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**The First Ever Maths Book to be a No.1 Bestseller** 'Wonderful ... superb' Daily Mail What makes a bridge wobble when it's not meant to? Billions of dollars mysteriously vanish into thin air? A building rock when its resonant frequency matches a gym class leaping to Snap's 1990 hit I've Got The Power? The answer is maths. Or, to be precise, what happens when maths goes wrong in the real world. As Matt Parker shows us, our modern lives are built on maths: computer programmes, finance, engineering. And most of the time this maths works quietly behind the scenes, until ... it doesn't. Exploring and explaining a litany of glitches, near-misses and mishaps involving the internet, big data, elections, street signs, lotteries, the Roman empire and a hapless Olympic shooting team, Matt Parker shows us the bizarre ways maths trips us up, and what this reveals about its essential place in our world. Mathematics doesn't have good 'people skills', but we would all be better off, he argues, if we saw it as a practical ally. This book shows how, by making maths our friend, we can learn from its pitfalls. It also contains puzzles, challenges, geometric socks, jokes about binary code and three deliberate mistakes. Getting it wrong has never been more fun.
"The son of a prominent Japanese mathematician who came to the United States after World War II, Ken Ono was raised on a diet of high expectations and little praise. Rebelling against his pressure-cooker of a life, Ken determined to drop out of high school to follow his own path. To obtain his father's approval, he invoked the biography of the famous Indian mathematical prodigy Srinivasa Ramanujan, whom his father revered, who had twice flunked out of college because of his single-minded devotion to mathematics. Ono describes his rocky path through college and graduate school, interweaving Ramanujan's story with his own and telling how at key moments, he was inspired by Ramanujan and guided by mentors who encouraged him to pursue his interest in exploring Ramanujan's mathematical legacy. Picking up where others left off, beginning with the great English mathematician G.H. Hardy, who brought Ramanujan to Cambridge in 1914, Ono has devoted his mathematical career to understanding how in his short life, Ramanujan was able to discover so many deep mathematical truths, which Ramanujan believed had been sent to him as visions from a Hindu goddess. And it was Ramanujan who was ultimately the source of reconciliation between Ono and his parents. Ono's search for Ramanujan ranges over three continents and crosses paths with mathematicians whose lives span the globe and the entire twentieth century and beyond. Along the way, Ken made many fascinating discoveries. The most important and surprising one of all was his own humanity."
How our understanding of calculus has evolved over more than three centuries, how this has shaped the way it is taught in the classroom, and why calculus pedagogy needs to change Calculus Reordered takes readers on a remarkable journey through hundreds of years to tell the story of how calculus evolved into the subject we know today. David Bressoud explains why calculus is credited to seventeenth-century figures Isaac Newton and Gottfried Leibniz, and how its current structure is based on developments that arose in the nineteenth century. Bressoud argues that a pedagogy informed by the historical development of calculus represents a sounder way for students to learn this fascinating area of mathematics. Delving into calculus (TM)s birth in the Hellenistic Eastern Mediterranean "particularly in Syracuse, Sicily and Alexandria, Egypt "as well as India and the Islamic Middle East, Bressoud considers how calculus developed in response to essential questions emerging from engineering and astronomy. He looks at how Newton and Leibniz built their work on a flurry of activity that occurred throughout Europe, and how Italian philosophers such as Galileo Galilei played a particularly important role. In describing calculus (TM)s evolution, Bressoud reveals problems with the standard ordering of its curriculum: limits, differentiation, integration, and series. He contends that the historical order "integration as accumulation, then differentiation as ratios of change, series as sequences of partial sums, and finally limits as they arise from the algebra of inequalities "makes more sense in the classroom environment. Exploring the motivations behind calculus (TM)s discovery, Calculus Reordered highlights how this essential tool of mathematics came to be.
A mathematician (TM)s ten-year quest to tell Fibonacci (TM)s story In 2000, Keith Devlin set out to research the life and legacy of the medieval mathematician Leonardo of Pisa, popularly known as Fibonacci, whose book Liber abbaci, or the oeBook of Calculation, introduced modern arithmetic to the Western world. Although most famous for the Fibonacci numbers "which, it so happens, he didn (TM)t discover "Fibonacci (TM)s greatest contribution was as an expositor of mathematical ideas at a level ordinary people could understand. Yet Fibonacci was forgotten after his death, and it was not until the 1960s that his true achievements were finally recognized. Drawing on the diary he kept of his quest, Devlin describes the false starts and disappointments, the unexpected turns, and the occasional lucky breaks he encountered in his search. Fibonacci helped to revive the West as the cradle of science, technology, and commerce, yet he vanished from the pages of history. This is Devlin (TM)s search to find him.
