's headlights switch to high-beam?What math can be found in an ocean wave, the strength of a honeycomb pattern, or a nautilus shell?How is math vital to the contruction of musical instruments?Is zero really a "number", and where does the concept come from?What are some currently unsolved problems in mathematics?A total layman could understand most of the book, but to understand all the mini essays you might at least want to have knowledge of math at the high school level.

The book is a fast read, and fun to flip back and forth through, because each example is summarized in its own 1 or 2 page section, with illustrations.The same goes for "Joy of Mathematics" so you don't necessarily have to read that one first; they just contain different sets of examples.And don't think that all the good ideas were already taken for the first book -- "More Joy of Mathematics" is just as exciting to read.Plus it has a single index listing the topics from both this book and the previous one, so if you buy both it's easy to find the article you want by only looking it up once.Perfect gift for a math enthusiast at any level, and it may even covert a few "mathphobes".

A Book of Equivalent Quality to Its Predecessor
If you enjoyed Pappas' "The Joy of Mathematics," then you should love this addition to the set.This book, like its predecessor, contains adiverse collection of concise, insightful discussions about mathematicaltopics and how they relate to the observed world.It develops ideas withan elegant simplicity by providing the reader with copious amounts ofillustrations and diagrams.Pappas communicates mathematical ideas clearlyand, unlike some mathematicians, stresses their relation to the lives andexperiences of humans. She reveals the appealing aspects of the subject byexcluding the technical, logical deductions that most frequently discouragepeople from studying it.The variety of topics presented in the bookdisplays the versatility of mathematics and its relevance to humanknowledge. For students interested in exploring the meaning andsignificance of mathematics or for teachers lacking the necessary materialsto enlighten their students about these topics, this book is ideal. ... Read more

Isbn: 093317473X
Sales Rank: 73800
Subjects:  1. Education    2. General    3. Mathematics    4. Mathematics (General)    5. Popular works   

The Magic of Mathematics: Discovering the Spell of Mathematics
by Theoni Pappas
Average Customer Review:
Paperback (01 April, 1994)
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Reviews (1)

Fun but leaves you wanting more
A fun introduction to numbers and their myriad uses. It is really just anoverview of concepts, applications and puzzles concerning numbers. It leftme wanting much more but not knowing where to go. Still it was a fun read. ... Read more

Isbn: 0933174993
Sales Rank: 128335
Subjects:  1. General    2. Mathematics    3. Mathematics (General)    4. Popular works    5. Reference   

Fractals
by John Briggs
Average Customer Review:
Paperback (01 November, 1992)
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Reviews (11)

Patterns to Inspire - A Captivating Look into Fractals
This book brings a comprehensive and visually intriguing approach to the study of fractal geometry and the chaos theory. Through thought provoking imagery and discernible explanations & comparisons, John Briggs has sparked my curiosity where I now look more closely at the world around me. I believe this book is intended to captivate those with the ability to visualize and appreciate the aesthetics and interconnectedness of the arts, sciences and the natural phenomena that surrounds us. An insightful & visually stimulating read!

Don't buy this book
This book says absolutely nothing.It has a few good pictures (the best one is one the cover by the way), but the text is utterly worthless and uninformative.My favorite quote from the book is "Nonlinear means not linear."Really?Don't waste your money.Now I understand why I found it at the used bookstore.

Great Photos, Poor Content
This is a fantastic source of images on the subject of fractals, but not a great source of learning. Most books on math and science are difficult for the general reader; few authors (like Isaac Asimov) can make complex things easily understood. But the author of this book is, in my opinion, doing the public a disservice by oversimplifying the subject. The explanations underestimate the public's ability to think, and even include a number of things which are either dead wrong or made-up! The subject of fractals is still new, and there are recently more books available to explain fractals to the general public. Again, this is a great source of images, if that's what you're looking for, but look for another source if you want to undersatnd and appreciate this incredible and important topic. ... Read more

Isbn: 0671742175
Sales Rank: 234260
Subjects:  1. Fractals    2. General    3. Mathematics    4. Science/Mathematics    5. Topology - Fractals    6. Science / General   

Life by the Numbers
by KeithDevlin
Average Customer Review:
Paperback (17 March, 1999)
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Editorial Review

