17 Equations That Changed the World

Author: Ian Stewart

Publisher: Basic Books

ISBN: 0465029744

Category: Mathematics

Page: 360

View: 5240

In In Pursuit of the Unknown, celebrated mathematician Ian Stewart uses a handful of mathematical equations to explore the vitally important connections between math and human progress. We often overlook the historical link between mathematics and technological advances, says Stewart—but this connection is integral to any complete understanding of human history. Equations are modeled on the patterns we find in the world around us, says Stewart, and it is through equations that we are able to make sense of, and in turn influence, our world. Stewart locates the origins of each equation he presents—from Pythagoras's Theorem to Newton's Law of Gravity to Einstein's Theory of Relativity—within a particular historical moment, elucidating the development of mathematical and philosophical thought necessary for each equation's discovery. None of these equations emerged in a vacuum, Stewart shows; each drew, in some way, on past equations and the thinking of the day. In turn, all of these equations paved the way for major developments in mathematics, science, philosophy, and technology. Without logarithms (invented in the early 17th century by John Napier and improved by Henry Briggs), scientists would not have been able to calculate the movement of the planets, and mathematicians would not have been able to develop fractal geometry. The Wave Equation is one of the most important equations in physics, and is crucial for engineers studying the vibrations in vehicles and the response of buildings to earthquakes. And the equation at the heart of Information Theory, devised by Claude Shannon, is the basis of digital communication today. An approachable and informative guide to the equations upon which nearly every aspect of scientific and mathematical understanding depends, In Pursuit of the Unknown is also a reminder that equations have profoundly influenced our thinking and continue to make possible many of the advances that we take for granted.
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The Power and Poetry of Mathematics

Author: Michael Guillen

Publisher: Hachette Books

ISBN: 1401304915

Category: Mathematics

Page: 288

View: 6942

A Publishers Weekly best book of 1995! Dr. Michael Guillen, known to millions as the science editor of ABC's Good Morning America, tells the fascinating stories behind five mathematical equations. As a regular contributor to daytime's most popular morning news show and an instructor at Harvard University, Dr. Michael Guillen has earned the respect of millions as a clear and entertaining guide to the exhilarating world of science and mathematics. Now Dr. Guillen unravels the equations that have led to the inventions and events that characterize the modern world, one of which -- Albert Einstein's famous energy equation, E=mc2 -- enabled the creation of the nuclear bomb. Also revealed are the mathematical foundations for the moon landing, airplane travel, the electric generator -- and even life itself. Praised by Publishers Weekly as "a wholly accessible, beautifully written exploration of the potent mathematical imagination," and named a Best Nonfiction Book of 1995, the stories behind The Five Equations That Changed the World, as told by Dr. Guillen, are not only chronicles of science, but also gripping dramas of jealousy, fame, war, and discovery.
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17 Equations that Changed the World

Author: Ian Stewart

Publisher: Basic Books (AZ)

ISBN: 9780465029730

Category: Mathematics

Page: 342

View: 9842

A guide to the major building blocks of contemporary mathematics--from the Pythagorian Theorem to Einstein's theory of relativity--explores how these equations are at the root of human progress.
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Author: Ian Stewart

Publisher: Profile Books

ISBN: 1847653510

Category: Mathematics

Page: 340

View: 5374

There are some mathematical problems whose significance goes beyond the ordinary - like Fermat's Last Theorem or Goldbach's Conjecture - they are the enigmas which define mathematics. The Great Mathematical Problems explains why these problems exist, why they matter, what drives mathematicians to incredible lengths to solve them and where they stand in the context of mathematics and science as a whole. It contains solved problems - like the Poincar Conjecture, cracked by the eccentric genius Grigori Perelman, who refused academic honours and a million-dollar prize for his work, and ones which, like the Riemann Hypothesis, remain baffling after centuries. Stewart is the guide to this mysterious and exciting world, showing how modern mathematicians constantly rise to the challenges set by their predecessors, as the great mathematical problems of the past succumb to the new techniques and ideas of the present.
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Lives and Works of Trailblazing Mathematicians