A magisterial history of calculus (and the people behind it) from one of the world's foremost mathematicians. This is the captivating story of mathematics' greatest ever idea: calculus. Without it, there would be no computers, no microwave ovens, no GPS, and no space travel. But before it gave modern man almost infinite powers, calculus was behind centuries of controversy, competition, and even death. Taking us on a thrilling journey through three millennia, professor Steven Strogatz charts the development of this seminal achievement from the days of Archimedes to today's breakthroughs in chaos theory and artificial intelligence.Filled with idiosyncratic characters from Pythagoras to Fourier, Infinite Powers is a compelling human drama that reveals the legacy of calculus on nearly every aspect of modern civilisation, including science, politics, medicine, philosophy, and much besides.
How a simple equation reshaped mathematics Leonhard Euler (TM)s polyhedron formula describes the structure of many objects "from soccer balls and gemstones to Buckminster Fuller (TM)s buildings and giant all-carbon molecules. Yet Euler (TM)s theorem is so simple it can be explained to a child. From ancient Greek geometry to today (TM)s cutting-edge research, Euler (TM)s Gem celebrates the discovery of Euler (TM)s beloved polyhedron formula and its far-reaching impact on topology, the study of shapes. Using wonderful examples and numerous illustrations, David Richeson presents this mathematical idea (TM)s many elegant and unexpected applications, such as showing why there is always some windless spot on earth, how to measure the acreage of a tree farm by counting trees, and how many crayons are needed to color any map. Filled with a who (TM)s who of brilliant mathematicians who questioned, refined, and contributed to a remarkable theorem (TM)s development, Euler (TM)s Gem will fascinate every mathematics enthusiast. This paperback edition contains a new preface by the author.
In 1988 The Mathematical Intelligencer, a quarterly mathematics journal, carried out a poll to find the most beautiful theorem in mathematics. Twenty-four theorems were listed and readers were invited to award each a 'score for beauty'. While there were many worthy competitors, the winner was 'Euler's equation'. In 2004 Physics World carried out a similar poll of 'greatest equations', and found that among physicists Euler's mathematical result came second only to Maxwell's equations. The Stanford mathematician Keith Devlin reflected the feelings of many in describing it as "like a Shakespearian sonnet that captures the very essence of love, or a painting which brings out the beauty of the human form that is far more than just skin deep, Euler's equation reaches down into the very depths of existence". What is it that makes Euler's identity, ei + 1 = 0, so special? In Euler's Pioneering Equation Robin Wilson shows how this simple, elegant, and profound formula links together perhaps the five most important numbers in mathematics, each associated with a story in themselves: the number 1, the basis of our counting system; the concept of zero, which was a major development in mathematics, and opened up the idea of negative numbers; an irrational number, the basis for the measurement of circles; the exponential e, associated with exponential growth and logarithms; and the imaginary number i, the square root of -1, the basis of complex numbers. Following a chapter on each of the elements, Robin Wilson discusses how the startling relationship between them was established, including the several near misses to the discovery of the formula.
Most of the time, the maths in our everyday lives works quietly behind the scenes. Until someone forgets to carry a '1' and a bridge collapses, a plane drops out of the sky or a building rocks when its resonant frequency matches a gym class leaping to Snap's 1990 hit I've Got The Power. This book is all about what happens when maths goes wrong in the real world. Exploring and explaining a litany of near-misses and mishaps involving the internet, big data, elections, street signs, lotteries and the Roman empire, Matt Parker shows us the bizarre ways maths trips us all up, and what this reveals about its essential place in our world. Mathematics doesn't have good 'people skills', but we would all be better off, he argues, if we saw it as a practical ally. By making maths our friend, we can use it to our advantage and learn from its pitfalls.
A comprehensive study of the historic development of division in extreme and mean ratio ("the golden number"), this text traces the concept's development from its first appearance in Euclid's Elements through the 18th century. The coherent but rigorous presentation offers clear explanations of DEMR's historical transmission, poses controversial views on the concept's relationship to other mathematical topics, and features numerous illustrations.
Mathematics opens new doors to the amazing world of maths. Telling the exciting story from a historical perspective, it shows how mathematical science advanced through the discoveries of the ancient Babylonians, Egyptians and Greeks, the great scholars of medieval Islam and Europe, and the Renaissance and the birth of the Scientific Revolution. This is all explored in a real world context by the renowned science writer Joel Levy. From the simplest concepts of numbers and arithmetic, geometry and algebra, trigonometry and calculus, right through to infinity and chaos theory, Mathematics introduces and explains the most important concepts in accessible, non-technical language. Along the way we meet the extraordinary characters who made great leaps in our understanding of mathematical concepts and theorems, from Pythagoras and Archimedes, to Fibonacci and Fermat, Godel and Turing.
