The Calculus Story

A Mathematical Adventure

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Author: David Acheson

Publisher: Oxford University Press

ISBN: 0198804547

Category:

Page: 160

View: 1825

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.

The Calculus Story

A Mathematical Adventure

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Author: David Acheson

Publisher: Oxford University Press

ISBN: 0192526715

Category: Mathematics

Page: 160

View: 6134

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.

The Calculus Story

A Mathematical Adventure

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Author: David Acheson

Publisher: Oxford University Press

ISBN: 0192526723

Category: Mathematics

Page: 160

View: 5021

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.

1089 and All that : a Journey Into Mathematics

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Author: D. J. Acheson

Publisher: Oxford University Press, USA

ISBN: 9780198516231

Category: Mathematics

Page: 178

View: 8938

This excellent book, written by the established author David Acheson, makes mathematics accessible to everyone. Providing an entertaining and witty overview of the subject, the text includes several fascinating puzzles, and is accompanied by numerous illustrations and sketches by world famous cartoonists. This unusual book is one of the most readable explanations of mathematics available.

Calculus and Its Origins

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Author: David Perkins

Publisher: MAA

ISBN: 0883855755

Category: Mathematics

Page: 165

View: 4750

" ... Is primarily a collection of results that show how calculus came to be, beginning in ancient Greece and climaxing with the discovery of calculus. The book requires only a basic knowledge of high school geometry and algebra. Exercises introduce further historical figures and their results." -- Cover, p.[4].

Wonders Beyond Numbers

A Brief History of All Things Mathematical

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Author: Johnny Ball

Publisher: Bloomsbury Publishing

ISBN: 1472939964

Category: Mathematics

Page: 336

View: 7833

In this book, Johnny Ball tells one of the most important stories in world history – the story of mathematics. By introducing us to the major characters and leading us through many historical twists and turns, Johnny slowly unravels the tale of how humanity built up a knowledge and understanding of shapes, numbers and patterns from ancient times, a story that leads directly to the technological wonderland we live in today. As Galileo said, 'Everything in the universe is written in the language of mathematics', and Wonders Beyond Numbers is your guide to this language. Mathematics is only one part of this rich and varied tale; we meet many fascinating personalities along the way, such as a mathematician who everyone has heard of but who may not have existed; a Greek philosopher who made so many mistakes that many wanted his books destroyed; a mathematical artist who built the largest masonry dome on earth, which builders had previously declared impossible; a world-renowned painter who discovered mathematics and decided he could no longer stand the sight of a brush; and a philosopher who lost his head, but only after he had died. Enriched with tales of colourful personalities and remarkable discoveries, there is also plenty of mathematics for keen readers to get stuck into. Written in Johnny Ball's characteristically light-hearted and engaging style, this book is packed with historical insight and mathematical marvels; join Johnny and uncover the wonders found beyond the numbers.

Mathematics Rebooted

A Fresh Approach to Understanding

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Author: Lara Alcock

Publisher: Oxford University Press

ISBN: 0192525948

Category: Mathematics

Page: 220

View: 6966

Would you like to understand more mathematics? Many people would. Perhaps at school you liked mathematics for a while but were then put off because you missed a key idea and kept getting stuck. Perhaps you always liked mathematics but gave it up because your main interest was music or languages or science or philosophy. Or perhaps you studied mathematics to advanced levels, but have now forgotten most of what you once knew. Whichever is the case, this book is for you. It aims to build on what you know, revisiting basic ideas with a focus on meaning. Each chapter starts with an idea from school mathematics - often primary school mathematics - and gradually builds up a network of links to more advanced material. It explores fundamental ideas in depth, using insights from research in mathematics education and psychology to explain why people often get confused, and how to overcome that confusion. For nervous readers, it will build confidence by clarifying basic ideas. For more experienced readers, it will highlight new connections to more advanced material. Throughout, the book explains how mathematicians think, and how ordinary people can understand and enjoy mathematical ideas and arguments. If you would like to be better informed about the intrinsic elegance of mathematics, this engaging guide is the place to start.

A Mathematical Gallery

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Author: Lisl Gaal

Publisher: American Mathematical Soc.

ISBN: 1470441594

Category: Mathematics

Page: 64

View: 4053

Embark on a playful mathematical tour, aided by Lisl Gaal's illustrations of familiar scenes and whimsical triggers for the imagination. Along the way, find fruit stands arranged using polynomial multiplication, checkerboard tablecloths sewed with patterns of primes in a two-dimensional number system, and deceptive cats revealing that simple counting is not always so simple. Grasping the mathematics in this book requires only a basic background in algebra and geometry, so while the ideas can be understood and enjoyed at a variety of levels, it is recommended for ages 13–99. Touching on topics in current research, this is a book to read and revisit, gaining new insights each time.

