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The most comprehensive and correct syllabus coverage, with unrivalled guidance and support straight from the IB. This online course book includes over 600 pages of practice to cement understanding. Blending crucial practice with inquiry, it adopts a truly IB approach to mathematics. - Full syllabus coverage - the truest match ...
Oxford IB Diploma Programme: Mathematical Studies Standard Level Course Companion
The most comprehensive and correct syllabus coverage, with unrivalled guidance and support straight from the IB. This online course book includes over 600 pages of practice to cement understanding. Blending crucial practice with inquiry, it adopts a truly IB approach to mathematics. - Full syllabus coverage - the truest match to the IB syllabus, written with the IB to exactly match IB specifications - Complete worked solutions - a full set of worked solutions is included online - Extensive practice - over 600 pages of practice cements comprehension - Up-to-date GDC support - take the confusion out of GDC use and help students focus on the theory - Definitive assessment preparation - exam-style papers and questions will build confidence - The Exploration - supported by a full chapter, to guide you through this new component - Real world approach - connect mathematics with human behaviour, language, morality and more About the series: The only DP resources developed directly with the IB, the Oxford IB Course Books are the most comprehensive core resources to support learners through their study. Fully incorporating the learner profile, resources are assessed by consulting experts in international-mindedness and TOK to ensure these crucial components are deeply embedded into learning.
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76.67 USD

Oxford IB Diploma Programme: Mathematical Studies Standard Level Course Companion

by Paula Waldman de Tokman, Jane Forrest, Jim Fensom, Peter Blythe
Mixed media product
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The new fifth edition of Barron's SAT Subject Test: Math Level 1 offers students intensive test preparation with A review of the most important test-taking strategies students need to know to succeed on this exam Topic review chapters covering all the math students need to know for this test, including: ...
Barron's SAT Subject Test Math Level 1
The new fifth edition of Barron's SAT Subject Test: Math Level 1 offers students intensive test preparation with A review of the most important test-taking strategies students need to know to succeed on this exam Topic review chapters covering all the math students need to know for this test, including: arithmetic, algebra, plane geometry, solid and coordinate geometry, trigonometry, functions and their graphs, probability and statistics, real and imaginary numbers, and logic Three full-length model tests with complete solutions for every problem The enclosed CD-ROM presents two additional full-length practice tests with answers, explanations, and automatic scoring.
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46.49 USD

Barron's SAT Subject Test Math Level 1

by Ira K. Wolf
Other book format
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What makes a bridge wobble when it's not meant to? How do billions of dollars mysteriously vanish into thin air? How does 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, ...
Humble Pi: A Comedy of Maths Errors
What makes a bridge wobble when it's not meant to? How do billions of dollars mysteriously vanish into thin air? How does 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. 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.
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16.31 USD

Humble Pi: A Comedy of Maths Errors

by Matt Parker
Paperback / softback
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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, ...
Quadrivium: The Four Classical Liberal Arts of Number, Geometry, Music, & Cosmology
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 us today.Beautifully produced in six different colors of ink, Quadrivium will appeal to anyone interested in mathematics, music, astronomy, and how the universe works.
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23.100000 USD

Quadrivium: The Four Classical Liberal Arts of Number, Geometry, Music, & Cosmology

by John Martineau, Jason Martineau, Anthony Ashton, Daud Sutton, Miranda Lundy
Hardback
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Why is the number seven lucky - even holy - in almost every culture? Why do we speak of the four corners of the earth? Why do cats have nine lives (except in Iran, where they have seven)? From literature to folklore to private superstitions, numbers play a conspicuous role ...
The Mystery of Numbers
Why is the number seven lucky - even holy - in almost every culture? Why do we speak of the four corners of the earth? Why do cats have nine lives (except in Iran, where they have seven)? From literature to folklore to private superstitions, numbers play a conspicuous role in our daily lives. In The Mystery of Numbers Annemarie Schimmel conducts an illuminating tour of the mysteries attributed to numbers over the centuries. She covers the origins of numbers, the symbolism of numbers, the source of this symbolism, and examines individual numbers from one to ten thousand. Using examples ranging from the Bible to Shakespeare, this engaging account uncovers the roots of a phenomenon we all feel every Friday the thirteenth.
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26.240000 USD

The Mystery of Numbers

by Annemarie Schimmel
Paperback / softback
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The period from the late fourth to the late second century B. C. witnessed, in Greek-speaking countries, an explosion of objective knowledge about the external world. WhileGreek culture had reached great heights in art, literature and philosophyalreadyin the earlier classical era, it is in the so-called Hellenistic period that we ...
The Forgotten Revolution: How Science Was Born in 300 BC and Why it Had to Be Reborn
The period from the late fourth to the late second century B. C. witnessed, in Greek-speaking countries, an explosion of objective knowledge about the external world. WhileGreek culture had reached great heights in art, literature and philosophyalreadyin the earlier classical era, it is in the so-called Hellenistic period that we see for the ?rst time - anywhere in the world - the appearance of science as we understand it now: not an accumulation of facts or philosophically based speculations, but an or- nized effort to model nature and apply such models, or scienti?ctheories in a sense we will make precise, to the solution of practical problems and to a growing understanding of nature. We owe this new approach to scientists such as Archimedes, Euclid, Eratosthenes and many others less familiar todaybut no less remarkable. Yet, not long after this golden period, much of this extraordinary dev- opment had been reversed. Rome borrowed what it was capable of from the Greeks and kept it for a little while yet, but created very little science of its own. Europe was soon smothered in theobscurantism and stasis that blocked most avenues of intellectual development for a thousand years - until, as is well known, the rediscovery of ancient culture in its fullness paved the way to the modern age.
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104.990000 USD

