Infinity A Very Short Introduction

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Infinity

Ian Stewart
Infinity Book PDF

Author : Ian Stewart
Publisher : Oxford University Press
Page : 161 pages
File Size : 42,7 Mb
Release : 2017
Category : Infinite
ISBN : 9780198755234

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Infinity by Ian Stewart Pdf

Infinity is an intriguing topic, with connections to religion, philosophy, metaphysics, logic, and physics as well as mathematics. Its history goes back to ancient times, with especially important contributions from Euclid, Aristotle, Eudoxus, and Archimedes. The infinitely large (infinite) isintimately related to the infinitely small (infinitesimal). Cosmologists consider sweeping questions about whether space and time are infinite. Philosophers and mathematicians ranging from Zeno to Russell have posed numerous paradoxes about infinity and infinitesimals. Many vital areas ofmathematics rest upon some version of infinity. The most obvious, and the first context in which major new techniques depended on formulating infinite processes, is calculus. But there are many others, for example Fourier analysis and fractals.In this Very Short Introduction, Ian Stewart discusses infinity in mathematics while also drawing in the various other aspects of infinity and explaining some of the major problems and insights arising from this concept. He argues that working with infinity is not just an abstract, intellectualexercise but that it is instead a concept with important practical everyday applications, and considers how mathematicians use infinity and infinitesimals to answer questions or supply techniques that do not appear to involve the infinite.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, andenthusiasm to make interesting and challenging topics highly readable.

Mathematics: A Very Short Introduction

Timothy Gowers
Mathematics A Very Short Introduction Book PDF

Author : Timothy Gowers
Publisher : Oxford Paperbacks
Page : 172 pages
File Size : 50,9 Mb
Release : 2002-08-22
Category : Mathematics
ISBN : 0192853619

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Mathematics: A Very Short Introduction by Timothy Gowers Pdf

The aim of this volume is to explain the differences between research-level mathematics and the maths taught at school. Most differences are philosophical and the first few chapters are about general aspects of mathematical thought.

A Brief History of Infinity

Brian Clegg
A Brief History of Infinity Book PDF

Author : Brian Clegg
Publisher : Robinson
Page : 185 pages
File Size : 49,7 Mb
Release : 2013-02-07
Category : Mathematics
ISBN : 9781472107640

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A Brief History of Infinity by Brian Clegg Pdf

'Space is big. Really big. You just won't believe how vastly, hugely, mind-bogglingly big it is. I mean, you may think it's a long way down the street to the chemist, but that's just peanuts to space.' Douglas Adams, Hitch-hiker's Guide to the Galaxy We human beings have trouble with infinity - yet infinity is a surprisingly human subject. Philosophers and mathematicians have gone mad contemplating its nature and complexity - yet it is a concept routinely used by schoolchildren. Exploring the infinite is a journey into paradox. Here is a quantity that turns arithmetic on its head, making it feasible that 1 = 0. Here is a concept that enables us to cram as many extra guests as we like into an already full hotel. Most bizarrely of all, it is quite easy to show that there must be something bigger than infinity - when it surely should be the biggest thing that could possibly be. Brian Clegg takes us on a fascinating tour of that borderland between the extremely large and the ultimate that takes us from Archimedes, counting the grains of sand that would fill the universe, to the latest theories on the physical reality of the infinite. Full of unexpected delights, whether St Augustine contemplating the nature of creation, Newton and Leibniz battling over ownership of calculus, or Cantor struggling to publicise his vision of the transfinite, infinity's fascination is in the way it brings together the everyday and the extraordinary, prosaic daily life and the esoteric. Whether your interest in infinity is mathematical, philosophical, spiritual or just plain curious, this accessible book offers a stimulating and entertaining read.

Infinity: A Very Short Introduction

Ian Stewart
Infinity A Very Short Introduction Book PDF

Author : Ian Stewart
Publisher : Oxford University Press
Page : 144 pages
File Size : 44,7 Mb
Release : 2017-03-13
Category : Mathematics
ISBN : 9780191071515

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Infinity: A Very Short Introduction by Ian Stewart Pdf

Infinity is an intriguing topic, with connections to religion, philosophy, metaphysics, logic, and physics as well as mathematics. Its history goes back to ancient times, with especially important contributions from Euclid, Aristotle, Eudoxus, and Archimedes. The infinitely large (infinite) is intimately related to the infinitely small (infinitesimal). Cosmologists consider sweeping questions about whether space and time are infinite. Philosophers and mathematicians ranging from Zeno to Russell have posed numerous paradoxes about infinity and infinitesimals. Many vital areas of mathematics rest upon some version of infinity. The most obvious, and the first context in which major new techniques depended on formulating infinite processes, is calculus. But there are many others, for example Fourier analysis and fractals. In this Very Short Introduction, Ian Stewart discusses infinity in mathematics while also drawing in the various other aspects of infinity and explaining some of the major problems and insights arising from this concept. He argues that working with infinity is not just an abstract, intellectual exercise but that it is instead a concept with important practical everyday applications, and considers how mathematicians use infinity and infinitesimals to answer questions or supply techniques that do not appear to involve the infinite. 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.

