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The Adventures Of Penrose The Mathematical Cat
by Theoni Pappas
For grammar school teachers. Pappas brings the joy of discovery to the subject of mathematics. This book is aimed at the grammar school audience and its teacher. It is understandable to adults who can then bring the joy and fun of mathematics to youngsters – encouraging their curiosity and pleasure in the subject.


The Book of Nothing: Vacuums, Voids, and the Latest Ideas About the Origins of the Univers
by John D. Barrow
What conceptual blind spot kept the ancient Greeks (unlike the Indians and the Mayans) from developing the concept of zero? Ranging through mathematics, theology, philosophy, literature, particle physics and cosmology, the book explores the enduring hold that vacuity has exercised on the human imagination.


e: The Story of a Number
by Eli Maor
An excellent choice for a high school or college student of trigonometry or calculus. e remains as the center of the natural logarithmic function and of calculus. Maor's book is the only more or less popular account of the history of this universal constant.


E = MC Squared
by David Bodanis
David Bodanis offers an easily grasped presentation on the equation. "Mass", he writes "is simply the ultimate type of condensed or concentrated energy." Whereas energy "is what billows out as an alternate form of mass under the right circumstances." He writes, creating useful imagery so that we can understand the enormity of the subject. There are interesting anecdotes about other scientists that both entertain and inform.


The Golden Ratio: The Story of Phi, the World's Most Astonishing Number
by Mario Livio
Phi is the golden ratio of antiquity (1.6180339887), a never-ending number so lauded for its harmonious qualities that in the 16th century it was dubbed the divine proportion. It was discovered by Euclid more than 2,000 years ago. It seems that for any line divided into two unequal segments, the resultant lengths of the two segments and the original line can be formed into a ratio that equals phi. This curiosity of plane and solid geometry might have remained just an oddity had the ratio not cropped up in unusual places, from the structure of crystals to botany to the shape of spiral galaxies. There's a whole mathematical community devoted to Fibonacci numbers, whose permutations produce phi again and again. Livio's encyclopedic selection of subjects, supported by dozens of illustrations, will snare anyone with a recreational interest in mathematics. This thoroughly enjoyable work vividly demonstrates to the general reader that, as Galileo put it, the universe is, indeed, written in the language of mathematics.


Imaginary Numbers : An Anthology of Marvelous Mathematical Stories, Diversions, Poems, and Musings
by William Frucht
Don't be fooled by the title. It isn't a book devoted to explicating the many mysteries of the square root of minus one. What he has done is far more impressive. Pursuing what he envisions as "a truly literary science fiction," Frucht has dared to collect an idiosyncratic company of writers--including such disparate names as Rudy Rucker, Italo Calvino, William Gibson, and Lewis Carroll--into one eclectic, accomplished anthology. The unifying theme of these writings, the short stories, essays, out-loud ponderings, even poetry, is the world of mathematics: every contributor is either "using mathematics to tell stories or using stories to explain mathematics," what Frucht describes as two sides of the same coin.


An Imaginary Tale: the Story of the Square Root of -1
by Paul J. Nahin
"This book will be most accessible to the million or so who each year complete a college course in freshman calculus." Readers will end up with a good sense for the mathematics of i and for its applications in physics and engineering. "Dispelling many common myths about the origin of the mystic 'imaginary' unit, Nahin tells the story of i from a historic as well as human perspective. His enthusiasm and informal style easily catch on to the reader. The book is a must for anyone curious about the evolution of our number concept. Today complex numbers have such widespread practical use--from electrical engineering to aeronautics--that few people would expect the story behind their derivation to be filled with adventure and enigma. The author tells the 2000-year-old history of one of mathematics' most elusive numbers, the square root of minus one, also known as i, re-creating the baffling mathematical problems that conjured it up and the colorful characters who tried to solve them.

Addressing readers with both a general and scholarly interest in mathematics, Nahin includes entertaining historical facts, mathematical discussions, and the application of complex numbers and functions to important problems, such as Kepler's laws of planetary motion and ac electrical circuits. This book can be read as a history, almost a biography, of one of the most evasive and pervasive "numbers" in all of mathematics.