The Forgotten Revolution: How Science Was Born in 300 BC and Why it Had to Be Reborn

by Lucio Russo
Paperback / softback
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This great-value pack contains a complete range of resources to help pupils aged 10-11 prepare for the Maths part of the 11+ and other entrance exams. It includes the CGP Maths Study Book with Parents' Guide (9781847628244), the Practice Book with Assessment Tests for Ages 10-11 (9781847628282) and the Multiple ...
The 11+ Maths Bundle Pack - Multiple Choice (for GL & Other Test Providers)
This great-value pack contains a complete range of resources to help pupils aged 10-11 prepare for the Maths part of the 11+ and other entrance exams. It includes the CGP Maths Study Book with Parents' Guide (9781847628244), the Practice Book with Assessment Tests for Ages 10-11 (9781847628282) and the Multiple Choice Practice Test Papers (9781847628305). For children taking the test in the 'Standard Answers' format, a pack containing Standard Answer Practice Test Papers is also available (9781847629661).
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42.68 USD

The 11+ Maths Bundle Pack - Multiple Choice (for GL & Other Test Providers)

by CGP Books
Paperback / softback
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Stephen Hawking is the world-famous physicist with a cameo in The Simpsons on his CV , but outside his academic field his work is little understood. To the public he is a tragic figure - a brilliant scientist and author of the 9 million-copy-selling A Brief History of Time , ...
Introducing Stephen Hawking: A Graphic Guide
Stephen Hawking is the world-famous physicist with a cameo in The Simpsons on his CV , but outside his academic field his work is little understood. To the public he is a tragic figure - a brilliant scientist and author of the 9 million-copy-selling A Brief History of Time , and yet confined to a wheelchair and almost completely paralysed. Hawking's major contribution to science has been to integrate the two great theories of 20th-century physics - Einstein's General Theory of Relativity and Quantum Mechanics. J.P. McEvoy and Oscar Zarate's brilliant graphic guide explores Hawking's life, the evolution of his work from his days as a student, and his breathtaking discoveries about where these fundamental laws break down or overlap, such as on the edge of a Black Hole or at the origin of the Universe itself.
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10.450000 USD

Introducing Stephen Hawking: A Graphic Guide

by J. P. McEvoy
Paperback / softback
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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 ...
A History of Mathematics
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 volume * Covers mathematical discoveries, concepts, and thinkers, from Ancient Egypt to the present * Includes 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.
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41.950000 USD

A History of Mathematics

by Uta C. Merzbach, Carl B. Boyer
Paperback / softback
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For seven years, Paul Lockhart's A Mathematician's Lament enjoyed a samizdat-style popularity in the mathematics underground, before demand prompted its 2009 publication to even wider applause and debate. An impassioned critique of K-12 mathematics education, it outlined how we shortchange students by introducing them to math the wrong way. Here ...
Measurement
For seven years, Paul Lockhart's A Mathematician's Lament enjoyed a samizdat-style popularity in the mathematics underground, before demand prompted its 2009 publication to even wider applause and debate. An impassioned critique of K-12 mathematics education, it outlined how we shortchange students by introducing them to math the wrong way. Here Lockhart offers the positive side of the math education story by showing us how math should be done. Measurement offers a permanent solution to math phobia by introducing us to mathematics as an artful way of thinking and living. In conversational prose that conveys his passion for the subject, Lockhart makes mathematics accessible without oversimplifying. He makes no more attempt to hide the challenge of mathematics than he does to shield us from its beautiful intensity. Favoring plain English and pictures over jargon and formulas, he succeeds in making complex ideas about the mathematics of shape and motion intuitive and graspable. His elegant discussion of mathematical reasoning and themes in classical geometry offers proof of his conviction that mathematics illuminates art as much as science. Lockhart leads us into a universe where beautiful designs and patterns float through our minds and do surprising, miraculous things. As we turn our thoughts to symmetry, circles, cylinders, and cones, we begin to see that almost anyone can do the math in a way that brings emotional and aesthetic rewards. Measurement is an invitation to summon curiosity, courage, and creativity in order to experience firsthand the playful excitement of mathematical work.
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33.38 USD