Author: Ian Stewart

Publisher: Profile Books

ISBN: 1782831495

Category: Science

Page: 236

View: 9313

Which mathematician elaborated a crucial concept the night before he died in a duel? Who funded his maths and medical career through gambling and chess? Who learned maths from her wallpaper? Ian Stewart presents the extraordinary lives and amazing discoveries of twenty-five of history's greatest mathematicians from Archimedes and Liu Hui to Benoit Mandelbrot and William Thurston. His subjects are the inspiring individuals from all over the world who have made crucial contributions to mathematics. They include the rediscovered geniuses Srinivasa Ramanujan and Emmy Noether, alongside the towering figures of Muhammad al-Khwarizmi (inventor of the algorithm), Pierre de Fermat, Isaac Newton, Carl Friedrich Gauss, Nikolai Ivanovich Lobachevsky, Bernhard Reimann (precursor to Einstein), Henri Poincar, Ada Lovelace (arguably the first computer programmer), Kurt Gdel and Alan Turing. Ian Stewart's vivid accounts are fascinating in themselves and, taken together, cohere into a riveting history of key steps in the development of mathematics.
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Author: Ian Stewart

Publisher: Basic Books

ISBN: 0465024408

Category: Science

Page: 368

View: 2842

Biologists have long dismissed mathematics as being unable to meaningfully contribute to our understanding of living beings. Within the past ten years, however, mathematicians have proven that they hold the key to unlocking the mysteries of our world--and ourselves. In The Mathematics of Life, Ian Stewart provides a fascinating overview of the vital but little-recognized role mathematics has played in pulling back the curtain on the hidden complexities of the natural world--and how its contribution will be even more vital in the years ahead. In his characteristically clear and entertaining fashion, Stewart explains how mathematicians and biologists have come to work together on some of the most difficult scientific problems that the human race has ever tackled, including the nature and origin of life itself.
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Author: Ian Stewart

Publisher: Profile Books

ISBN: 1847651283

Category: Mathematics

Page: 320

View: 7668

School maths is not the interesting part. The real fun is elsewhere. Like a magpie, Ian Stewart has collected the most enlightening, entertaining and vexing 'curiosities' of maths over the years... Now, the private collection is displayed in his cabinet. There are some hidden gems of logic, geometry and probability -- like how to extract a cherry from a cocktail glass (harder than you think), a pop up dodecahedron, the real reason why you can't divide anything by zero and some tips for making money by proving the obvious. Scattered among these are keys to unlocking the mysteries of Fermat's last theorem, the Poincar Conjecture, chaos theory, and the P/NP problem for which a million dollar prize is on offer. There are beguiling secrets about familiar names like Pythagoras or prime numbers, as well as anecdotes about great mathematicians. Pull out the drawers of the Professor's cabinet and who knows what could happen...
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Modeling Aspects of Urban Life

Author: John A. Adam

Publisher: Princeton University Press

ISBN: 1400841690

Category: Mathematics

Page: 336

View: 7640

X and the City, a book of diverse and accessible math-based topics, uses basic modeling to explore a wide range of entertaining questions about urban life. How do you estimate the number of dental or doctor's offices, gas stations, restaurants, or movie theaters in a city of a given size? How can mathematics be used to maximize traffic flow through tunnels? Can you predict whether a traffic light will stay green long enough for you to cross the intersection? And what is the likelihood that your city will be hit by an asteroid? Every math problem and equation in this book tells a story and examples are explained throughout in an informal and witty style. The level of mathematics ranges from precalculus through calculus to some differential equations, and any reader with knowledge of elementary calculus will be able to follow the materials with ease. There are also some more challenging problems sprinkled in for the more advanced reader. Filled with interesting and unusual observations about how cities work, X and the City shows how mathematics undergirds and plays an important part in the metropolitan landscape.
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Author: Ian Stewart

Publisher: Quercus

ISBN: 1623654734

Category: Mathematics

Page: 384

View: 6488

From ancient Babylon to the last great unsolved problems, Ian Stewart brings us his definitive history of mathematics. In his famous straightforward style, Professor Stewart explains each major development--from the first number systems to chaos theory--and considers how each affected society and changed everyday life forever. Maintaining a personal touch, he introduces all of the outstanding mathematicians of history, from the key Babylonians, Greeks and Egyptians, via Newton and Descartes, to Fermat, Babbage and Godel, and demystifies math's key concepts without recourse to complicated formulae. Written to provide a captivating historic narrative for the non-mathematician, Taming the Infinite is packed with fascinating nuggets and quirky asides, and contains 100 illustrations and diagrams to illuminate and aid understanding of a subject many dread, but which has made our world what it is today.
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How Mathematics Unveils the Universe