Math for Scientists

Refreshing the Essentials

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Author: Natasha Maurits,Branislava Ćurčić-Blake

Publisher: Springer

ISBN: 3319573543

Category: Mathematics

Page: 233

View: 8706

This book reviews math topics relevant to non-mathematics students and scientists, but which they may not have seen or studied for a while. These math issues can range from reading mathematical symbols, to using complex numbers, dealing with equations involved in calculating medication equivalents, the General Linear Model (GLM) used in e.g. neuroimaging analysis, finding the minimum of a function, independent component analysis, or filtering approaches. Almost every student or scientist, will at some point run into mathematical formulas or ideas in scientific papers that may be hard to understand, given that formal math education may be some years ago. In this book we will explain the theory behind many of these mathematical ideas and expressions and provide readers with the tools to better understand them. We will revisit high school mathematics and extend and relate this to the mathematics you need to understand the math you may encounter in the course of your research. This book will help you understand the math and formulas in the scientific papers you read. To achieve this goal, each chapter mixes theory with practical pen-and-paper exercises such that you (re)gain experience with solving math problems yourself. Mnemonics will be taught whenever possible. To clarify the math and help readers apply it, each chapter provides real-world and scientific examples.

Music by the Numbers

From Pythagoras to Schoenberg

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Author: Eli Maor

Publisher: Princeton University Press

ISBN: 1400889898

Category: Mathematics

Page: 176

View: 558

How music has influenced mathematics, physics, and astronomy from ancient Greece to the twentieth century Music is filled with mathematical elements, the works of Bach are often said to possess a math-like logic, and Igor Stravinsky said "musical form is close to mathematics," while Arnold Schoenberg, Iannis Xenakis, and Karlheinz Stockhausen went further, writing music explicitly based on mathematical principles. Yet Eli Maor argues that music has influenced math at least as much as math has influenced music. Starting with Pythagoras, proceeding through the work of Schoenberg, and ending with contemporary string theory, Music by the Numbers tells a fascinating story of composers, scientists, inventors, and eccentrics who played a role in the age-old relationship between music, mathematics, and the sciences, especially physics and astronomy. Music by the Numbers explores key moments in this history, particularly how problems originating in music have inspired mathematicians for centuries. Perhaps the most famous of these problems is the vibrating string, which pitted some of the greatest mathematicians of the eighteenth century against each other in a debate that lasted more than fifty years and that eventually led to the development of post-calculus mathematics. Other highlights in the book include a comparison between meter in music and metric in geometry, complete with examples of rhythmic patterns from Bach to Stravinsky, and an exploration of a suggestive twentieth-century development: the nearly simultaneous emergence of Einstein's theory of relativity and Schoenberg's twelve-tone system. Weaving these compelling historical episodes with Maor's personal reflections as a mathematician and lover of classical music, Music by the Numbers will delight anyone who loves mathematics and music.

A Tour of the Calculus

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Author: David Berlinski

Publisher: Vintage

ISBN: 9780307789730

Category: Mathematics

Page: 352

View: 9174

Were it not for the calculus, mathematicians would have no way to describe the acceleration of a motorcycle or the effect of gravity on thrown balls and distant planets, or to prove that a man could cross a room and eventually touch the opposite wall. Just how calculus makes these things possible and in doing so finds a correspondence between real numbers and the real world is the subject of this dazzling book by a writer of extraordinary clarity and stylistic brio. Even as he initiates us into the mysteries of real numbers, functions, and limits, Berlinski explores the furthest implications of his subject, revealing how the calculus reconciles the precision of numbers with the fluidity of the changing universe. "An odd and tantalizing book by a writer who takes immense pleasure in this great mathematical tool, and tries to create it in others."--New York Times Book Review From the Trade Paperback edition.

Towards Higher Mathematics: A Companion

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Author: Richard Earl

Publisher: Cambridge University Press

ISBN: 1108326382

Category: Mathematics

Page: N.A

View: 4684

Containing a large and varied set of problems, this rich resource will allow students to stretch their mathematical abilities beyond the school syllabus, and bridge the gap to university-level mathematics. Many proofs are provided to better equip students for the transition to university. The author covers substantial extension material using the language of sixth form mathematics, thus enabling students to understand the more complex material. Exercises are carefully chosen to introduce students to some central ideas, without building up large amounts of abstract technology. There are over 1500 carefully graded exercises, with hints included in the text, and solutions available online. Historical and contextual asides highlight each area of mathematics and show how it has developed over time.

The Calculus of Happiness

How a Mathematical Approach to Life Adds Up to Health, Wealth, and Love

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Author: Oscar Fernandez

Publisher: Princeton University Press

ISBN: 1400884810

Category: Mathematics

Page: 176

View: 6641

How math holds the keys to improving one's health, wealth, and love life What's the best diet for overall health and weight management? How can we change our finances to retire earlier? How can we maximize our chances of finding our soul mate? In The Calculus of Happiness, Oscar Fernandez shows us that math yields powerful insights into health, wealth, and love. Using only high-school-level math (precalculus with a dash of calculus), Fernandez guides us through several of the surprising results, including an easy rule of thumb for choosing foods that lower our risk for developing diabetes (and that help us lose weight too), simple "all-weather" investment portfolios with great returns, and math-backed strategies for achieving financial independence and searching for our soul mate. Moreover, the important formulas are linked to a dozen free online interactive calculators on the book’s website, allowing one to personalize the equations. Fernandez uses everyday experiences—such as visiting a coffee shop—to provide context for his mathematical insights, making the math discussed more accessible, real-world, and relevant to our daily lives. Every chapter ends with a summary of essential lessons and takeaways, and for advanced math fans, Fernandez includes the mathematical derivations in the appendices. A nutrition, personal finance, and relationship how-to guide all in one, The Calculus of Happiness invites you to discover how empowering mathematics can be.