Symmetry: A Very Short Introduction

Ian Stewart
Symmetry A Very Short Introduction Book PDF

Author : Ian Stewart
Publisher : OUP Oxford
Page : 152 pages
File Size : 48,5 Mb
Release : 2013-05-30
Category : Mathematics
ISBN : 9780191652745

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Symmetry: A Very Short Introduction by Ian Stewart Pdf

In the 1800s mathematicians introduced a formal theory of symmetry: group theory. Now a branch of abstract algebra, this subject first arose in the theory of equations. Symmetry is an immensely important concept in mathematics and throughout the sciences, and its applications range across the entire subject. Symmetry governs the structure of crystals, innumerable types of pattern formation, how systems change their state as parameters vary; and fundamental physics is governed by symmetries in the laws of nature. It is highly visual, with applications that include animal markings, locomotion, evolutionary biology, elastic buckling, waves, the shape of the Earth, and the form of galaxies. In this Very Short Introduction, Ian Stewart demonstrates its deep implications, and shows how it plays a major role in the current search to unify relativity and quantum theory. 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.

Game Theory: A Very Short Introduction

Ken Binmore
Game Theory A Very Short Introduction Book PDF

Author : Ken Binmore
Publisher : Oxford University Press
Page : 201 pages
File Size : 49,9 Mb
Release : 2007-10-25
Category : Business & Economics
ISBN : 9780199218462

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Game Theory: A Very Short Introduction by Ken Binmore Pdf

Games are played everywhere: from economics to evolutionary biology, and from social interactions to online auctions. This title shows how to play such games in a rational way, and how to maximize their outcomes.

Nothing: A Very Short Introduction

Frank Close
Nothing A Very Short Introduction Book PDF

Author : Frank Close
Publisher : OUP Oxford
Page : 177 pages
File Size : 44,8 Mb
Release : 2009-06-25
Category : Philosophy
ISBN : 9780191574641

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Nothing: A Very Short Introduction by Frank Close Pdf

What is 'nothing'? What remains when you take all the matter away? Can empty space - a void - exist? This Very Short Introduction explores the science and the history of the elusive void: from Aristotle who insisted that the vacuum was impossible, via the theories of Newton and Einstein, to our very latest discoveries and why they can tell us extraordinary things about the cosmos. Frank Close tells the story of how scientists have explored the elusive void, and the rich discoveries that they have made there. He takes the reader on a lively and accessible history through ancient ideas and cultural superstitions to the frontiers of current research. He describes how scientists discovered that the vacuum is filled with fields; how Newton, Mach, and Einstein grappled with the nature of space and time; and how the mysterious 'aether' that was long ago supposed to permeate the void may now be making a comeback with the latest research into the 'Higgs field'. We now know that the vacuum is far from being empty - it seethes with virtual particles and antiparticles that erupt spontaneously into being, and it also may contain hidden dimensions that we were previously unaware of. These new discoveries may provide answers to some of cosmology's most fundamental questions: what lies outside the universe, and, if there was once nothing, then how did the universe begin? 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.

The Beginning of Infinity

David Deutsch
The Beginning of Infinity Book PDF

Author : David Deutsch
Publisher : Penguin UK
Page : 571 pages
File Size : 48,5 Mb
Release : 2011-03-31
Category : Science
ISBN : 9780141969695

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The Beginning of Infinity by David Deutsch Pdf