Innumeracy: Mathematical Illiteracy and Its Consequences
by John Allen Paulos
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 be indifferent to the innumeracy and scientific illiteracy of so many of its citizens." It remains to be seen if Innumeracy will indeed be able to "help launch a revolution in math education that would do for innumeracy what Sabin and Salk did for polio". Many of the improvements Paulos suggested have come to pass within the past 10 years. Only time will tell if the generation raised on these new principles is more or less resistant to innumeracy.


Islands of Truth: A Mathematical Mystery Cruise
by Ivars Peterson
Peterson , author of The Mathematical Tourist, explores topics at the frontier of mathematics research, among them: new developments in fractal geometry, applications of number theory, computer graphics, and artificial intelligence.


It Must Be Beautiful: Great Equations of Modern Science
by Graham Farmelo (editor)
"A fascinating history of science for educated nonmathematical readers. The power of equations can seem magical, writes MIT physics professor Frank Wilczek in an essay on the Dirac Equation, which describes the movement of quantum particles. Like the brooms created by the Sorcerer's Apprentice, they can take on a life of their own, giving birth to consequences that their creator did not expect, cannot control, and may even find repugnant. Though it seems like an odd reversal of the scientific method to do the math first and then find the data that fit, it has happened time and again. These 11 essays contributed by various scientists and science writers (e.g., Roger Penrose, Peter Galison, Oliver Morton, and Steven Weinberg) describe scientific advances that derived from mathematical theory such as Einstein's thought experiments on relativity, a game theory equation that predicted animal behavior, or the discovery that the mathematics of chaos describes the real-world phenomenon."


The Joy of Pi
by David Blatner
We all use the number. How was it discovered? Are you aware that it never divides out evenly? What is its history? Who discovered it? Read on!


Just Six Numbers: The Deep Forces That Shape the Universe
by Martin Rees
Just six numbers govern the shape, size, and texture of our universe. If their values were only fractionally different, we would not exist: nor, in many cases, would matter have had a chance to form. If the numbers that govern our universe were elegant such as 1 or pi, or the Golden Mean, we would simply shrug and say that the universe was an elegant mathematical puzzle. But the numbers Martin Rees discusses are far from tidy. Rees is the Astronomer Royal of Great Britain.


Keys To Infinity
by Clifford A. Pickover
A perpetual idea machine, Clifford Pickover is one of the most creative, original thinkers in the world today. By most standards he is a mathematics geek (Ph.D. research scientist for IBM, associate editor for two computer journals), but he is the coolest math geek you might ever meet. For this book he has compiled 30 chapters of mathematical puzzles (and one short story), all having some connection to the concept of infinity. These problems are open-ended; in the event that the reader actually solves the main puzzle, there are enough digressions, diversions, and tangents to keep even the fastest computer running for hours. Computer modelers will be happy to find that instructive BASIC and C language has been provided for most of the problems. Many puzzles have been previously posted on the Internet, and the best or weirdest replies have been included in this book.


The Language of Mathematics
by Keith Devlin
The perfect book for people who have questions about math they've always wanted to ask but were afraid they wouldn't understand the answers to. Devlin speaks in "readable" English. Mr. Devlin 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." Wanting mathematics without abstract notation "is rather like saying that Shakespeare would be much easier to understand if it were written in simpler language.


Math Talk
by Theoni Pappas
A handy little dictionary of mathematical terms. If you are insecure in math terminology, this is for you.


Mathematical Cranks (Maa Spectrum)
by Underwood Dudley
An entertaining book about a variety of strange people obsessed by mathematics. A mathematical proof of the impossibility of doing something simply does not deter some people from claiming they have done it. Dudley labels such people as cranks. While the reading is entertaining, it is also somewhat depressing, in that no amount of logic or reason can convince a crank that their work is flawed. They give so many different reasons for why their work is rejected. Unfortunately, a crank never arrives at the real reason, namely that their work is simply wrong.


Mathematical Mystery Tour
by A.K.Dewdney
The author asks the question: Did humans make up mathematics, or did mathematics make up everything, including humans? Beginning his journey in Miletus, the ancient home of Pythagoras and other deep thinkers, he meets the fictional Dr. Petros Pygonopolis, the first of his guides through space and time in search of mathematical meaning in history. His journey continues with stops in the Arabian desert, Venice, and England. Dewdney's style is accessible, his knowledge is thorough, and his sense of humor refreshing. It is not a difficult read, although the ideas are quite abstract. The fictional tour guides at each port of call are helpful in humanizing the subject matter.