Elementary Fluid Dynamics

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Author: D. J. Acheson

Publisher: Oxford University Press

ISBN: 0198596790

Category: Mathematics

Page: 397

View: 7862

This textbook provides a clear and concise introduction to both theory and application of fluid dynamics, suitable for all undergraduates coming to the subject for the first time. It has a wide scope, with frequent references to experiments, and numerous exercises illustrating the main ideas.

The Joy of X

A Guided Tour of Math, from One to Infinity

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Author: Steven Henry Strogatz

Publisher: Houghton Mifflin Harcourt

ISBN: 0547517653

Category: MATHEMATICS

Page: 316

View: 4786

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.

Significant Figures

The Lives and Work of Great Mathematicians

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Author: Ian Stewart

Publisher: Basic Books

ISBN: 0465096131

Category: Mathematics

Page: 320

View: 9616

A celebrated mathematician traces the history of math through the lives and work of twenty-five pioneering mathematicians In Significant Figures, acclaimed mathematician Ian Stewart introduces the visionaries of mathematics throughout history. Delving into the lives of twenty-five great mathematicians, Stewart examines the roles they played in creating, inventing, and discovering the mathematics we use today. Through these short biographies, we get acquainted with the history of mathematics from Archimedes to Benoit Mandelbrot, and learn about those too often left out of the cannon, such as Muhammad ibn Musa al-Khwarizmi (c. 780-850), the creator of algebra, and Augusta Ada King (1815-1852), Countess of Lovelace, the world's first computer programmer. Tracing the evolution of mathematics over the course of two millennia, Significant Figures will educate and delight aspiring mathematicians and experts alike.

The Calculus Gallery

Masterpieces from Newton to Lebesgue

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Author: William Dunham

Publisher: Princeton University Press

ISBN: 0691184542

Category: Mathematics

Page: 257

View: 7908

More than three centuries after its creation, calculus remains a dazzling intellectual achievement and the gateway to higher mathematics. This book charts its growth and development by sampling from the work of some of its foremost practitioners, beginning with Isaac Newton and Gottfried Wilhelm Leibniz in the late seventeenth century and continuing to Henri Lebesgue at the dawn of the twentieth. Now with a new preface by the author, this book documents the evolution of calculus from a powerful but logically chaotic subject into one whose foundations are thorough, rigorous, and unflinching—a story of genius triumphing over some of the toughest, subtlest problems imaginable. In touring The Calculus Gallery, we can see how it all came to be.

The Calculus of Friendship

What a Teacher and a Student Learned about Life while Corresponding about Math

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Author: Steven Strogatz

Publisher: Princeton University Press

ISBN: 9781400830886

Category: Mathematics

Page: 184

View: 9613

The Calculus of Friendship is the story of an extraordinary connection between a teacher and a student, as chronicled through more than thirty years of letters between them. What makes their relationship unique is that it is based almost entirely on a shared love of calculus. For them, calculus is more than a branch of mathematics; it is a game they love playing together, a constant when all else is in flux. The teacher goes from the prime of his career to retirement, competes in whitewater kayaking at the international level, and loses a son. The student matures from high school math whiz to Ivy League professor, suffers the sudden death of a parent, and blunders into a marriage destined to fail. Yet through it all they take refuge in the haven of calculus--until a day comes when calculus is no longer enough. Like calculus itself, The Calculus of Friendship is an exploration of change. It's about the transformation that takes place in a student's heart, as he and his teacher reverse roles, as they age, as they are buffeted by life itself. Written by a renowned teacher and communicator of mathematics, The Calculus of Friendship is warm, intimate, and deeply moving. The most inspiring ideas of calculus, differential equations, and chaos theory are explained through metaphors, images, and anecdotes in a way that all readers will find beautiful, and even poignant. Math enthusiasts, from high school students to professionals, will delight in the offbeat problems and lucid explanations in the letters. For anyone whose life has been changed by a mentor, The Calculus of Friendship will be an unforgettable journey.

The Mathematics Lover's Companion

Masterpieces for Everyone

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Author: Edward R. Scheinerman

Publisher: Yale University Press

ISBN: 0300223005

Category: Mathematics

Page: 296

View: 5181

Twenty-three mathematical masterpieces for exploration and enlightenment

The Calculus Wars

Newton, Leibniz, and the Greatest Mathematical Clash of All Time

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Author: Jason Socrates Bardi

Publisher: Basic Books

ISBN: 0786733640

Category: Science

Page: 304

View: 6994

This vibrant and gripping history ultimately exposes how these twin mathematical giants (Newton, Leibniz) were proud, brilliant, at times mad, and in the end completely human.