Most of us think mathematics is about numbers and counting. That's just the basics, though, and Keith Devlin's companion book to the PBS series "Life by the Numbers" gives examples of the versatility of math as a tool for understanding just about everything.Devlin loves math--he calls it "one of the greatest creations of mankind" in a chapter entitled "It's an M World"--and he wants everyone to love it.He shows, through fascinating photos and examples, that mathematics is all around us, determining everything from the shape of a flower to how our CD players and insurance policies work. For the math-phobic, Life by the Numbers can be a reintroduction to a subject they may have mistakenly thought dry and boring.Forget about long division, we're talking about understanding virtual reality, leopard spots, and viruses.This book would be perfect to introduce a high-school student to some of the great careers available to mathematicians.The experts introduced throughout are hip and cutting-edge, putting math to work in movie special effects, sports and art.Profusely illustrated and engagingly written, Devlin's tour of modern mathematics brings the subject to life. --Therese Littleton ... Read more

Reviews (2)

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

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

An easily understood description of exciting mathematics
I recently purchased a videotape of the Star Wars™ movie, `The PhantomMenace.' It is difficult to believe that a more convincing point ofevidence for the power of applied mathematics will exist for some time. Thescenes where the generated creatures are in motion have a degree of realitythat is astounding. As Devlin spends a great deal of time explaining inthis book, what you see is a complex series of numbers translated by acomputer into pictures on a screen.
Other topics concerning imagegeneration by computer involve the visualization of scientific data. Peopleworking in this area are often a combination of graphics artist andcomputer scientist. With such enormous amounts of data being collected,interpreting it and filtering out the points of interest has become ahorrifically difficult task. The only way that it can be done is to findways to filter the data as much as possible and then display it in a visualmanner where the key points are easily discernible. No quote betterdescribes the situation than that uttered by R. W. Hamming, `The purpose ofcomputing is insight, not numbers.'
The physics of sports is alsodescribed in some detail. No matter how well trained their bodies are,athletes are still bound by the laws of physics, so at some point theirtraining must incorporate these laws. A simple question such as whether tojump higher or spin faster when figure skating can determine the differencebetween a medal winning performance and simply watching it happen ontelevision.
This book is a tour de force in how many applicationsthere are for mathematics, with many that appeal to young people. Anappreciation for the value of mathematics is the first step towards adesire to study it, and this book will no doubt spark the appreciation.

Published in Journal of Recreational Mathematics, reprinted withpermission. ... Read more

Isbn: 0471328227
Subjects:  1. General    2. History & Philosophy    3. Life by the numbers (Televisio    4. Life by the numbers (Television program)    5. Mathematics    6. Mathematics (General)    7. Popular works    8. Science/Mathematics    9. Mathematics / History    10. Science: General Issues   

Powers of Ten (Scientific American Library Paperback)
by Philip Morrison, Phylis Morrison
Average Customer Review:
Paperback (01 September, 1994)
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Editorial Review

Back in 1968, designers Charles and Ray Eames made a 10-minute documentary film, titled Powers of Ten, showing what the universe looks like at different scales. Philip and Phylis Morrison were scientific advisors on the movie, which Philip narrated, and it was chosen in 1998 for preservation in the National Film Registry, which selects "culturally, historically or aesthetically significant motion pictures" for preservation. The Morrisons' book translates the film onto paper.

Starting with a view of a billion light-years, the book (like the film) moves inward, with each page being at one-tenth the scale of the previous one. In 25 steps, you're looking at a picnic by the shores of Lake Michigan, then plunging into a human hand, down through the cells inside it, the DNA inside the cells, the atoms inside the DNA, and the subatomic particles inside the atom. By the time you've gone a total of 40 steps, you're in a world of quantum uncertainty.

There is no better guide to the relative sizes of things in the universe, and no better teacher about what exponential, scientific notation really means. --Mary Ellen Curtin ... Read more

Reviews (18)

Another Scientific American Masterpiece
I purchased this book years ago when I began collecting the magnificent Scientific American Collection.It has since been published in paperback and I have heard there is a corresponding book that decreases by powers of ten.This is easily the most approachable of all the books in the series and I have used it with both my boys when they were younger.