Author: Ian Stewart

Publisher: Profile Books

ISBN: 1782831509

Category: Science

Page: 285

View: 6912

Ian Stewart's up-to-the-minute guide to the cosmos moves from the formation of the Earth and its Moon to the planets and asteroids of the solar system and from there out into the galaxy and the universe. He describes the architecture of space and time, dark matter and dark energy, how galaxies form, why stars implode, how everything began, and how it will end. He considers parallel universes, what forms extra-terrestrial life might take, and the likelihood of Earth being hit by an asteroid. Mathematics, Professor Stewart shows, has been the driving force in astronomy and cosmology since the ancient Babylonians. He describes how Kepler's work on planetary orbits led Newton to formulate his theory of gravity, and how two centuries later irregularities in the motion of Mars inspired Einstein's theory of general relativity. In crystal-clear terms he explains the fundamentals of gravity, spacetime, relativity and quantum theory, and shows how they all relate to each other. Eighty years ago the discovery that the universe is expanding led to the Big Bang theory of its origins. This in turn led cosmologists to posit features such as dark matter and dark energy. But does dark matter exist? Could another scientific revolution be on the way to challenge current scientific orthodoxy? These are among the questions Ian Stewart raises in his quest through the realms of astronomy and cosmology.
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Author: George Johnson

Publisher: Vintage

ISBN: 0307268667

Category: Science

Page: 208

View: 6636

A dazzling, irresistible collection of the ten most groundbreaking and beautiful experiments in scientific history. With the attention to detail of a historian and the storytelling ability of a novelist, New York Times science writer George Johnson celebrates these groundbreaking experiments and re-creates a time when the world seemed filled with mysterious forces and scientists were in awe of light, electricity, and the human body. Here, we see Galileo staring down gravity, Newton breaking apart light, and Pavlov studying his now famous dogs. This is science in its most creative, hands-on form, when ingenuity of the mind is the most useful tool in the lab and the rewards of a well-considered experiment are on exquisite display.
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Author: Ian Stewart

Publisher: Courier Corporation

ISBN: 0486134954

Category: Mathematics

Page: 368

View: 5267

In this charming volume, a noted English mathematician uses humor and anecdote to illuminate the concepts of groups, sets, subsets, topology, Boolean algebra, and other mathematical subjects. 200 illustrations.
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Author: Ian Stewart

Publisher: Basic Books

ISBN: 0465042716

Category: Mathematics

Page: 352

View: 8188

At its heart, mathematics is about numbers, our fundamental tools for understanding the world. In Professor Stewart's Incredible Numbers, Ian Stewart offers a delightful introduction to the numbers that surround us, from the common (Pi and 2) to the uncommon but no less consequential (1.059463 and 43,252,003,274,489,856,000). Along the way, Stewart takes us through prime numbers, cubic equations, the concept of zero, the possible positions on the Rubik's Cube, the role of numbers in human history, and beyond! An unfailingly genial guide, Stewart brings his characteristic wit and erudition to bear on these incredible numbers, offering an engaging primer on the principles and power of math.
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A Mathematical Adventure

Author: David Acheson

Publisher: Oxford University Press

ISBN: 0192526715

Category: Mathematics

Page: 160

View: 6280

Calculus is the key to much of modern science and engineering. It is the mathematical method for the analysis of things that change, and since in the natural world we are surrounded by change, the development of calculus was a huge breakthrough in the history of mathematics. But it is also something of a mathematical adventure, largely because of the way infinity enters at virtually every twist and turn... In The Calculus Story David Acheson presents a wide-ranging picture of calculus and its applications, from ancient Greece right up to the present day. Drawing on their original writings, he introduces the people who helped to build our understanding of calculus. With a step by step treatment, he demonstrates how to start doing calculus, from the very beginning.
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Euler's Formula and the Beauty of Mathematics

Author: David Stipp

Publisher: Basic Books

ISBN: 0465093787

Category: Mathematics

Page: 240

View: 867

An award-winning science writer introduces us to mathematics using the extraordinary equation that unites five of mathematics' most important numbers Bertrand Russell wrote that mathematics can exalt "as surely as poetry." This is especially true of one equation: ei(pi) + 1 = 0, the brainchild of Leonhard Euler, the Mozart of mathematics. More than two centuries after Euler's death, it is still regarded as a conceptual diamond of unsurpassed beauty. Called Euler's identity or God's equation, it includes just five numbers but represents an astonishing revelation of hidden connections. It ties together everything from basic arithmetic to compound interest, the circumference of a circle, trigonometry, calculus, and even infinity. In David Stipp's hands, Euler's identity formula becomes a contemplative stroll through the glories of mathematics. The result is an ode to this magical field.
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Author: Ian Stewart