Measurement

by Paul Lockhart
Paperback / softback
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This is an accessible, fascinating book that unravels the mysteries and beauty of mathematics. It covers 250 milestones in mathematical history. This paperback version of the bestselling title includes facts about scientists' lives and real-world applications of the theorems. Maths' infinite mysteries and beauty unfold in this fascinating book. Beginning ...
The Math Book: From Pythagoras to the 57th Dimension, 250 Milestones in the History of Mathematics
This is an accessible, fascinating book that unravels the mysteries and beauty of mathematics. It covers 250 milestones in mathematical history. This paperback version of the bestselling title includes facts about scientists' lives and real-world applications of the theorems. Maths' infinite mysteries and beauty unfold in this fascinating book. Beginning millions of years ago with ancient ant odometers and moving through time to our modern-day quest for new dimensions, it covers 250 milestones in mathematical history. Among the numerous delights readers will learn about in this inviting anthology include: cicada-generated prime numbers, magic squares from centuries ago, the discovery of pi and calculus and the butterfly effect.
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20.950000 USD

The Math Book: From Pythagoras to the 57th Dimension, 250 Milestones in the History of Mathematics

by Clifford A. Pickover
Paperback / softback
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It is one of the wonders of mathematics that, for every problem mathematicians solve, another awaits to perplex and galvanize them. Some of these problems are new, while others have puzzled and bewitched thinkers across the ages. Such challenges offer a tantalizing glimpse of the field's unlimited potential, and keep ...
Visions of Infinity
It is one of the wonders of mathematics that, for every problem mathematicians solve, another awaits to perplex and galvanize them. Some of these problems are new, while others have puzzled and bewitched thinkers across the ages. Such challenges offer a tantalizing glimpse of the field's unlimited potential, and keep mathematicians looking toward the horizons of intellectual possibility. In Visions of Infinity, celebrated mathematician Ian Stewart provides a fascinating overview of the most formidable problems mathematicians have vanquished, and those that vex them still. He explains why these problems exist, what drives mathematicians to solve them, and why their efforts matter in the context of science as a whole. The three-century effort to prove Fermat's last theorem--first posited in 1630, and finally solved by Andrew Wiles in 1995--led to the creation of algebraic number theory and complex analysis. The Poincare conjecture, which was cracked in 2002 by the eccentric genius Grigori Perelman, has become fundamental to mathematicians' understanding of three-dimensional shapes. But while mathematicians have made enormous advances in recent years, some problems continue to baffle us. Indeed, the Riemann hypothesis, which Stewart refers to as the Holy Grail of pure mathematics, and the P/NP problem, which straddles mathematics and computer science, could easily remain unproved for another hundred years. An approachable and illuminating history of mathematics as told through fourteen of its greatest problems, Visions of Infinity reveals how mathematicians the world over are rising to the challenges set by their predecessors--and how the enigmas of the past inevitably surrender to the powerful techniques of the present.
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19.46 USD

Visions of Infinity

by Ian Stewart
Paperback / softback
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More than three centuries after its creation, calculus remains a dazzling intellectual achievement and the gateway into 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 ...
The Calculus Gallery: Masterpieces from Newton to Lebesgue
More than three centuries after its creation, calculus remains a dazzling intellectual achievement and the gateway into 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--mathematicians whose achievements are comparable to those of Bach in music or Shakespeare in literature. William Dunham lucidly presents the definitions, theorems, and proofs. Students of literature read Shakespeare; students of music listen to Bach, he writes. But this tradition of studying the major works of the masters is, if not wholly absent, certainly uncommon in mathematics. This book seeks to redress that situation. Like a great museum, The Calculus Gallery is filled with masterpieces, among which are Bernoulli's early attack upon the harmonic series (1689), Euler's brilliant approximation of pi (1779), Cauchy's classic proof of the fundamental theorem of calculus (1823), Weierstrass's mind-boggling counterexample (1872), and Baire's original category theorem (1899). Collectively, these selections document 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, most subtle problems imaginable. Anyone who has studied and enjoyed calculus will discover in these pages the sheer excitement each mathematician must have felt when pushing into the unknown. In touring The Calculus Gallery, we can see how it all came to be.
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44.64 USD

The Calculus Gallery: Masterpieces from Newton to Lebesgue

by William Dunham
Paperback / softback
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This is the first full-scale biography of Leonhard Euler (1707-83), one of the greatest mathematicians and theoretical physicists of all time. In this comprehensive and authoritative account, Ronald Calinger connects the story of Euler's eventful life to the astonishing achievements that place him in the company of Archimedes, Newton, and ...
Leonhard Euler: Mathematical Genius in the Enlightenment
This is the first full-scale biography of Leonhard Euler (1707-83), one of the greatest mathematicians and theoretical physicists of all time. In this comprehensive and authoritative account, Ronald Calinger connects the story of Euler's eventful life to the astonishing achievements that place him in the company of Archimedes, Newton, and Gauss. Drawing chiefly on Euler's massive published works and correspondence, which fill more than eighty volumes so far, this biography sets Euler's work in its multilayered context--personal, intellectual, institutional, political, cultural, religious, and social. It is a story of nearly incessant accomplishment, from Euler's fundamental contributions to almost every area of pure and applied mathematics--especially calculus, number theory, notation, optics, and celestial, rational, and fluid mechanics--to his advancements in shipbuilding, telescopes, ballistics, cartography, chronology, and music theory. The narrative takes the reader from Euler's childhood and education in Basel through his first period in St. Petersburg, 1727-41, where he gained a European reputation by solving the Basel problem and systematically developing analytical mechanics. Invited to Berlin by Frederick II, Euler published his famous Introductio in analysin infinitorum, devised continuum mechanics, and proposed a pulse theory of light. Returning to St. Petersburg in 1766, he created the analytical calculus of variations, developed the most precise lunar theory of the time that supported Newton's dynamics, and published the best-selling Letters to a German Princess--all despite eye problems that ended in near-total blindness. In telling the remarkable story of Euler and how his achievements brought pan-European distinction to the Petersburg and Berlin academies of sciences, the book also demonstrates with new depth and detail the central role of mathematics in the Enlightenment.
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85.54 USD