Parenthetically, anything that would stimulate American interest in science - and stem the tide toward a universal scientific illiteracy - should be welcome.I have seen this powers of ten device several times but the one that stands out in my mind is the opening scene of CONTACT that was marred only by the pitiful displays of stupidity heard from the members of the audience. ("Is that Saturn?" "Yeah, it was once a star and that's how it got its rings.""That's what I thought.")

Back to the book, we start off matter of factly then proceed outward.The commentary is sparse because little is needed.In this case, the picture IS worth a thousand words - more if you get down to it.Get this now-affordable volume and give it to a youngster.

Scale and exponential notation.
This book is an introductory peek at one of the most foundational mathematical tools needed for any consideration of cosmology, astronomy, and/or particle physics:
"At one end, far out where the galaxies appear like glowing froth in darkness, all our sciences become only one: cosmology. ... At the other end, for the very small we again have one science only: particle physics. There are even hints that the two ends inform each other." Evidence, perhaps, that television isn't all bad, the concept here was developed for a TV special program (quite a few years ago now), then plucked from video to print. It's a 'can't miss' premise but I find the writing to be slightly awkward and there may be too many illustrations. For a book that begs me to pick it up, it too easily invites me to put it down. Even so, it makes for a reasonably good overview of a universe more than 20 billion light years wide made out of stuff so small that we must describe it using negative powers of ten. The idea here is to illustrate the dramatic changes of scale involved in only a few powers of ten, and thus the "power" of powers of ten. The book's theme is itself quite modest, but for the reader unfamiliar with the concept of exponential notation, this small volume may be a startling revelation. To those familiar with the concept, the book may be a mere novelty, perhaps a "coffee table book."

A picture is worth a 10³ words! Amazing!
I've seen this book for the first time in 1985, when I was kid. It is still my all-time favorite.

Although the book does have lots of textual info pages, the core of the book is a series of 42 full-page pictures which depict the an ordinary picnic photo in different scales.

Starting from an ordinary dude resting on the grass, each page turn shows the scene from 10 times farther away. First we see the park he is picnicing on, then the entire city, and before you know it we are in deep space racing towards the outskirts of the Universe.

On the other side of the journey, each page turn magnifies the last picture tenfold. First by viewing a close-up view of the picnicing guy's hand, you quickly find yourself probing deeper and deeper through the realms of biology and chemistry right into the core of a single atom.

The really cool thing about the whole deal, is that all the images are centered at the same object: a single atom on the picnicing dude's hand.

In short, the idea is absolutely brilliant. The images chosen for the presentation is not perfect, but they are still amazing. Of-course, the film is much more impressive then the book, but you can't take a film with you to a camping trip... ... Read more

Isbn: 0716760088
Subjects:  1. General    2. Science    3. Science/Mathematics   

A Tour of the Calculus
by DAVID BERLINSKI
Average Customer Review:
Paperback (28 January, 1997)
list price: $14.95 -- our price: $10.17
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Reviews (104)

Evaluate the book for what it is.
When Galileo dropped his objects off the tower and told of his findings, three of the possible reactions different sorts of people might have made could have been 1) who cares? 2) Great! Now I have a new "tool" to go apply to the world or 3) This changes everything! Berlinski is definitely writing to the last group. This is not a book to teach the reader a series of mathematical tools to go do something with, it is a book for the reader who wants to stop and contemplate "what does it mean?" Berlinski tries to address these different approaches to calculus (or geometry, or life) by showing different students and indicating, I believe, how educational systems fail to impart the big questions to students. Berlinski isn't writing to the "student" or "teacher" that evaluates understanding by how well or quickly one can manipulate numbers and formulas, but to the person that marvels at the world around them. The comparisons to language are excellent - many people can write "well" in a purely technical way, the grammar is correct and it flows quickly, but they really have nothing of interest to say, perhaps because they do not know what to ask. Berlinski isn't speaking to technical aptitude with calculus, and wishes the reader to see what is behind the technique. Not to be only a manipulator of tools, but a manipulator of concepts. In this, Berlinski, who indicates his failures as a teacher, actually gives the reader access to means of explaining to others WHY they find this stuff fascinating.

