How did the replication bomb we call "life" begin and where in the world, or rather, in the universe, is it heading? Writing with characteristic wit and an ability to clarify complex phenomena (the New York Times described his style as "the sort of science writing that makes the reader feel like a genius"), Richard Dawkins confronts this ancient mystery.
Ronald W. Clark's definitive biography of Einstein, the Promethean figure of our age, goes behind the phenomenal intellect to reveal the human side of the legendary absent-minded professor who confidently claimed that space and time were not what they seemed.
Here is the classic portrait of the scientist and the man: the boy growing up in the Swiss Alps, the young man caught in an unhappy first marriage, the passionate pacifist who agonized over making The Bomb, the indifferent Zionist asked to head the Israeli state, the physicist who believed in God.
"A wealth of intriguing and lovely ideas." -- Information Technology & Learning.
While the beauty of mathematics is often discussed, the aesthetic appeal of the discipline is seldom demonstrated as clearly as in this intriguing journey into the realms where art and mathematics merge. Aimed at a wide range of ages and abilities, this engrossing book explores the possibilities of mathematical drawing through compass constructions and computer graphics.
Compass construction is an extremely ancient art, requiring no special skills other than the care it takes to place a compass point accurately. For the computer graphics part of the present work, however, readers will need some familiarity with basic high school mathematics-mainly algebra and trigonometry. Still, much of the book can be enjoyed even by "mathophobes," for it is about lines and circles and how to put them together to make various patterns, both abstract and natural.
One hundred and six full-page drawings, ranging from totally abstract to somewhat pictorial, demonstrate the possibilities of mathematical drawing and serve as inspiration to readers to carry out their own creative investigations. Among the illustrations are such intriguing configurationsas a five-point egg, golden ratio, 17-gon, plughole vortex, blancmange curve, Durer's pentagons, pentasnow, turtle geometry, and many more. In guiding students toward the comprehension and creation of such figures, the author explains helpful basic principles (of number, length and angle) as well as reviewing relevant fundamentals of trigonometry. In addition, he has provided numerous useful exercises (with answers} at the ends of the chapters, together with recommended further reading, detailed in the bibliography. 211 black-and-white illustrations. Bibliography. Index.
"I have discovered a truly marvelous proof, which this margin is too narrow to contain". With these tantalizing words the seventeenth-century French mathematician Pierre de Fermat threw down the gauntlet to future generations. What came to be known as Fermat's Last Theorem looked simple, yet the finest mathematical minds would be baffled for more than three and a half centuries.
Fermat's Last Theorem became the Holy Grail of mathematics. Whole and colorful lives were devoted, and even sacrificed, to finding a solution. Leonhard Euler, the greatest mathematician of the 18th century, had to admit defeat. Sophie Germain had to take on the identity of a man to do research in a field forbidden to females, and made the most significant breakthrough of the 19th century. The clashing Evariste Galois scribbled down the results of his research deep into the night before venturing out to die in a duel in 1832. Yutaka Taniyama, whose insights would lead directly to the ultimate solution to Fermat, tragically killed himself in despair. On the other hand, Paul Wolfskehl, a famous German industrialist, claimed Fermat had saved him from suicide, and established a rich prize for the first person to prove the theorem.
And then came Princeton Professor Andrew Wiles, who had dreamed of proving Fermat ever since he first read of it as a boy of ten in his local library. In 1993, some 356 years after Fermat's challenge, and after seven years of working in isolation and secrecy, Wiles stunned the world by announcing a proof -- though his own journey would be far from over.
"Fermat's Enigma" is the story of the epic quest to solve the greatest math problem of all time. Written by the award-winningfilm-maker who has had more access to Andrew Wiles than any other journalist, it is a human drama of high dreams, intellectual brilliance, and extraordinary determination.
Using simple mathematical formulas, most as basic as Pythagoras's theorem and requiring only a very limited knowledge of mathematics, Professor Huntley explores the fascinating relationship between geometry and aesthetics. Poetry, patterns like Pascal's triangle, philosophy, psychology, music, and dozens of simple mathematical figures are enlisted to show that the "divine proportion" or "golden ratio" is a feature of geometry and analysis which awakes answering echoes in the human psyche. When we judge a work of art aesthetically satisfying, according to his formulation, we are making it conform to a pattern whose outline is laid down in simple geometrical figures; and it is the analysis of these figures which forms the core of Professor Huntley's book.
For the philosopher, scientist, poet, art historian, music listener, artist, as well as the general reader who wants to understand more about the fascinating properties of numbers, this is a beautifully written, exciting account of the search for a naturally manifested aesthetic that has occupied man since he first asked the question "why?"
"This is a delightful book to read. . . . It wanders here and there through some of the most attractive byways of simple mathematics, returning always to the oddities and pleasures of the golden section. This is a browser's book -- a happy, untidy traveling or bedside book for those who know how to enjoy the charm of numbers and shapes." -- Dr. J. Bronowski, The Salk Institute.
Brilliant...as audacious as its title....Mr. Dennett's exposition is nothing short of brilliant. --George Johnson, New York Times Book ReviewConsciousness Explained is a a full-scale exploration of human consciousness. In this landmark book, Daniel Dennett refutes the traditional, commonsense theory of consciousness and presents a new model, based on a wealth of information from the fields of neuroscience, psychology, and artificial intelligence. Our current theories about conscious life-of people, animal, even robots--are transformed by the new perspectives found in this book.
Elegant, suggestive, and clarifying, Lewis Thomas's profoundly humane vision explores the world around us and examines the complex interdependence of all things. Extending beyond the usual limitations of biological science and into a vast and wondrous world of hidden relationships, this provocative book explores in personal, poetic essays to topics such as computers, germs, language, music, death, insects, and medicine. Lewis Thomas writes, Once you have become permanently startled, as I am, by the realization that we are a social species, you tend to keep an eye out for the pieces of evidence that this is, by and large, good for us.