Mathematical Sorcery: Revealing the Secrets of Numbers
by Calvin C. Clawson
A unique guide to the history of mathematics. An overview of the history of mathematics, this book explains how ancient scholars devised the rules of mathematics and illustrates the significance of these rules for modern life. Balancing the elusiveness of numbers with the rigor of mathematical theory, the author discusses the experiments that have defined the field and the results they have produced. In his quest for pure knowledge, the author takes readers on a journey of discovery to divulge the wisdom of the ancient Greeks, Sumerians, Babylonians, and Egyptians, whose stunning revelations have deep meaning to this day. The secret of constellations, the enigma of the golden mean, and the brilliance of a proof; these are just some of the wonders the author explores in this recreational math book.


Mathematics: From the Birth of Numbers
by Jan Gullberg & Peter Hilton
This book is an enthusiastic and utterly amazing popularization that promises to be in print for decades. It is a book for school or home library, where there are people eager to learn or in need of an in-depth understanding of algebra, calculus, trigonometry, topology, or more advanced studies. It is an important reference and a book that is plain fun to dip into. If a family is to have only one mathematics book on the reference shelf, then this is the one. It is worth the price and will not quickly become obsolete like so many other scientific texts.


The New Ambidextrous Universe
by Martin Gardner
Symmetry and asymmetry from mirror reflections to superstrings.


Nature's Numbers : The Unreal Reality of Mathematics (Science Masters Series)
by Ian Stewart
First-rate popular mathematics writing...Stewart achieves what other popular mathematics writers merely strive for: an accurate, informative portrayal of contemporary mathematics without a single equation in sight. If someone you know wants to know what mathematics really is, buy them a copy of Nature's Numbers. Have you ever wondered? Why do many flowers have five or eight petals, but very few have six or seven? Why do snowflakes have six-fold symmetry? Why do tigers have stripes, but leopards spots? Science writer Ian Stewart suggests mathematical regularities in natural forms and explains why math is the best tool yet for understanding the world around us.


Nothing That Is: A Natural History of Zero
by Robert & Ellen Kaplan
Usually the invention (or discovery) of zero is given as occurring in India in about the year 600 CE. The author goes back further to Sumerian, Babylonian, and Greek experiments with abacuses, counting boards, positional notation, and abstract thought. He makes the story very interesting with a wonderful combination of literature, history and philosophy. Even if the reader does not particularly care much for math, if you enjoy literature and philosophy you'll learn something.


Number File
by Adrian Jenkins
A collection of numbers that have interesting properties. There are lists of primes, squares, Pythagorean triples, numbers with many factors,etc. An interesting source book for teachers looking for interesting material to perk up the class.


Number Puzzler
by Roy Mullins
Mastering the art of cracking number sequence problems. Logical thinking is required to discover the hidden rules and the book systematically explains how to set about solving this intriguing type of puzzle.


Number Sense
by Stanislas Dehaene
How the mind creates mathematics.


Numbers : The Universal Language (Discoveries Series)
by Denis Guedj & Lory Frankel
A superb historical survey from the history of the zero to infinity. The art work is superb, and there is a Chronology at the end of the book. An excellent source book for teachers as well as curious individuals.


Numbers and Words: A Problem per Day
by Marcy Cook


Numbers Facts and Fiction
by Richard Phillips
For everyone: Fascinating facts, properties and anecdotes about the numbers 1 to 159 (plus a few larger ones). An unfailing resource for collectors of number trivia. For example: the number 1729 is the smallest number expressible as the sum of two cubes in two different ways: 10 cubed + 9 cubed = 1729. 12 cubed + 1 cubed = 1729. Beautifully presented in full color.


On Beyond a Million : An Amazing Math Journey
by David M. Schwartz and Paul Meisel
Amazing facts about millions, trillions, and much bigger numbers are explained in picture-book cartoon scenarios, contributed by Paul Meisel. They show kids in the classroom, at the seashore, in the rain forest, and all over the place, learning how to count by powers of 10. The sheer numbers are astounding, whether they refer to the population of the U.S. or the number of stars in the Milky Way; and the explanation of exponents gives kids a way to count what seems unimaginable. In a funny gag, one kid keeps asking, "Have we reached infinity yet?" and the answers make math awesome and yet accessible--even for those of us who are scared of all those zeros.