On the writing style, well, it does have to grow on you. Some of the words and stories could have been left out - like a bad joke in a good comedian's routine. But the anecdotes and examples are constant attempts to relate the calculus to everyday meaning and point out where everyday meaning is challenged. The actual words, odd usages, and .. well Berlinski.. are, I think, often just the writer having fun. And what is wrong with that? Like his math, Berlinski seems to want to enjoy and revel in language. Not write a masterpiece, but to communicate with his own unique personality.

I've invested a lot of time and thought into Leibniz's published writings, Berlinski reminds me of why those writings originally altered my view of the world.

Very good
I have a BS in physics and I'm working on a MS in EE.I say that only to show that I am not stupid and to give my opinion of the book some context.I liked the book a great deal.Sometimes I think I ought to be in philosophy because of the way I think, and I find that probably I think a lot like the author.For example, at one point he goes on about the concept of "area."And he talks for several pages about the idea and meaning of an irrational number.He says things that you will never read in a textbook.We all understand things in very human ways like it or not, and some simple concepts such as area or what a number is, are not so simple and boring if you aren't proud or dismissive.I like Berlinski because he doesn't wave his hands over things and say they're easy, he discusses them.
I highly recommend the book if you want a subjective, human-like discussion of calculus and some related basic mathematical concepts.

why mathematicians should stick to math
Without any doubt, the single worst book I have ever read in my life.If you cherish the sanctity of your own mind, stay away from this book at all costs. It is convoluted, poorly written, and only complicated my knowledge of THE calculus.Berlinkski seems to rely on a very big thesarus to attempt to convey any point he tries to make.I got absolutely nothing out of this book. ... Read more

Isbn: 0679747885
Sales Rank: 26263
Subjects:  1. Calculus    2. Mathematics    3. Popular works    4. Science/Mathematics    5. Mathematics / Calculus   

e: The Story of a Number
by Eli Maor
Average Customer Review:
Paperback (04 May, 1998)
list price: $18.95 -- our price: $12.89
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Editorial Review

Until about 1975, logarithms were every scientist's best friend. They were the basis of the slide rule that was the totemic wand of the trade, listed in huge books consulted in every library. Then hand-held calculators arrived, and within a few years slide rules were museum pieces.

But e remains, the center of the natural logarithmic function and of calculus. Eli Maor's book is the only more or less popular account of the history of this universal constant. Maor gives human faces to fundamental mathematics, as in his fantasia of a meeting between Johann Bernoulli and J.S. Bach. e: The Story of a Number would be an excellent choice for a high school or college student of trigonometry or calculus. --Mary Ellen Curtin ... Read more

Reviews (41)

A must for students of Mathematics
This book was written well, and every student interested in Mathematics or pursuing a career in engineering or the sciences should read this.You really don't need to be a math genious to enjoy this book.I would recommend that high school Math teachers and even college professors assign a little reading each day of the history of their profession.This is one of those history books.

Great book Great author - Worth Reading!!
This is great book. Besides `e' it covers all the history and good stories about calculus. I did not get bored at all. This explains all the difficult concepts with great detail and fun to read. I never got bored. Maor does wonderful job of bringing together maths, fun and history.
From Napier to Newton he covers everything. It gives the insight to the common used notations today. This books is collectors item.

Never a boring moment.
How much have computers changed our lives?John Napier spend 20 years from 1594 to 1614 performing calculations for his logarithm tables.Today, that entire body of work is easily reproduced in minutes, using Microsoft Excel.But Napier'sinvention quickly spread around the world, creating a calculation revolution that empowered grateful scientists with speed they could only imagine before.I suppose it was the greatest computation breakthrough since the abacus.

From Napier forward, the story of e proceeds, eloquently recounted by Maor.There is not a boring moment in the book.
... Read more

Isbn: 0691058547
Subjects:  1. History & Philosophy    2. History Of Mathematics    3. Mathematics    4. Number Theory    5. Science/Mathematics    6. History of Science and Medicine, Philosophy of Science    7. Mathematics / History   

The Joy of Mathematica : Instant Mathematica for Calculus, Differential Equations, and Linear Algebra
by Alan Shuchat, Fred Shultz
Average Customer Review:
Plastic Comb (February, 2000)
list price: $70.95 -- our price: $70.95
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Reviews (3)

Second edition is optimized for Mathematica 4.0...
Joy does work on Mathematica 5.1, however, the current version, and it runs on both Mac and PC platforms (OS X for the Mac and Windows XP for the PC).