Publisher: Basic Books

ISBN: 0465056881

Category: Mathematics

Page: 320

View: 3851

In Professor Stewart's Casebook of Mathematical Mysteries, acclaimed mathematician Ian Stewart presents an enticing collection of mathematical curios and conundrums. With a new puzzle on each page, this compendium of brainteasers will both teach and delight. Guided by stalwart detective Hemlock Soames and his sidekick, Dr. John Watsup, readers will delve into almost two hundred mathematical problems, puzzles, and facts. Tackling subjects from mathematical dates (such as Pi Day), what we don't know about primes, and why the Earth is round, this clever, mind-expanding book demonstrates the power and fun inherent in mathematics.
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From Klein Bottles to Chaos Theory, a Guide to the Nerdiest Math Facts, Theorems, and Equations

Author: Raphael Rosen

Publisher: Simon and Schuster

ISBN: 1440583811

Category: Mathematics

Page: 256

View: 8868

The new "sine" of mathematical geekdom! Do you dream about long division in your sleep? Does the thought of solving abstruse equations bring a smile to your face? Do you love celebrating pi every March? Then, Math Geek was made for you! With this guide, you'll learn even more about the power of numbers as you explore their brilliant nature in ways you've never imagined. From manhole covers to bubbles to subway maps, each page gives you a glimpse of the world through renowned mathematicians' eyes and reveals how their theorems and equations can be applied to nearly everything you encounter. Covering dozens of your favorite math topics, you'll find fascinating answers to questions like: How are the waiting times for buses determined? Why is Romanesco Broccoli so mesmerizing? How do you divide a cake evenly? Should you run or walk to avoid rain showers? Filled with compelling mathematical explanations, Math Geek sheds light on the incredible world of numbers hidden deep within your day-to-day life.
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A Family Field Trip to the Arctic's Edge in Search of Adventure, Truth, and Mini-Marshmallows

Author: Zac Unger

Publisher: Da Capo Press

ISBN: 030682163X

Category: Nature

Page: 320

View: 4107

“I like to go out for walks, but it’s a little awkward to push the baby stroller and carry a shotgun at the same time.”—housewife from Churchill, Manitoba Yes, welcome to Churchill, Manitoba. Year-round human population: 943. Yet despite the isolation and the searing cold here at the arctic’s edge, visitors from around the globe flock to the town every fall, driven by a single purpose: to see polar bears in the wild. Churchill is “The Polar Bear Capital of the World,” and for one unforgettable “bear season,” Zac Unger, his wife, and his three children moved from Oakland, California, to make it their temporary home. But they soon discovered that it’s really the polar bears who are at home in Churchill, roaming past the coffee shop on the main drag, peering into garbage cans, languorously scratching their backs against fence posts and front doorways. Where kids in other towns receive admonitions about talking to strangers, Churchill schoolchildren get “Let’s All Be Bear Aware” booklets to bring home. (Lesson number 8: Never explore bad-smelling areas.) Zac Unger takes readers on a spirited and often wildly funny journey to a place as unique as it is remote, a place where natives, tourists, scientists, conservationists, and the most ferocious predators on the planet converge. In the process he becomes embroiled in the controversy surrounding “polar bear science”—and finds out that some of what we’ve been led to believe about the bears’ imminent extinction may not be quite the case. But mostly what he learns is about human behavior in extreme situations . . . and also why you should never even think of looking a polar bear in the eye.
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A Guided Tour of Math, from One to Infinity

Author: Steven Henry Strogatz

Publisher: Houghton Mifflin Harcourt

ISBN: 0547517653

Category: MATHEMATICS

Page: 316

View: 3597

A comprehensive tour of leading mathematical ideas by an award-winning professor and columnist for the New York Times Opinionator series demonstrates how math intersects with philosophy, science and other aspects of everyday life. By the author of The Calculus of Friendship. 50,000 first printing.
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Author: Dara O Briain

Publisher: Oxford University Press

ISBN: 0198701810

Category: Mathematics

Page: 198

View: 7555

Relax: no one understands technical mathematics without lengthy training but we all have an intuitive grasp of the ideas behind the symbols. This book is designed to showcase the beauty of mathematics - including images inspired by mathematical problems - together with its unreasonable effectiveness and applicability, without frying your brain.
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