'Science has never had an advocate quite like David Deutsch ... A computational physicist on a par with his touchstones Alan Turing and Richard Feynman, and a philosopher in the line of his greatest hero, Karl Popper. His arguments are so clear that to read him is to experience the thrill of the highest level of discourse available on this planet and to understand it' Peter Forbes, Independent In our search for truth, how far have we advanced? This uniquely human quest for good explanations has driven amazing improvements in everything from scientific understanding and technology to politics, moral values and human welfare. But will progress end, either in catastrophe or completion - or will it continue infinitely? In this profound and seminal book, David Deutsch explores the furthest reaches of our current understanding, taking in the Infinity Hotel, supernovae and the nature of optimism, to instill in all of us a wonder at what we have achieved - and the fact that this is only the beginning of humanity's infinite possibility. 'This is Deutsch at his most ambitious, seeking to understand the implications of our scientific explanations of the world ... I enthusiastically recommend this rich, wide-ranging and elegantly written exposition of the unique insights of one of our most original intellectuals' Michael Berry, Times Higher Education Supplement 'Bold ... profound ... provocative and persuasive' Economist 'David Deutsch may well go down in history as one of the great scientists of our age' Scotsman

Numbers: A Very Short Introduction

Peter M. Higgins
Numbers A Very Short Introduction Book PDF

Author : Peter M. Higgins
Publisher : Oxford University Press
Page : 153 pages
File Size : 46,9 Mb
Release : 2011-02-24
Category : Mathematics
ISBN : 9780199584055

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Numbers: A Very Short Introduction by Peter M. Higgins Pdf

In this Very Short Introduction Peter M. Higgins presents an overview of the number types featured in modern science and mathematics. Providing a non-technical account, he explores the evolution of the modern number system, examines the fascinating role of primes, and explains their role in contemporary cryptography.

From Here to Infinity

Ian Stewart
From Here to Infinity Book PDF

Author : Ian Stewart
Publisher : Oxford Paperbacks
Page : 338 pages
File Size : 48,8 Mb
Release : 1996
Category : Mathematics
ISBN : 9780192832023

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From Here to Infinity by Ian Stewart Pdf

A retitled and revised edition of Ian Stewart's The Problem of Mathematics, this is the perfect guide to today's mathematics. Read about the latest discoveries, including Andrew Wile's amazing proof of Fermat's Last Theorem, the newest advances in knot theory, the Four Colour Theorem, Chaos Theory, and fake four-dimensial spaces. See how simple concepts from probability theory shed light on the National Lottery and tell you how to maximize your winnings. Discover howinfinitesimals become respectable, why there are different kinds of infinity, and how to square the circle with the mathematical equivalent of a pair of scissors.

Topology

Richard Earl
Topology Book PDF

Author : Richard Earl
Publisher : Oxford University Press, USA
Page : 169 pages
File Size : 47,5 Mb
Release : 2020-01-11
Category : MATHEMATICS
ISBN : 9780198832683

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Topology by Richard Earl Pdf

How is a subway map different from other maps? What makes a knot knotted? What makes the M�bius strip one-sided? These are questions of topology, the mathematical study of properties preserved by twisting or stretching objects. In the 20th century topology became as broad and fundamental as algebra and geometry, with important implications for science, especially physics. In this Very Short Introduction Richard Earl gives a sense of the more visual elements of topology (looking at surfaces) as well as covering the formal definition of continuity. Considering some of the eye-opening examples that led mathematicians to recognize a need for studying topology, he pays homage to the historical people, problems, and surprises that have propelled the growth of this field. 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.

Trigonometry: A Very Short Introduction

Glen Van Brummelen
Trigonometry A Very Short Introduction Book PDF

Author : Glen Van Brummelen
Publisher : Oxford University Press
Page : 193 pages
File Size : 50,7 Mb
Release : 2020-01-23
Category : Mathematics
ISBN : 9780192545473

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Trigonometry: A Very Short Introduction by Glen Van Brummelen Pdf

Born of the desire to understand the workings of motions of the heavenly bodies, trigonometry gave the ancient Greeks the ability to predict their futures. Most of what we see of the subject in school comes from these heavenly origins; 15th century astronomer Regiomontanus called it "the foot of the ladder to the stars". In this Very Short Introduction Glen Van Brummelen shows how trigonometry connects mathematics to science, and has today become an indispensable tool in predicting cyclic patterns like animal populations and ocean tides. Its historical journey through major cultures such as medieval India and the Islamic World has taken it through disciplines such as geography and even religious practice. Trigonometry has also been a major player in the most startling mathematical developments of the modern world. Its interactions with the concept of infinity led to Taylor and Fourier series, some of the most practical tools of modern science. The birth of complex numbers led to a shocking union of exponential and trigonometric functions, creating the most beautiful formulas and powerful modelling tools in science. Finally, as Van Brummelen shows, trigonometry allows us to explore the strange new worlds of non-Euclidean geometries, opening up bizarre possibilities for the shape of space itself. And indeed, one of those new geometries - spherical - takes us full circle back to ancient Greek astronomers and European navigators, who first used it to chart their ways across the heavens and the earth. 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.