Joy is a wonderful compilation of program-based notebooks that shorten the time-to-use Mathematica dramatically, for both novice and computer-savvy students and learners.The manual is well-written, visually attractive, and uncluttered.

Joy of Mathematica makes it far easier to graph (2- and 3-D, parametric, polar coordinates, and more), manipulate expressions (simplify, solve), differentiate and integrate functions, work with series and sequences, vector fields, matrices, multiple variables, and so forth.

Writing adjuncts to Mathematica is something of a cottage industry, and several other Mathematica-based programs can help: Calculus Wiz (for high school and college students), Explorer, and Navigator, for instance.

Wolfram Research (publisher of Mathematica) wants to penetrate the secondary-level educational market and is offering very attractive site licenses to schools and individual licenses to students at those schools.It is not clear whether the publishers of Joy will offer a similar site license and individual student purchase rate.

Finally, it is not known at this point whether the authors will re-optimize Joy for Mathematica 5.1 version.

Fantastic!!!!
A wonderful book!Maple has been described as "the force" in CAS with Mathematica described as "the dark force". This wonderful book brings Mathematica into the light.

Making Mathematica a Joy to Use
"The Joy of Mathematica" really does make Mathematica software a "Joy" to use, and to learn. Users of Mathematica know and love the powerful capabilities of this excellent mathematical softwareenvironment for symbolic and numeric computation with incredible supportfor 2D and 3D graphics. Students and professionals considering adoptingMathematica are often awestruck by the enormous range of mathematicalcapabilities suddenly put at their fingertips. However, Mathematica is nota Joy to use, as each powerful command (and there are many) is accompaniedby so many parameters and modifiers (all necessary), requiring a not soJoyful syntax. "The Joy of Mathematica" comes to the rescue, andindeed, it is a real JOY to use! "Joy" comes in the form of abook, an easy to use tutorial and guide, with an accompanying CD. Thesoftware on the CD installs easily, and modifies your own Mathematica"front end" environment by providing very useful and wellorganized pull-down menus which launch diaglog boxes. The diaglog boxes aregreat! They remind the user which parameters and choices need to bespecified in the context of a particular Mathematica command. They provideimmediate examples for the student to try. They output clear summaries ofthe entered requests, organize the computed output, and allow the user toview the actual Mathematica commands which "Joy" issues. This inturn helps the user learn Mathematica's arcane command syntax (if you wantto bother). "Joy" provides the student and experienced user withthe menu structure we all wish we had when using Mathematica."Joy" is really a terrific teaching and learning tool for collegestudents of science and engineering, and a great way to bring great mathsoftware into the hands of high school students. It's a "Joy" forme and my son, and it will work for you too. ... Read more

Isbn: 0126407304
Sales Rank: 651951
Subjects:  1. Computer Bks - Other Applications    2. Computer Science    3. Computers    4. Data processing    5. Discrete Mathematics    6. Mathematica    7. Mathematica (Computer file)    8. Mathematical & Statistical Software    9. Mathematics    10. Science/Mathematics    11. Computers / Educational Software / General   

Innumeracy: Mathematical Illiteracy and Its Consequences
by John Allen Paulos
Average Customer Review:
Paperback (18 August, 2001)
list price: $13.00 -- our price: $10.40
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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   

A Mathematician Reads the Newspaper
by JOHN ALLEN PAULOS
Average Customer Review:
Paperback (01 March, 1996)
list price: $12.95 -- our price: $10.36
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Editorial Review

In this book the author of Innumeracy : Mathematical Illiteracy and Its Consequences reveals the hidden mathematical angles in countless media stories.His real life perspective on the statistics we rely on and how they can mislead is for anyone interested in gaining a more accurate view of their world.The book is written with a humorous and knowledgeable style that makes it great reading. ... Read more

Reviews (25)

Unique little book
Dr. Paulos is a mathematician who likes to read and think about newspapers and their stories. He admits to having a sentimental fondness for several of them and to being an avid news junkie, despite conceding some of their faults. He admits the average paper may concentrate too much on the bad news and on political reportage and crime, sometimes making them look like nothing more than glorified police blotters.