`Fascinating ... so enlightening that suddenly maths doesn't seem so fearsome as it once did' SIMON WINCHESTER From Aristotle to Ada Lovelace: a brief history of the mathematical ideas that have forever changed the world and the everyday people and pioneers behind them. The story of our best invention yet. From our ability to calculate the passing of time to the algorithms that control computers and much else in our lives, numbers are everywhere. They are so indispensable that we forget how fundamental they are to our way of life. In this international bestseller, Mickael Launay mixes history and anecdotes from around the world to reveal how mathematics became pivotal to the story of humankind. It is a journey into numbers with Launay as a guide. In museums, monuments or train stations, he uses the objects around us to explain what art can reveal about geometry, how Babylonian scholars developed one of the first complex written languages, and how `Arabic' numbers were adopted from India. It All Adds Up also tells the story of how mapping the trajectory of an eclipse has helped to trace the precise day of one of the oldest battles in history, how the course of the modern-day Greenwich Meridian was established, and why negative numbers were accepted just last century. This book is a vital compendium of the great men and women of mathematics from Aristotle to Ada Lovelace, which demonstrates how mathematics shaped the written word and the world. With clarity, passion and wisdom, the author unveils the unexpected and at times serendipitous ways in which big mathematical ideas were created. Supporting the belief that - just like music or literature - maths should be accessible to everyone, Launay will inspire a new fondness for the numbers that surround us and the rich stories they contain.
A panoramic survey of the vast spectrum of modern and contemporary mathematics and the new philosophical possibilities they suggest. A panoramic survey of the vast spectrum of modern and contemporary mathematics and the new philosophical possibilities they suggest, this book gives the inquisitive non-specialist an insight into the conceptual transformations and intellectual orientations of modern and contemporary mathematics. The predominant analytic approach, with its focus on the formal, the elementary and the foundational, has effectively divorced philosophy from the real practice of mathematics and the profound conceptual shifts in the discipline over the last century. The first part discusses the specificity of modern (1830-1950) and contemporary (1950 to the present) mathematics, and reviews the failure of mainstream philosophy of mathematics to address this specificity. Building on the work of the few exceptional thinkers to have engaged with the "real mathematics" of their era (including Lautman, Deleuze, Badiou, de Lorenzo and Chatelet), Zalamea challenges philosophy's self-imposed ignorance of the "making of mathematics." In the second part, thirteen detailed case studies examine the greatest creators in the field, mapping the central advances accomplished in mathematics over the last half-century, exploring in vivid detail the characteristic creative gestures of modern master Grothendieck and contemporary creators including Lawvere, Shelah, Connes, and Freyd. Drawing on these concrete examples, and oriented by a unique philosophical constellation (Peirce, Lautman, Merleau-Ponty), in the third part Zalamea sets out the program for a sophisticated new epistemology, one that will avail itself of the powerful conceptual instruments forged by the mathematical mind, but which have until now remained largely neglected by philosophers.
This is the captivating story of mathematics' greatest ever idea: calculus. Without it, there would be no computers, no microwave ovens, no GPS, and no space travel. But before it gave modern man almost infinite powers, calculus was behind centuries of controversy, competition, and even death. Taking us on a thrilling journey through three millennia, professor Steven Strogatz charts the development of this seminal achievement from the days of Archimedes to today's breakthroughs in chaos theory and artificial intelligence. Filled with idiosyncratic characters from Pythagoras to Fourier, Infinite Powers is a compelling human drama that reveals the legacy of calculus on nearly every aspect of modern civilisation, including science, politics, medicine, philosophy, and much besides.
An exploration of mathematical style through 99 different proofs of the same theorem This book offers a multifaceted perspective on mathematics by demonstrating 99 different proofs of the same theorem. Each chapter solves an otherwise unremarkable equation in distinct historical, formal, and imaginative styles that range from Medieval, Topological, and Doggerel to Chromatic, Electrostatic, and Psychedelic. With a rare blend of humor and scholarly aplomb, Philip Ording weaves these variations into an accessible and wide-ranging narrative on the nature and practice of mathematics. Inspired by the experiments of the Paris-based writing group known as the Oulipo "whose members included Raymond Queneau, Italo Calvino, and Marcel Duchamp "Ording explores new ways to examine the aesthetic possibilities of mathematical activity. 99 Variations on a Proof is a mathematical take on Queneau (TM)s Exercises in Style, a collection of 99 retellings of the same story, and it draws unexpected connections to everything from mysticism and technology to architecture and sign language. Through diagrams, found material, and other imagery, Ording illustrates the flexibility and creative potential of mathematics despite its reputation for precision and rigor. Readers will gain not only a bird (TM)s-eye view of the discipline and its major branches but also new insights into its historical, philosophical, and cultural nuances. Readers, no matter their level of expertise, will discover in these proofs and accompanying commentary surprising new aspects of the mathematical landscape.