Leonhard Euler: Mathematical Genius in the Enlightenment

by Ronald S. Calinger
Hardback
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Elliptic Tales describes the latest developments in number theory by looking at one of the most exciting unsolved problems in contemporary mathematics--the Birch and Swinnerton-Dyer Conjecture. In this book, Avner Ash and Robert Gross guide readers through the mathematics they need to understand this captivating problem. The key to the ...
Elliptic Tales: Curves, Counting, and Number Theory
Elliptic Tales describes the latest developments in number theory by looking at one of the most exciting unsolved problems in contemporary mathematics--the Birch and Swinnerton-Dyer Conjecture. In this book, Avner Ash and Robert Gross guide readers through the mathematics they need to understand this captivating problem. The key to the conjecture lies in elliptic curves, which may appear simple, but arise from some very deep--and often very mystifying--mathematical ideas. Using only basic algebra and calculus while presenting numerous eye-opening examples, Ash and Gross make these ideas accessible to general readers, and, in the process, venture to the very frontiers of modern mathematics.
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31.450000 USD

Elliptic Tales: Curves, Counting, and Number Theory

by Robert Gross, Avner Ash
Hardback
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Good graphs make complex problems clear. From the weather forecast to the Dow Jones average, graphs are so ubiquitous today that it is hard to imagine a world without them. Yet they are a modern invention. This book is the first to comprehensively plot humankind's fascinating efforts to visualize data, ...
Graphic Discovery: A Trout in the Milk and Other Visual Adventures
Good graphs make complex problems clear. From the weather forecast to the Dow Jones average, graphs are so ubiquitous today that it is hard to imagine a world without them. Yet they are a modern invention. This book is the first to comprehensively plot humankind's fascinating efforts to visualize data, from a key seventeenth-century precursor--England's plague-driven initiative to register vital statistics--right up to the latest advances. In a highly readable, richly illustrated story of invention and inventor that mixes science and politics, intrigue and scandal, revolution and shopping, Howard Wainer validates Thoreau's observation that circumstantial evidence can be quite convincing, as when you find a trout in the milk. The story really begins with the eighteenth-century origins of the art, logic, and methods of data display, which emerged, full-grown, in William Playfair's landmark 1786 trade atlas of England and Wales. The remarkable Scot singlehandedly popularized the atheoretical plotting of data to reveal suggestive patterns--an achievement that foretold the graphic explosion of the nineteenth century, with atlases published across the observational sciences as the language of science moved from words to pictures. Next come succinct chapters illustrating the uses and abuses of this marvelous invention more recently, from a murder trial in Connecticut to the Vietnam War's effect on college admissions. Finally Wainer examines the great twentieth-century polymath John Wilder Tukey's vision of future graphic displays and the resultant methods--methods poised to help us make sense of the torrent of data in our information-laden world.
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39.380000 USD

Graphic Discovery: A Trout in the Milk and Other Visual Adventures

by Howard Wainer
Paperback / softback
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Demonstrating the different roles that logic plays in the disciplines of computer science, mathematics, and philosophy, this concise undergraduate textbook covers select topics from three different areas of logic: proof theory, computability theory, and nonclassical logic. The book balances accessibility, breadth, and rigor, and is designed so that its materials ...
Three Views of Logic: Mathematics, Philosophy, and Computer Science
Demonstrating the different roles that logic plays in the disciplines of computer science, mathematics, and philosophy, this concise undergraduate textbook covers select topics from three different areas of logic: proof theory, computability theory, and nonclassical logic. The book balances accessibility, breadth, and rigor, and is designed so that its materials will fit into a single semester. Its distinctive presentation of traditional logic material will enhance readers' capabilities and mathematical maturity. The proof theory portion presents classical propositional logic and first-order logic using a computer-oriented (resolution) formal system. Linear resolution and its connection to the programming language Prolog are also treated. The computability component offers a machine model and mathematical model for computation, proves the equivalence of the two approaches, and includes famous decision problems unsolvable by an algorithm. The section on nonclassical logic discusses the shortcomings of classical logic in its treatment of implication and an alternate approach that improves upon it: Anderson and Belnap's relevance logic. Applications are included in each section. The material on a four-valued semantics for relevance logic is presented in textbook form for the first time. Aimed at upper-level undergraduates of moderate analytical background, Three Views of Logic will be useful in a variety of classroom settings. * Gives an exceptionally broad view of logic * Treats traditional logic in a modern format * Presents relevance logic with applications * Provides an ideal text for a variety of one-semester upper-level undergraduate courses
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65.00 USD