Once upon a Number
by John Paulos
The hidden mathematical logic of stories. For example, Paulos demonstrates mathematically that minority status makes achieving equality extraordinarily difficult. An interesting read.


One Two Three Infinity
by George Gamow
Gamow demonstrates that there are different sizes of infinity. He didn't originate the idea. It was first thought of by a mathematician named Georg Cantor. But Gamow makes the mathematics clear and accessible. The reviews from his former students were dazzling.


Penguin Dictionary of Curious and Interesting Numbers
by David Wells
Revised with nearly 200 new entries, this dictionary contains all the information that anyone ever wanted to know about numbers--from minus one and its square root to cyclic, weird, perfect, untouchable and lucky numbers to Pascal's triangle and the Syracuse algorithm to numbers so large they boggle the imagination.


Piece of pi: Wit-Sharpening, Brain-Bruising, Number Crunching Activities With Pi
by Naila Bokhari, Stephanie O'Shaughnessy
This is a great book for anyone trying to discover the mysterious connections of pi to various things in the world. The book is well-written, has great step-by-step instructions and includes an answer key. This book is a wonderful way to motivate students (and adults) to discover pi in intriguing ways.


The Rainbow of Mathematics – A History Of The Mathematical Sciences
by Ivor Grattan-Guiness
The story of how numbers were invented and harnessed. A passionate physical saga.


Roman Numerals I to MM
by Arthur Geisert
A delightful book using Roman instead of Arabic numerals demonstrating the clumsiness of the Roman system.


A Tour Of The Calculus
by David Berlinski
A writer with a sense of humor and a readable writing style on a very intellectual subject.


Tracking the Automatic Ant: And Other Mathematical Explorations
by David Gale
For those fascinated by the abstract universe of mathematics, David Gale's columns in The Mathematical Intelligencer have been a prime source of entertainment. Here Gale's columns are collected for the first time in book form. Encouraged by the magazine's editor, Sheldon Axler, to write on whatever pleased him, Gale ranged far and wide across the field of mathematics but frequently returned to favorite themes: triangles, tilings, the mysterious properties of sequences given by simple recursions, games and paradoxes, and the particular automaton that gives this collection its title, the "automatic ant". The level is suitable for those with some familiarity with mathematical ideas, but great sophistication is not needed.


Wonder of Numbers: Adventures in Math, Mind, and Meaning
by Clifford Pickover
Grab a pencil. Relax. Then take off on a mind-boggling journey to the ultimate frontier of math, mind, and meaning, as Dr. Clifford Pickover and legendary, eccentric mathematician Dr. Francis Googol explore some of the oddest and quirkiest highways and byways of the numerically obsessed. With numerous illustrations and appendices pointing to computer explorations, this is an original, fun-filled, and thoroughly unique introduction to numbers and their role in creativity, computers, games, practical research, and absurd adventures that teeter on the edge of logic and insanity. Who are the eight most influential female mathematicians? Why aren't Roman numerals used anymore? Why was the first woman mathematician brutally murdered? What were the Unabomber's ten most mathematical technical papers? Prepare yourself for a shattering odyssey as Wonders of Numbers unlocks the doors of your imagination. The thought-provoking mysteries, puzzles, and problems range from the most beautiful formula of Ramanujan (India's most famous mathematician) to the Leviathan number, a number so big that it makes a trillion pale in comparison. The mysterious puzzles and games should cause even the most left-brained readers to fall in love with numbers. The quirky and exclusive surveys on mathematicians' lives, scandals, and passions will entertain people at all levels of mathematical sophistication.


The Zen of Magic Squares, Circles, and Stars: An Exhibition of Surprising Structures across Dimensions
by Clifford Pickover
A magic square is an array of numbers in which the sums of numbers in rows, columns, and diagonals are equal. A magic square uses consecutive numbers from 1 to N. This book is essentially an exhibit of magnificent forms discovered through the centuries. All sorts of historical and quirky-human aspects are also described. Centuries ago, people believed that magic squares to had special, magical powers. Perhaps the most famous person to create them was the immensely talented Benjamin Franklin. Pickover writes with his usual style and straightforward simplicity. The material is presented well and can be understood by anyone with a basic middle school mathematics background.