A symbol for what is not there, an emptiness that increases any number it's added to, an inexhaustible and indispensable paradox. As we enter the year 2000, zero is once again making its presence felt. Nothing itself, it makes possible a myriad of calculations. Indeed, without zero mathematics as we know it would not exist. And without mathematics our understanding of the universe would be vastly impoverished. But where did this nothing, this hollow circle, come from? Who created it? And what, exactly, does it mean?
Robert Kaplan's The Nothing That Is: A Natural History of Zero begins as a mystery story, taking us back to Sumerian times, and then to Greece and India, piecing together the way the idea of a symbol for nothing evolved. Kaplan shows us just how handicapped our ancestors were in trying to figure large sums without the aid of the zero. (Try multiplying CLXIV by XXIV). Remarkably, even the Greeks, mathematically brilliant as they were, didn't have a zero--or did they? We follow the trail to the East where, a millennium or two ago, Indian mathematicians took another crucial step. By treating zero for the first time like any other number, instead of a unique symbol, they allowed huge new leaps forward in computation, and also in our understanding of how mathematics itself works.
In the Middle Ages, this mathematical knowledge swept across western Europe via Arab traders. At first it was called dangerous Saracen magic and considered the Devil's work, but it wasn't long before merchants and bankers saw how handy this magic was, and used it to develop tools like double-entry bookkeeping. Zero quickly became an essential part of increasingly sophisticated equations, and with the invention of calculus, one could say it was a linchpin of the scientific revolution. And now even deeper layers of this thing that is nothing are coming to light: our computers speak only in zeros and ones, and modern mathematics shows that zero alone can be made to generate everything.
Robert Kaplan serves up all this history with immense zest and humor; his writing is full of anecdotes and asides, and quotations from Shakespeare to Wallace Stevens extend the book's context far beyond the scope of scientific specialists. For Kaplan, the history of zero is a lens for looking not only into the evolution of mathematics but into very nature of human thought. He points out how the history of mathematics is a process of recursive abstraction: how once a symbol is created to represent an idea, that symbol itself gives rise to new operations that in turn lead to new ideas. The beauty of mathematics is that even though we invent it, we seem to be discovering something that already exists.
The joy of that discovery shines from Kaplan's pages, as he ranges from Archimedes to Einstein, making fascinating connections between mathematical insights from every age and culture. A tour de force of science history, The Nothing That Is takes us through the hollow circle that leads to infinity.
Quantum theorist Erwin Schrvdinger invented his now-famous cat to illustrate the apparently impossible conundrums associated with quantum physics. The cat lives in an opaque box with a fiendish device that randomly feeds it either food, allowing it to live, or poison, which kills it. But in the quantum world, all possibilities coexist and have a reality of their own, and they ensure that the cat is both alive and dead, simultaneously.
Who's Afraid of Schrvdinger's Cat? is a clear, concise explanation of the new sciences of quantum mechanics, chaos and complexity theory, relativity, new theories of mind, and the new cosmology. It studies worlds beyond the realm of common sense, and the new kinds of thinking that we need to understand ourselves, our minds, and our human place in the larger scheme of things.
If there's one question that many parents would rather not hear when Sophia or Aiden gets home from school, it's, "Mom, can you help me with my algebra homework?"
And nowadays that question gets asked by younger and younger children because algebraic thinking has been inserted into the math curriculum as early as 5th grade, sometimes even in 4th grade
So what helps parents recall algebra and also helps students learn it in a friendly way? The Algebra Survival Guide, now updated in its Second Edition.
Following on the success of the award-winning First Edition book and written by teacher/tutor Josh Rappaport, the Second Edition Guide offers time-tested advice for understanding the key areas of this gateway math subject.
The new Algebra Survival Guide features a unique Q&A format so students hear their own questions echoed in the text. The book's answers, written in the voice of a friendly tutor, provide conversational responses, along with step-by-step instructions in English right next to the math steps.
Each page is a one-page mini-lesson so students can focus without feeling overwhelmed. Following each lesson is a short set of practice problems, offering students instant feedback. At the end of each section, chapter tests provide comprehensive checks on understanding.
Since word problems are often the highest "hurdle" of algebra, the Second Edition contains a new 62-page chapter on advanced word problems. This chapter provides detailed strategies for setting up and solving word problems on such dastardly areas as rate, time and distance, work performed, mixture formulas, and even those crazy problems about Joe being three years older than four times Jane's age 10 years in the future.
In its twelve content chapters the 352-page Second Edition covers all key areas of PreAlgebra and Algebra 1: Algebraic Properties, Sets of Numbers, Positive and Negative Numbers, Order of Operations, Absolute Value, Exponents, Radicals, Factoring, Cancelling, Solving Equations, the Coordinate Plane, and Word Problems.
As a major bonus, the Guide buzzes with lively illustrations by award-winning artist Sally Blakemore. Ms. Blakemore's cartoons not only provide comic relief, they also offer a visual way to grasp algebra's challenging abstractions. (Example: to illustrate the Reflexive Property of x = x, a cartoon shows a sad 'x' gazing at itself in the mirror while suffering a 'bad hair day.') With all of these features, the Second Edition Algebra Survival Guide appeals equally to homeschoolers, students, parents, teachers, tutors and adult students striving to recall the math they learned a decade or so ago.
The Second Edition aligns with the Common Core State Standards for Math, so it's up-to-date for today's teachers.
Loaded with thorough explanations, practice problems and answers, the new Algebra Survival Guide gives anyone and everyone the needed boost for learning or teaching the timeless and critical subject of algebra.