Three Views of Logic: Mathematics, Philosophy, and Computer Science

by S G Sterrett, Richard E. Hodel, Donald W. Loveland
Paperback / softback
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This comprehensive history traces the development of mathematical ideas and the careers of the men responsible for them. Volume 1 looks at the discipline's origins in Babylon and Egypt, the creation of geometry and trigonometry by the Greeks, and the role of mathematics in the medieval and early modern periods. ...
Mathematical Thought from Ancient to Modern Times: Mathematical Thought from Ancient to Modern Times, Volume 2
This comprehensive history traces the development of mathematical ideas and the careers of the men responsible for them. Volume 1 looks at the discipline's origins in Babylon and Egypt, the creation of geometry and trigonometry by the Greeks, and the role of mathematics in the medieval and early modern periods. Volume 2 focuses on calculus, the rise of analysis in the nineteenth century, and the number theories of Dedekind and Dirichlet. The concluding volume covers the revival of projective geometry, the emergence of abstract algebra, the beginnings of topology, and the influence of Goedel on recent mathematical study.
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29.74 USD

Mathematical Thought from Ancient to Modern Times: Mathematical Thought from Ancient to Modern Times, Volume 2

by Morris Kline
Paperback / softback
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This comprehensive history traces the development of mathematical ideas and the careers of the mathematicians responsible for them. Originally published in 1972, it is now available as a three volume paperback edition. Volume 1 looks at the discipline's origins in Babylon and Egypt, the creation of geometry and trigonometry by ...
Mathematical Thought from Ancient to Modern Times: Mathematical Thought from Ancient to Modern Times, Volume 1
This comprehensive history traces the development of mathematical ideas and the careers of the mathematicians responsible for them. Originally published in 1972, it is now available as a three volume paperback edition. Volume 1 looks at the discipline's origins in Babylon and Egypt, the creation of geometry and trigonometry by the Greeks, and the role of mathematics in the medieval and early modern periods. Volume 2 focuses on calculus, the rise of analysis in the nineteenth century, and the number theories of Dedekind and Dirichlet. The concluding volume covers the revival of projective geometry, the emergence of abstract algebra, the beginnings of topology, and the influence of Goedel on recent mathematical study.
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24.16 USD

Mathematical Thought from Ancient to Modern Times: Mathematical Thought from Ancient to Modern Times, Volume 1

by Morris Kline
Paperback / softback
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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 ...
The Mathematics of Life
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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20.990000 USD

The Mathematics of Life

by Ian Stewart
Paperback / softback
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For more than two thousand years a familiarity with mathematics has been regarded as an indispensable part of the intellectual equipment of every cultured person. Today, unfortunately, the traditional place of mathematics in education is in grave danger. The teaching and learning of mathematics has degenerated into the realm of ...
What Is Mathematics?: An Elementary Approach to Ideas and Methods
For more than two thousand years a familiarity with mathematics has been regarded as an indispensable part of the intellectual equipment of every cultured person. Today, unfortunately, the traditional place of mathematics in education is in grave danger. The teaching and learning of mathematics has degenerated into the realm of rote memorization, the outcome of which leads to satisfactory formal ability but does not lead to real understanding or to greater intellectual independence. This new edition of Richard Courant's and Herbert Robbins's classic work seeks to address this problem. Its goal is to put the meaning back into mathematics. Written for beginners and scholars, for students and teachers, for philosophers and engineers, What is Mathematics?, Second Edition is a sparkling collection of mathematical gems that offers an entertaining and accessible portrait of the mathematical world. Covering everything from natural numbers and the number system to geometrical constructions and projective geometry, from topology and calculus to matters of principle and the Continuum Hypothesis, this fascinating survey allows readers to delve into mathematics as an organic whole rather than an empty drill in problem solving. With chapters largely independent of one another and sections that lead upward from basic to more advanced discussions, readers can easily pick and choose areas of particular interest without impairing their understanding of subsequent parts. Brought up to date with a new chapter by Ian Stewart, What is Mathematics?, Second Edition offers new insights into recent mathematical developments and describes proofs of the Four-Color Theorem and Fermat's Last Theorem, problems that were still open when Courant and Robbins wrote this masterpiece, but ones that have since been solved. Formal mathematics is like spelling and grammar-a matter of the correct application of local rules. Meaningful mathematics is like journalism-it tells an interesting story. But unlike some journalism, the story has to be true. The best mathematics is like literature-it brings a story to life before your eyes and involves you in it, intellectually and emotionally. What is Mathematics is like a fine piece of literature-it opens a window onto the world of mathematics for anyone interested to view.
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29.74 USD