From ancient Babylon to the last great unsolved problems, an acclaimed mathematician and popular science writer brings us his witty, engaging, and definitive history of mathematics In his famous straightforward style, Ian 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, this book is packed with fascinating nuggets and quirky asides, and contains plenty of illustrations and diagrams to illuminate and aid understanding of a subject many dread, but which has made the world what it is today.
The full measure of Wolfgang Doeblin's mathematical stature became apparent only in 2000 when the sealed envelope containing his construction of diffusion processes in terms of a time change of Brownian motion was finally opened, 60 years after it was sent to the Academy of Sciences in Paris.
This film documents scientific and human aspects of this amazing discovery and throws new light on the startling circumstances of his death at the age of 25.
You can't present the history of art without pictures; equally equations are central to any history of mathematics. Spanning 4,000 years of civilisation, The Story of Mathematics describes twenty -four great equations that have shaped science and society - from the elementary (1+1=2) to the sophisticated (the Black -Scholes formula) and from the famous (E=mc2) to the arcane (Hamilton's quaternion equations). This is a tale of genius, drama and beauty brought vividly to life in a compelli ng narrative by Dana Mackenzie and at the same time he tells us why these equations have something timeless to say about the universe.
A Nobel Prize-winning physicist argues that beauty is the fundamental organizing principle for the entire universe In this scientific tour de force, world-class physicist Frank Wilczek argues that beauty is at the heart of the logic of the universe. As the quest to find the beauty embodied in the universe has connected all scientific pursuit, from Pythagoras to Einstein, Wilczek shows us just how deeply intertwined our ideas about beauty and art are with our understanding of the cosmos. A Beautiful Question is a mind-expanding book combining the age-old human quest for beauty with the age-old human quest for truth.
This graphic novel is both a historical novel as well as an entertaining way of using mathematics to solve a crime. The plot, the possible motive of every suspect, and the elements of his or her character are based on actual historical figures. The 2nd International Congress of Mathematicians is being held in Paris in 1900. The main speaker, the renowned Professor X, is found dead in the hotel dining room. Foul play is suspected. The greatest mathematicians of all time (who are attending the Congress) are called in for questioning. Their statements to the police, however, take the form of mathematical problems. The Chief Inspector enlists the aid of a young mathematician to help solve the crime. Do numbers always tell the truth? Or don't they?
Because we have ten fingers, grouping by ten seems natural, but it has serious shortcomings. Twelve would be better for divisibility, and eight is well suited to repeated halving. Grouping by two, as in binary code, has turned out to have its own remarkable advantages. Paul Lockhart presents arithmetic not as a rote manipulation of numbers-a practical if mundane branch of knowledge best suited for filling out tax forms-but a fascinating, sometimes surprising intellectual craft that arises from our desire to add, divide, and multiply important things. Passionate and entertaining, Arithmetic invites us to experience the beauty of mathematics through the eyes of a beguiling teacher. "Inspiring and informative ... deserves to be widely read." -Wall Street Journal "A nuanced understanding of working with numbers, gently connecting procedures that we once learned by rote with intuitions long since muddled by education...Lockhart presents arithmetic as a pleasurable pastime, and describes it as a craft like knitting." -Jonathon Keats, New Scientist "This fun book offers a philosophical take on number systems and revels in the beauty of math." -Science News "What are numbers, how did they arise, why did our ancestors invent them, and how did they represent them? They are, after all, one of humankind's most brilliant inventions, arguably having greater impact on our lives than the wheel. Lockhart recounts their fascinating story...A wonderful book." -Keith Devlin, author of Finding Fibonacci
The updated new edition of the classic and comprehensive guide to the history of mathematics
For more than forty years, "A History of Mathematics" has been the reference of choice for those looking to learn about the fascinating history of humankind's relationship with numbers, shapes, and patterns. This revised edition features up-to-date coverage of topics such as Fermat's Last Theorem and the Poincare Conjecture," " in addition to recent advances in areas such as finite group theory and computer-aided proofs.Distills thousands of years of mathematics into a single, approachable volumeCovers mathematical discoveries, concepts, and thinkers, from Ancient Egypt to the presentIncludes up-to-date references and an extensive chronological table of mathematical and general historical developments.