But there are other, more subtle ways in which newspapers can mislead. Because the selection of stories seems so diverse, disjointed, and unrelated--a tornado hits Kansas, an earthquake in Japan, a gang-related murder in L.A., a psychic in London predicts the end of the world, a story on global warming, a farmer in Korea grows the world's largest turnip--he feels they enourage the illusion of being well-informed by providing us with a snapshot, as it were, of the world beyond our own limited purview, when in fact, all one has done is read a disjointed collection of stories that might merely reflect the selection biases of the newspaper, or what stories they could actually obtain because the reporter was there and not somewhere else, vs. the more important ones that they couldn't, for whatever reason.

Despite these shortcomings, Paulos finds newspaper stories a fascinating source of usually good information on many topics, and for the ones that don't, he finds they provide interesting food for the thought for a mathematician like himself, and he likes to use his mathematical and logical skills to show why a particular story's interpretation is probably false, misleading, or doesn't follow logically from the facts in the story. The book is devoted to showing how the application of simple mathematical and logical skills can provide insights into the real "facts" behind a news story.

One of the best examples was a story in which it was claimed that black voters voted along racial lines for a particular mayorial candidate. (I don't recall the exact percentages, but I'll use a similar example to show how Paulos analyzes the statistics). Suppose 85% of blacks had voted for the black candidate. Does that support the story's claim? Paulos points out that the story failed to consider that most blacks are democatic, and the black candidate was a democrat. If 80% of blacks are democrats, that means only 5% more voted for the black candidate than one could expect based on that percentage, which is probably not very significant.

Contrast that with the white situation. White voters are fairly evenly divided between republicans and democrats. If 70% voted for the republican candidate, that means that 20% more voted for the white candidate, and against the black candidate, than one would expect based on the distribution of party affiliation, which could be significant. Hence in this case, it's actually the white voters who appear to vote along racial lines than the blacks. Paulos shows how this kind of simple mathematical analysis can provide a useful foil to the often overly facile, unjustified, and distorted claims made in newspaper stories.

One brief note on how to read the book. It's divided up into several sections, reflecting the typical format of most newspapers, which are:

1. Politics, Economics, and the Nation

2. Local, Business, and Social Issues

3.Lifestyle, Spin, and Soft News

4. Science, Medicine, and the Environment

There are so many examples in the book in each section that you could just read the section or two that interested you, or the stories that interested you, and you could still learn a lot.

This book should be required reading for students and probably most adults in our increasingly illiterate and innumerate society. It's the only book I've ever seen on applying mathematical concepts to things as fuzzy and inexact as newspapers stories often are, and if someone had told me there was a book on it, I would have been sceptical, in the same way Paulos approaches each newspaper story with a healthy does of scepticism. In fact, the book really is about how to use simple math and logic and even common sense thinking to develop a healthy BS filter, probably a useful tool in many areas of life, in addition to reading the newspaper. Paulos has done a fine job and the book counts as one of the most interesting and practical applications of math and logic to everyday life that I've seen.

should be required reading for EVERY adult 16yrs and older
As a mathematician living in a high-tech, post-industrial society of highly literate citizens, I am often astounded (and disturbed) by the naivete and incapacity of educated, intelligent people to grasp simple mathematic concepts and their profound relevance to much of our everyday lives.

Paulos has done something about it.

This book (and his book 'Innumeracy') should be required reading for every high school student - nay, every adult - in this country.Many of the most important mathematical concepts that we need are horrendously misunderstood by large portions of our 'educated' society, and as this book illustrates, we all suffer for it.

This book is eminently accessible to most any reader beyond junior high school, and the organization into multiple independent little chapters means it can be broken up into bathroom reading sessions if necessary.

Paulos is America's greatest mass educator of math for the lay person, and belongs in the "Math Is Fun For Everyone" pantheon with Eli Maor, Colin Bruce, Ivars Peterson, Martin Gardner, and Ivar Ekeland.