What Is Mathematics?: An Elementary Approach to Ideas and Methods

by Herbert Robbins, Richard Courant
Paperback / softback
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While all of us regularly use basic math symbols such as those for plus, minus, and equals, few of us know that many of these symbols weren't available before the sixteenth century. What did mathematicians rely on for their work before then? And how did mathematical notations evolve into what ...
Enlightening Symbols: A Short History of Mathematical Notation and Its Hidden Powers
While all of us regularly use basic math symbols such as those for plus, minus, and equals, few of us know that many of these symbols weren't available before the sixteenth century. What did mathematicians rely on for their work before then? And how did mathematical notations evolve into what we know today? In Enlightening Symbols, popular math writer Joseph Mazur explains the fascinating history behind the development of our mathematical notation system. He shows how symbols were used initially, how one symbol replaced another over time, and how written math was conveyed before and after symbols became widely adopted. Traversing mathematical history and the foundations of numerals in different cultures, Mazur looks at how historians have disagreed over the origins of the numerical system for the past two centuries. He follows the transfigurations of algebra from a rhetorical style to a symbolic one, demonstrating that most algebra before the sixteenth century was written in prose or in verse employing the written names of numerals. Mazur also investigates the subconscious and psychological effects that mathematical symbols have had on mathematical thought, moods, meaning, communication, and comprehension. He considers how these symbols influence us (through similarity, association, identity, resemblance, and repeated imagery), how they lead to new ideas by subconscious associations, how they make connections between experience and the unknown, and how they contribute to the communication of basic mathematics. From words to abbreviations to symbols, this book shows how math evolved to the familiar forms we use today.
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33.550000 USD

Enlightening Symbols: A Short History of Mathematical Notation and Its Hidden Powers

by Joseph Mazur
Hardback
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Number theory is the branch of mathematics that is primarily concerned with the counting numbers. Of particular importance are the prime numbers, the 'building blocks' of our number system. The subject is an old one, dating back over two millennia to the ancient Greeks, and for many years has been ...
Number Theory: A Very Short Introduction
Number theory is the branch of mathematics that is primarily concerned with the counting numbers. Of particular importance are the prime numbers, the 'building blocks' of our number system. The subject is an old one, dating back over two millennia to the ancient Greeks, and for many years has been studied for its intrinsic beauty and elegance, not least because several of its challenges are so easy to state that everyone can understand them, and yet no-one has ever been able to resolve them. But number theory has also recently become of great practical importance - in the area of cryptography, where the security of your credit card, and indeed of the nation's defence, depends on a result concerning prime numbers that dates back to the 18th century. Recent years have witnessed other spectacular developments, such as Andrew Wiles's proof of 'Fermat's last theorem' (unproved for over 250 years) and some exciting work on prime numbers. In this Very Short Introduction Robin Wilson introduces the main areas of classical number theory, both ancient and modern. Drawing on the work of many of the greatest mathematicians of the past, such as Euclid, Fermat, Euler, and Gauss, he situates some of the most interesting and creative problems in the area in their historical context. ABOUT THE SERIES: The Very Short Introductions series from Oxford University Press contains hundreds of titles in almost every subject area. These pocket-sized books are the perfect way to get ahead in a new subject quickly. Our expert authors combine facts, analysis, perspective, new ideas, and enthusiasm to make interesting and challenging topics highly readable.
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12.550000 USD

Number Theory: A Very Short Introduction

Paperback / softback
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The legendary Renaissance math duel that ushered in the modern age of algebra The Secret Formula tells the story of two Renaissance mathematicians whose jealousies, intrigues, and contentious debates led to the discovery of a formula for the solution of the cubic equation. Niccolo Tartaglia was a talented and ambitious ...
The Secret Formula: How a Mathematical Duel Inflamed Renaissance Italy and Uncovered the Cubic Equation
The legendary Renaissance math duel that ushered in the modern age of algebra The Secret Formula tells the story of two Renaissance mathematicians whose jealousies, intrigues, and contentious debates led to the discovery of a formula for the solution of the cubic equation. Niccolo Tartaglia was a talented and ambitious teacher who possessed a secret formula-the key to unlocking a seemingly unsolvable, two-thousand-year-old mathematical problem. He wrote it down in the form of a poem to prevent other mathematicians from stealing it. Gerolamo Cardano was a physician, gifted scholar, and notorious gambler who would not hesitate to use flattery and even trickery to learn Tartaglia's secret. Set against the backdrop of sixteenth-century Italy, The Secret Formula provides new and compelling insights into the peculiarities of Renaissance mathematics while bringing a turbulent and culturally vibrant age to life. It was an era when mathematicians challenged each other in intellectual duels held outdoors before enthusiastic crowds. Success not only enhanced the winner's reputation, but could result in prize money and professional acclaim. After hearing of Tartaglia's spectacular victory in one such contest in Venice, Cardano invited him to Milan, determined to obtain his secret by whatever means necessary. Cardano's intrigues paid off. In 1545, he was the first to publish a general solution of the cubic equation. Tartaglia, eager to take his revenge by establishing his superiority as the most brilliant mathematician of the age, challenged Cardano to the ultimate mathematical duel. A lively and compelling account of genius, betrayal, and all-too-human failings, The Secret Formula reveals the epic rivalry behind one of the fundamental ideas of modern algebra.
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40.91 USD

