Books by Subject
Books by Subject
Mathematics
Editorial Reviews
Amazon.com
In the tradition of
Innumeracy by John Allen Paulos, German scientist Gerd Gigerenzer offers
his own take on numerical illiteracy. "In Western countries, most children
learn to read and write, but even in adulthood, many people do not know how
to think with numbers," he writes. "I focus on the most important
form of innumeracy in everyday life, statistical innumeracy--that is, the inability
to reason about uncertainties and risk." The author wisely uses concrete
examples from the real world to make his points, and he shows the devastating
impact of this problem. In one example, he describes a surgeon who advised many
of his patients to accept prophylactic mastectomies in order to dodge breast
cancer. In a two-year period, this doctor convinced 90 "high-risk"
women without cancer to sacrifice their breasts "in a heroic exchange for
the certainty of saving their lives and protecting their loved ones from suffering
and loss." But Gigerenzer shows that the vast majority of these women (84
of them, to be exact) would not have developed breast cancer at all. If the
doctor or his patients had a better understanding of probabilities, they might
have chosen a different course. Fans of Innumeracy will enjoy Calculated
Risks, as will anyone who appreciates a good puzzle over numbers. --John
Miller
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Life by the Numbers
by Keith Devlin
Paperback - 224 pages
Reprint edition (March 17, 1999)
John Wiley & Sons;
ISBN: 0471328227 ; Dimensions (in inches): 0.54 x 8.81 x 7.08
Other Editions: Hardcover
Editorial Reviews
Amazon.com
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 --This
text refers to the Hardcover
edition.
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The Language of Mathematics : Making
the Invisible Visible
by Keith Devlin
Paperback - 352 pages
(March 2000)
W H Freeman & Co; ISBN:
0716739674 ; Dimensions (in inches): 0.98 x 9.25 x 6.12
Other Editions: Hardcover
Editorial
Reviews
Amazon.com
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."
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Reviews
Amazon.com
At first glance, neuropsychologist Brian Butterworth's What 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
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Editorial
Reviews
Amazon.com
Stanislas Dehaene is a French neurophysiologist of mathematics. There
are innumerable books on the psychology of language (as Dehaene shows, by "innumerable"
the brain naturally assumes "more than three"), but The Number
Sense is the only one devoted to the psychology of mathematics. As a result,
it is full of interesting facts and unique insights. Did you know that Chinese
may be the perfect spoken language for mathematics, while the arabic numerals
are the best written system? That the abilities of lightning calculators and
autistic savants probably owe as much to practice as to genius? That some people
associate numbers with colors? That there are better ways to learn multiplication
than memorizing a table? Dehaene's book is extremely practical as well as fascinating.
He never forgets "that mathematics is an extraordinarily difficult activity"
for which the human brain--not being a computer--is ill suited, and he suggests
many ways to improve its teaching. The Number Sense should be required
reading for anyone who has to teach mathematics--or learn it. --Mary Ellen
Curtin
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Mathematics - The New Golden Age
by Keith Devlin
Hardcover - 312 pages 5000
edition (November 15, 1999)
Columbia Univ Pr; ISBN:
0231116381 ; Dimensions (in inches): 1.03 x 9.24 x 6.27
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Models in Biology: Mathematics, Statistics, and Computing
By Donald E. Brown & P. Rothery
(Contributor)
Paperback
Amazon.com Price: $84.95
John Wiley & Sons, Dec, 1993
ISBN:0471933228
Review by:
The
publisher, John Wiley & Sons
An accessible, integrated treatment of mathematical models in biology,
the statistical techniques for fitting and testing them, and associated computer
methods. Properties of models, and of methods of fitting and testing them, are
demonstrated by computer simulation and illustrated by biological examples.
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Innumeracy : Mathematical Illiteracy
and Its Consequences
by John Allen Paulos
Paperback - 180 pages
Reprint edition (January 1990)
Vintage Books; ISBN: 0679726012
; Dimensions (in inches): 0.55 x 7.91 x 5.24
Editorial
Reviews
Amazon.com
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
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Fractal Geometry of NatureThe Fractal Geometry of Nature is a mathematics text. But buried in the deltas and lambdas and integrals, even a layperson can pick out and appreciate Mandelbrot's point: that somewhere in mathematics, there is an explanation for nature. It is not a coincidence that fractal math is so good at generating images of cliffs and shorelines and capillary beds.
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Syntactic Structures (Anua Linguarum
Series Minor 4, Series Volume 4)
by Norm Chomsky
Paperback Reprint edition
(June 1978)
Peter Lang Publishing;
ISBN: 3110154129
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The Child's Understanding of Number
by Rochel Gelman, C. R. Gallistel (Photographer)
Paperback - 260 pages
(December 1978)
Unknown; ISBN: 0674116372
; Dimensions (in inches): 0.83 x 9.29 x 6.05
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