Real Analysis and Infinity

Hassan Sedaghat
Real Analysis and Infinity Book PDF

Author : Hassan Sedaghat
Publisher : Oxford University Press
Page : 464 pages
File Size : 49,8 Mb
Release : 2022-03-07
Category : Mathematics
ISBN : 9780192649539

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Real Analysis and Infinity by Hassan Sedaghat Pdf

Real Analysis and Infinity presents the essential topics for a first course in real analysis with an emphasis on the role of infinity in all of the fundamental concepts. After introducing sequences of numbers, it develops the set of real numbers in terms of Cauchy sequences of rational numbers, and uses this development to derive the important properties of real numbers like completeness. The book then develops the concepts of continuity, derivative, and integral, and presents the theory of infinite sequences and series of functions. Topics discussed are wide-ranging and include the convergence of sequences, definition of limits and continuity via converging sequences, and the development of derivative. The proofs of the vast majority of theorems are presented and pedagogical considerations are given priority to help cement the reader's knowledge. Preliminary discussion of each major topic is supplemented with examples and diagrams, and historical asides. Examples follow most major results to improve comprehension, and exercises at the end of each chapter help with the refinement of proof and calculation skills.

Critical Theory

Stephen Eric Bronner
Critical Theory Book PDF

Author : Stephen Eric Bronner
Publisher : Oxford University Press
Page : 161 pages
File Size : 52,7 Mb
Release : 2017
Category : Philosophy
ISBN : 9780190692674

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Critical Theory by Stephen Eric Bronner Pdf

Secondary edition statement from sticker on cover.

Basics Box

Oxford
Basics Box Book PDF

Author : Oxford
Publisher : Unknown
Page : 0 pages
File Size : 46,8 Mb
Release : 2006-11
Category : History
ISBN : 0199209065

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Basics Box by Oxford Pdf

Books that are perfect to pop in your pocket now packaged to make the ideal gift!Five of the best-selling introductory books from the highly acclaimed Very Short Introductions series packaged in a stylish case to make the ideal gift or way-in to five of the most important subjects.This boxed set gives a great introduction to five key subjects: politics, mathematics, philosophy, psychology, and history.Philosophy: A Very Short Introduction by Edward CraigISBN-10: 0-19-285421-6/ ISBN-13 978-0-19-285421-6'[The Very Short Introduction to Philosophy] shows that philosophy really can be fascinating, broad-minded and full of surprise. As a means of stimulating interest in the subject it has few rivals.' Julian Baggini, The Philosopher's MagazineMathematics: A Very Short Introduction by Timothy GowersISBN-10: 0-19-285361-9/ ISBN-13 978-0-19-285361-5'a marvellously lucid guide to the beauty and mystery of numbers' Gilbert AdairThis book explains, carefully but not technically, the differences between advanced, research-level mathematics, and the sort of mathematics we learn at school. The most fundamental differences are philosophical, and readers of this book will emerge with a clearer understanding ofparadoxical-sounding concepts such as infinity, curved space, and imaginary numbers.History: A Very Short Introduction by John ArnoldISBN-10: 0-19-285352-X/ ISBN-13 978-0-19-285352-3The book begins by inviting us to think about various questions provoked by our investigation of history, and explores the ways these questions have been answered in the past. Concepts such as causation, interpretation, and periodization, are introduced by means of concrete examples of howhistorians work, to give a sense of the excitement of discovering not only the past, but also ourselves.Politics: A Very Short Introduction by Kenneth Minogue ISBN-10: 0-19-285388-0/ ISBN-13: 978-0-19-285388-2In this provocative but balanced essay, Kenneth Minogue discusses the development of politics from the ancient world to the twentieth century. He prompts us to consider why political systems evolve, how politics offers both power and order in our society, whether democracy is always a good thing,and what future politics may have in the twenty-first century.Psychology: A Very Short Introduction by Gilian Butler and Freda McManusISBN-10: 0-19-285381-3/ ISBN-13: 978-0-19-285381-3Psychology is part of everyone's experience: it influences the way we think about everything from education and intelligence, to relationships and emotions, advertising and criminality. But what exactly are psychologists trying to do? This book provides an understanding of some of psychology'sleading ideas and their practical relevance, making it a stimulating introduction for anyone interested in understanding the human mind.