Whether you're interested in the age of Plato and Aristotle or Poincare and Hilbert, whether you want to know more about the Pythagorean theorem or the golden mean, "A History of Mathematics" is an essential reference that will help you explore the incredible history of mathematics and the men and women who created it.
The genesis of the digital idea and why it transformed civilization A few short decades ago, we were informed by the smooth signals of analog television and radio; we communicated using our analog telephones; and we even computed with analog computers. Today our world is digital, built with zeros and ones. Why did this revolution occur? The Discrete Charm of the Machine explains, in an engaging and accessible manner, the varied physical and logical reasons behind this radical transformation. The spark of individual genius shines through this story of innovation: the stored program of Jacquard (TM)s loom; Charles Babbage (TM)s logical branching; Alan Turing (TM)s brilliant abstraction of the discrete machine; Harry Nyquist (TM)s foundation for digital signal processing; Claude Shannon (TM)s breakthrough insights into the meaning of information and bandwidth; and Richard Feynman (TM)s prescient proposals for nanotechnology and quantum computing. Ken Steiglitz follows the progression of these ideas in the building of our digital world, from the internet and artificial intelligence to the edge of the unknown. Are questions like the famous traveling salesman problem truly beyond the reach of ordinary digital computers? Can quantum computers transcend these barriers? Does a mysterious magical power reside in the analog mechanisms of the brain? Steiglitz concludes by confronting the moral and aesthetic questions raised by the development of artificial intelligence and autonomous robots. The Discrete Charm of the Machine examines why our information technology, the lifeblood of our civilization, became digital, and challenges us to think about where its future trajectory may lead.
The quadrivium--the classical curriculum--comprises the four
liberal arts of number, geometry, music, and cosmology. It was
studied from antiquity to the Renaissance as a way of glimpsing the
nature of reality. Geometry is number in space; music is number in
time; and comology expresses number in space and time. Number,
music, and geometry are metaphysical truths: life across the
universe investigates them; they foreshadow the physical sciences.
"Quadrivium" is the first volume to bring together these four
subjects in many hundreds of years. Composed of six successful
titles in the Wooden Books series--"Sacred Geometry," "Sacred
Number," "Harmonograph," "The Elements of Music," "Platonic &
Archimedean Solids," and "A Little Book of Coincidence"--it makes
ancient wisdom and its astonishing interconnectedness accessible to
Beautifully produced in six different colors of ink, "Quadrivium" will appeal to anyone interested in mathematics, music, astronomy, and how the universe works.
GOD CREATED THE INTEGERS is Stephen Hawking's personal choice of the greatest mathematical works in history. He allows the reader to peer into the mind of genius by providing us with excerpts from original mathematical proofs and results. He also helps us understand the progression of mathematical thought, and the very foundations of our presentday technologies. The book includes landmark discoveries spanning 2500 years and representing the work of mathematicians such as Euclid, Georg Cantor, Kurt Godel, Augustin Cauchy, Bernard Riemann and Alan Turing. Each chapter begins with a biography of the featured mathematician, clearly explaining the significance of the result, followed by the full proof of the work, reproduced from the original publication, many in new translations.
A compelling firsthand account of Keith Devlin's ten-year quest to tell Fibonacci's story In 2000, Keith Devlin set out to research the life and legacy of the medieval mathematician Leonardo of Pisa, popularly known as Fibonacci, whose book Liber abbaci has quite literally affected the lives of everyone alive today. Although he is most famous for the Fibonacci numbers--which, it so happens, he didn't invent--Fibonacci's greatest contribution was as an expositor of mathematical ideas at a level ordinary people could understand. In 1202, Liber abbaci--the "Book of Calculation"--introduced modern arithmetic to the Western world. Yet Fibonacci was long forgotten after his death, and it was not until the 1960s that his true achievements were finally recognized. Finding Fibonacci is Devlin's compelling firsthand account of his ten-year quest to tell Fibonacci's story. Devlin, a math expositor himself, kept a diary of the undertaking, which he draws on here to describe the project's highs and lows, its false starts and disappointments, the tragedies and unexpected turns, some hilarious episodes, and the occasional lucky breaks. You will also meet the unique individuals Devlin encountered along the way, people who, each for their own reasons, became fascinated by Fibonacci, from the Yale professor who traced modern finance back to Fibonacci to the Italian historian who made the crucial archival discovery that brought together all the threads of Fibonacci's astonishing story. Fibonacci helped to revive the West as the cradle of science, technology, and commerce, yet he vanished from the pages of history. This is Devlin's search to find him.
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