The Secret Formula: How a Mathematical Duel Inflamed Renaissance Italy and Uncovered the Cubic Equation

by Fabio Toscano
Hardback
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What is algebra? For some, it is an abstract language of x's and y's. For mathematics majors and professional mathematicians, it is a world of axiomatically defined constructs like groups, rings, and fields. Taming the Unknown considers how these two seemingly different types of algebra evolved and how they relate. ...
Taming the Unknown: A History of Algebra from Antiquity to the Early Twentieth Century
What is algebra? For some, it is an abstract language of x's and y's. For mathematics majors and professional mathematicians, it is a world of axiomatically defined constructs like groups, rings, and fields. Taming the Unknown considers how these two seemingly different types of algebra evolved and how they relate. Victor Katz and Karen Parshall explore the history of algebra, from its roots in the ancient civilizations of Egypt, Mesopotamia, Greece, China, and India, through its development in the medieval Islamic world and medieval and early modern Europe, to its modern form in the early twentieth century. Defining algebra originally as a collection of techniques for determining unknowns, the authors trace the development of these techniques from geometric beginnings in ancient Egypt and Mesopotamia and classical Greece. They show how similar problems were tackled in Alexandrian Greece, in China, and in India, then look at how medieval Islamic scholars shifted to an algorithmic stage, which was further developed by medieval and early modern European mathematicians. With the introduction of a flexible and operative symbolism in the sixteenth and seventeenth centuries, algebra entered into a dynamic period characterized by the analytic geometry that could evaluate curves represented by equations in two variables, thereby solving problems in the physics of motion. This new symbolism freed mathematicians to study equations of degrees higher than two and three, ultimately leading to the present abstract era. Taming the Unknown follows algebra's remarkable growth through different epochs around the globe.
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36.750000 USD

Taming the Unknown: A History of Algebra from Antiquity to the Early Twentieth Century

by Karen Hunger Parshall, Victor J. Katz
Paperback / softback
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A fun, entertaining exploration of the ideas and people behind the growth of trigonometry Trigonometry has a reputation as a dry, difficult branch of mathematics, a glorified form of geometry complicated by tedious computation. In Trigonometric Delights, Eli Maor dispels this view. Rejecting the usual descriptions of sine, cosine, and ...
Trigonometric Delights
A fun, entertaining exploration of the ideas and people behind the growth of trigonometry Trigonometry has a reputation as a dry, difficult branch of mathematics, a glorified form of geometry complicated by tedious computation. In Trigonometric Delights, Eli Maor dispels this view. Rejecting the usual descriptions of sine, cosine, and their trigonometric relatives, he brings the subject to life in a compelling blend of history, biography, and mathematics. From the proto-trigonometry of the Egyptian pyramid builders and the first true trigonometry developed by Greek astronomers, to the epicycles and hypocycles of the toy Spirograph, Maor presents both a survey of the main elements of trigonometry and a unique account of its vital contribution to science and social growth. A tapestry of stories, curiosities, insights, and illustrations, Trigonometric Delights irrevocably changes how we see this essential mathematical discipline.
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18.850000 USD

Trigonometric Delights

by Eli Maor
Paperback / softback
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Recently, debates about mathematical structuralism have picked up steam again within the philosophy of mathematics, probing ontological and epistemological issues in novel ways. These debates build on discussions of structuralism which began in the 1960s in the work of philosophers such as Paul Benacerraf and Hilary Putnam; going further than ...
The Prehistory of Mathematical Structuralism
Recently, debates about mathematical structuralism have picked up steam again within the philosophy of mathematics, probing ontological and epistemological issues in novel ways. These debates build on discussions of structuralism which began in the 1960s in the work of philosophers such as Paul Benacerraf and Hilary Putnam; going further than these previous thinkers, however, these new debates also recognize that the motivation for structuralist views should be tied to methodological developments within mathematics. In fact, practically all relevant ideas and methods have roots in the structuralist transformation that modern mathematics underwent in the 19th and early 20th centuries. This edited volume of new essays by top scholars in the philosophy of mathematics explores this previously overlooked 'pre-history' of mathematical structuralism. The contributors explore this historical background along two distinct but interconnected dimensions. First, they reconsider the methodological contributions of major figures in the history of mathematics, such as Dedekind, Hilbert, and Bourbaki, who are responsible for the introduction of new number systems, algebras, and geometries that transformed the landscape of mathematics. Second, they reexamine a range of philosophical reflections by mathematically inclined philosophers, like Russell, Cassirer, and Quine, whose work led to profound conclusions about logical, epistemological, and metaphysical aspects of structuralism. Overall, the essays in this volume show not only that the pre-history of mathematical structuralism is much richer than commonly appreciated, but also that it is crucial to take into account this broader intellectual history for enriching current debates in the philosophy of mathematics. The insights included in this volume will interest scholars and students in the philosophy of mathematics, the philosophy of science, and the history of philosophy.
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103.950000 USD

