Infinity A Very Short Introduction
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Infinity A Very Short Introduction
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Author : Ian Stewart
language : en
Publisher: Oxford University Press
Release Date : 2017-03-16
Infinity A Very Short Introduction written by Ian Stewart and has been published by Oxford University Press this book supported file pdf, txt, epub, kindle and other format this book has been release on 2017-03-16 with Mathematics categories.
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.
Mathematics A Very Short Introduction
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Author : Timothy Gowers
language : en
Publisher: Oxford Paperbacks
Release Date : 2002-08-22
Mathematics A Very Short Introduction written by Timothy Gowers and has been published by Oxford Paperbacks this book supported file pdf, txt, epub, kindle and other format this book has been release on 2002-08-22 with Mathematics categories.
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.
Symmetry A Very Short Introduction
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Author : Ian Stewart
language : en
Publisher: OUP Oxford
Release Date : 2013-05-30
Symmetry A Very Short Introduction written by Ian Stewart and has been published by OUP Oxford this book supported file pdf, txt, epub, kindle and other format this book has been release on 2013-05-30 with Mathematics categories.
Symmetry is an immensely important concept in mathematics and throughout the sciences. In this Very Short Introduction, Ian Stewart highlights the deep implications of symmetry and its important scientific applications across the entire subject.
Nothing
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Author : Frank Close
language : en
Publisher: OUP Oxford
Release Date : 2009-06-25
Nothing written by Frank Close and has been published by OUP Oxford this book supported file pdf, txt, epub, kindle and other format this book has been release on 2009-06-25 with Philosophy categories.
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.
Trigonometry
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Author : Glen Van Brummelen
language : en
Publisher:
Release Date : 2020
Trigonometry written by Glen Van Brummelen and has been published by this book supported file pdf, txt, epub, kindle and other format this book has been release on 2020 with Mathematics categories.
Rooted in ancient astronomy, trigonometry is mathematics' powerful toolkit for scientific measurement. It has been at the heart of the study of infinity, complex and imaginary numbers, and the shape of the space itself. Our experience of the universe has been made possible, and deeply challenged, by this surprisingly deep and fruitful subject.
A Brief History Of Infinity
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Author : Brian Clegg
language : en
Publisher: Hachette UK
Release Date : 2013-02-07
A Brief History Of Infinity written by Brian Clegg and has been published by Hachette UK this book supported file pdf, txt, epub, kindle and other format this book has been release on 2013-02-07 with Mathematics categories.
'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.
Gravity A Very Short Introduction
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Author : Timothy Clifton
language : en
Publisher: Oxford University Press
Release Date : 2017-02-16
Gravity A Very Short Introduction written by Timothy Clifton and has been published by Oxford University Press this book supported file pdf, txt, epub, kindle and other format this book has been release on 2017-02-16 with Science categories.
Gravity is one of the four fundamental interactions that exist in nature. It also has the distinction of being the oldest, weakest, and most difficult force to quantize. Understanding gravity is not only essential for understanding the motion of objects on Earth, but also the motion of all celestial objects, and even the expansion of the Universe itself. It was the study of gravity that led Einstein to his profound realisations about the nature of space and time. Gravity is not only universal, it is also essential for understanding the behaviour of the Universe, and all astrophysical bodies within it. In this Very Short Introduction Timothy Clifton looks at the development of our understanding of gravity since the early observations of Kepler and Newtonian theory. He discusses Einstein's theory of gravity, which now supplants Newton's, showing how it allows us to understand why the frequency of light changes as it passes through a gravitational field, why GPS satellites need their clocks corrected as they orbit the Earth, and why the orbits of distant neutron stars speed up. Today, almost 100 years after Einstein published his theory of gravity, we have even detected the waves of gravitational radiation that he predicted. Clifton concludes by considering the testing and application of general relativity in astrophysics and cosmology, and looks at dark energy and efforts such as string theory to combine gravity with quantum mechanics. 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.
An Introduction To Infinite Products
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Author : Charles H. C. Little
language : en
Publisher: Springer Nature
Release Date : 2022-01-10
An Introduction To Infinite Products written by Charles H. C. Little and has been published by Springer Nature this book supported file pdf, txt, epub, kindle and other format this book has been release on 2022-01-10 with Mathematics categories.
This text provides a detailed presentation of the main results for infinite products, as well as several applications. The target readership is a student familiar with the basics of real analysis of a single variable and a first course in complex analysis up to and including the calculus of residues. The book provides a detailed treatment of the main theoretical results and applications with a goal of providing the reader with a short introduction and motivation for present and future study. While the coverage does not include an exhaustive compilation of results, the reader will be armed with an understanding of infinite products within the course of more advanced studies, and, inspired by the sheer beauty of the mathematics. The book will serve as a reference for students of mathematics, physics and engineering, at the level of senior undergraduate or beginning graduate level, who want to know more about infinite products. It will also be of interest to instructors who teach courses that involve infinite products as well as mathematicians who wish to dive deeper into the subject. One could certainly design a special-topics class based on this book for undergraduates. The exercises give the reader a good opportunity to test their understanding of each section.
Abstraction And Infinity
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Author : Paolo Mancosu
language : en
Publisher: Oxford University Press
Release Date : 2016
Abstraction And Infinity written by Paolo Mancosu and has been published by Oxford University Press this book supported file pdf, txt, epub, kindle and other format this book has been release on 2016 with Mathematics categories.
Mancosu offers an original investigation of key notions in mathematics: abstraction and infinity, and their interaction. He gives a historical analysis of the theorizing of definitions by abstraction, and explores a novel approach to measuring the size of infinite sets, showing how this leads to deep mathematical and philosophical problems.
History
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Author : John H. Arnold
language : en
Publisher: OUP Oxford
Release Date : 2000-02-24
History written by John H. Arnold and has been published by OUP Oxford this book supported file pdf, txt, epub, kindle and other format this book has been release on 2000-02-24 with History categories.
There are many stories we can tell about the past, and we are not, perhaps, as free as we might imagine in our choice of which stories to tell, or where those stories end. John Arnold's Very Short Introduction is a stimulating essay about how we study and understand history. The 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 how historians work, giving the reader a sense of the excitement of discovering not only the past, but also ourselves. 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.