Half Assorted (Numerical) Trivia, Half Useful Content
Paulos's second effort, A Mathematician Reads the Newspaper, is a motley of topics culled from his avid(and perhaps rabid)devotion to reading a variety of newspapers.While some of the vignettes struck me as off-beat and at times annoying, others did impart some very useful information.This leads me to believe that different readers will assign a different value to some things in the text.One man's trash is another man's treasure, so they say.

The book is actually quite a demonstrable improvement over some of his previous efforts, most notably his book Innumeracy in particular.Compared to Innumeracy, this book contains less smug academic snobbishness, less intellectual elitism and much less of an obvious attempt to show how much smarter Professor Paulos is to the average, everyday simpletons he must unjustly suffer.Instead, there is a concerted effort throughout the book to show and tell.In terms of accessibility, both in writing style and content, I feel compelled to give it high marks.

In particular, this book contains a short bibliography as well as an extensive index.The actual book does not have formal chapters per se, but it does have sections, five in all, devoted to all the topics one normally finds represented in the local newspaper.This in turn allows one to pick and choose topics of interest, as opposed to embarking from page one and setting one's jaw firmly for difficult and staid reading.Actually, the book is more of a series of vignettes on a particular theme, short essays, usually not more than five pages, which highlight the hidden but crucial role of mathematics in the stories that we read in the newspapers.Paulos also includes many diagrams and charts as an aid in presenting each topic and helping the reader to understand some of the more arcane(and often bizarre)concepts involved.

I especially liked his treatment of Bayes' rule, or conditional probabilities.It often pops up in medical statistics, and is almost always never appropriately understood.Moreover, section four of the text, which deals with newsworthy statistics from science, medicine and the environment, will probably be the most informative section of practical interest to most readers.

However, be forewarned that even in this book, Paulos has succumbed to the urge to recycle some of his material, both from his previous book, Innumeracy, and going forward to other books.So if you've read this book, you pretty much have the gist of his subsequent books.Still, the content is mostly fresh, and much of it is interesting, at least to me.Overall, I found the book to be a good learning experience, and one that I would really lend to others seeking enlightenment on statistics in the news.

In sum, this little book is not nearly as painful a read as Innumeracy, and is definitely more entertaining, educational and informative.The good professor has allowed his liberal roots (he was once, perish the thought, an English major in college, but defected to math, and as such he is an embarassment and an affront to all self-respecting humanitarians everywhere) to come briefly out of the closet, so to speak, and it shows in the crisp, clear writing consistently appearing in the text.This book is without a doubt the best of all his musings on mathematics and society. ... Read more

Isbn: 038548254X
Subjects:  1. General    2. Mathematics    3. Media Studies - Print Media    4. Newspapers    5. Popular works    6. Probability & Statistics - General    7. Science/Mathematics    8. Science / General   

Beta Mathematics Handbook: Concepts, Theorems, Methods, Algorithms, Formulas, Graphs, Tables
by Lennart Rade, Bertil Westergren
Average Customer Review:
Hardcover (31 October, 1997)
list price: $49.95
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Reviews (2)

Comprehensive.
If you're involved in any aspect of applied mathematics, this book is worth its weight in gold. It is probably considered somewhat obscure in the US, since it's a Swedish book that isn't really marketed outside of Sweden,but I haven't seen anything as comprehensive anywhere.

The book containsall the formulae, theorems and tables that any student or professionalinvolved with mathematics or engineering could hope for. It assumes thatthe reader has a level of understanding equal to "I've taken thecourse, but forgotten the details".

It is comparable to the morewell-known"Mathematical Handbook" by Spiegel, but in my opinionmuch better. The coverage of the areas that Spiegel cover is equal orbetter. "Beta" also covers probability theory, random processes,numerical methods, simulation, and other areas that are used extensively inpractice but not even mentioned by Spiegel.

In my opinion, if you areonly going to buy one mathematical reference book, "Beta" is anexcellent choice.

A great 'dictionary' of Mathematics
I have found Beta Mathematics Handbook to be the most organized, informative, concise and well-written reference for mathematics of all levels, esp. for probabilities and statistics. I highly recommend it. Amust in every mathematician's bookshelf. ... Read more

Isbn: 0849377587
Sales Rank: 680659
Subjects:  1. Formulae    2. General    3. Mathematics    4. Mathematics (General)    5. Science/Mathematics    6. Tables    7. Mathematics / General