The Prehistory of Mathematical Structuralism

Hardback
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Exploring more than seventy-five well-known paradoxes in mathematics, philosophy, physics, and the social sciences showing how reason and logic can dispel the illusion of contradiction. Paradox is a sophisticated kind of magic trick. A magician's purpose is to create the appearance of impossibility, to pull a rabbit from an empty ...
Sleight of Mind: 75 Ingenious Paradoxes in Mathematics, Physics, and Philosophy
Exploring more than seventy-five well-known paradoxes in mathematics, philosophy, physics, and the social sciences showing how reason and logic can dispel the illusion of contradiction. Paradox is a sophisticated kind of magic trick. A magician's purpose is to create the appearance of impossibility, to pull a rabbit from an empty hat. Yet paradox doesn't require tangibles, like rabbits or hats. Paradox works in the abstract, with words and concepts and symbols, to create the illusion of contradiction. There are no contradictions in reality, but there can appear to be. In Sleight of Mind, Matt Cook and a few collaborators dive deeply into more than 75 paradoxes in mathematics, physics, philosophy, and the social sciences. As each paradox is discussed and resolved, Cook helps readers discover the meaning of knowledge and the proper formation of concepts-and how reason can dispel the illusion of contradiction. The journey begins with a most ingenious paradox from Gilbert and Sullivan's Pirates of Penzance. Readers will then travel from Ancient Greece to cutting-edge laboratories, encounter infinity and its different sizes, and discover mathematical impossibilities inherent in elections. They will tackle conundrums in probability, induction, geometry, and game theory; perform supertasks ; build apparent perpetual motion machines; meet twins living in different millennia; explore the strange quantum world-and much more.
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36.700000 USD

Sleight of Mind: 75 Ingenious Paradoxes in Mathematics, Physics, and Philosophy

by Matt Cook
Hardback
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A sophisticated, original introduction to the philosophy of mathematics from one of its leading thinkers Mathematics is a model of precision and objectivity, but it appears distinct from the empirical sciences because it seems to deliver nonexperiential knowledge of a nonphysical reality of numbers, sets, and functions. How can these ...
Philosophy of Mathematics
A sophisticated, original introduction to the philosophy of mathematics from one of its leading thinkers Mathematics is a model of precision and objectivity, but it appears distinct from the empirical sciences because it seems to deliver nonexperiential knowledge of a nonphysical reality of numbers, sets, and functions. How can these two aspects of mathematics be reconciled? This concise book provides a systematic, accessible introduction to the field that is trying to answer that question: the philosophy of mathematics. Oystein Linnebo, one of the world's leading scholars on the subject, introduces all of the classical approaches to the field as well as more specialized issues, including mathematical intuition, potential infinity, and the search for new mathematical axioms. Sophisticated but clear and approachable, this is an essential book for all students and teachers of philosophy and of mathematics.
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35.31 USD

Philosophy of Mathematics

by Oystein Linnebo
Paperback / softback
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How science changed the way artists understand reality Exploring the Invisible shows how modern art expresses the first secular, scientific worldview in human history. Now fully revised and expanded, this richly illustrated book describes two hundred years of scientific discoveries that inspired French Impressionist painters and Art Nouveau architects, as ...
Exploring the Invisible: Art, Science, and the Spiritual - Revised and Expanded Edition
How science changed the way artists understand reality Exploring the Invisible shows how modern art expresses the first secular, scientific worldview in human history. Now fully revised and expanded, this richly illustrated book describes two hundred years of scientific discoveries that inspired French Impressionist painters and Art Nouveau architects, as well as Surrealists in Europe, Latin America, and Japan. Lynn Gamwell describes how the microscope and telescope expanded the artist's vision into realms unseen by the naked eye. In the nineteenth century, a strange and exciting world came into focus, one of microorganisms in a drop of water and spiral nebulas in the night sky. The world is also filled with forces that are truly unobservable, known only indirectly by their effects-radio waves, X-rays, and sound-waves. Gamwell shows how artists developed the pivotal style of modernism-abstract, non-objective art-to symbolize these unseen worlds. Starting in Germany with Romanticism and ending with international contemporary art, she traces the development of the visual arts as an expression of the scientific worldview in which humankind is part of a natural web of dynamic forces without predetermined purpose or meaning. Gamwell reveals how artists give nature meaning by portraying it as mysterious, dangerous, or beautiful. With a foreword by Neil deGrasse Tyson and a wealth of stunning images, this expanded edition of Exploring the Invisible draws on the latest scholarship to provide a global perspective on the scientists and artists who explore life on Earth, human consciousness, and the space-time universe.
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78.11 USD

Exploring the Invisible: Art, Science, and the Spiritual - Revised and Expanded Edition

by Lynn Gamwell
Hardback
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