Infinity: a Very Short Introduction

Author: Ian Stewart

Publisher: Oxford University Press

ISBN: 0198755236

Category: Mathematics

Page: 144

View: 5013

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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.

Symmetry: A Very Short Introduction

Author: Ian Stewart

Publisher: OUP Oxford

ISBN: 0199651981

Category: Mathematics

Page: 160

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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.

Mathematics: A Very Short Introduction

Author: Timothy Gowers

Publisher: OUP Oxford

ISBN: 9780191579417

Category: Mathematics

Page: 160

View: 5501

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The aim of this book is to explain, 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 of paradoxical-sounding concepts such as infinity, curved space, and imaginary numbers. The first few chapters are about general aspects of mathematical thought. These are followed by discussions of more specific topics, and the book closes with a chapter answering common sociological questions about the mathematical community (such as "Is it true that mathematicians burn out at the age of 25?") 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.

Numbers: A Very Short Introduction

Author: Peter M. Higgins

Publisher: Oxford University Press

ISBN: 0199584052

Category: Mathematics

Page: 132

View: 5397

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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.

Deserts: A Very Short Introduction

Author: Nick Middleton

Publisher: Oxford University Press

ISBN: 0199564302

Category: Nature

Page: 135

View: 9694

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In this Very Short Introduction Nick Middleton tells the story of the desert, demonstrating its beautiful landscapes and remarkable climates. He challenges the common notion that they are dry and barren and uncovers fascinating life-forms, a rich biodiversity, and a long history of human habitation.

Fractals: A Very Short Introduction

Author: K. J. Falconer

Publisher: Oxford University Press

ISBN: 0199675988

Category: Mathematics

Page: 132

View: 1867

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An essential discussion of the popular science and mathematics behind fractals reveals how fractal shapes can be found everywhere in nature from clouds to coastlines, explaining how basic concepts in fractal geometry produced a revolution in mathematical understandings of patterns in the 20th century. Original.

Gravity: A Very Short Introduction

Author: Timothy Clifton

Publisher: Oxford University Press

ISBN: 0191045330

Category: Science

Page: 144

View: 4541

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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.

Marine Biology: A Very Short Introduction

Author: Philip V. Mladenov

Publisher: Oxford University Press

ISBN: 0199695059

Category: Science

Page: 156

View: 8011

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In this Very Short Introduction, Philip Mladenov provides a fascinating overview of marine biology. Including a tour of marine life and marine processes that ranges from the polar oceans to tropical coral reefs, he outlines the principles of marine biology whilst demonstrating the fundamental impact humans have on the oceans and their ecology.

Algebra: A Very Short Introduction

Author: Peter M. Higgins

Publisher: OUP Oxford

ISBN: 0191047465

Category: Mathematics

Page: 144

View: 8555

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Algebra marked the beginning of modern mathematics, moving it beyond arithmetic, which involves calculations featuring given numbers, to problems where some quantities are unknown. Now, it stands as a pillar of mathematics, underpinning the quantitative sciences, both social and physical. This Very Short Introduction explains algebra from scratch. Over the course of ten logical chapters, Higgins offers a step by step approach for readers keen on developing their understanding of algebra. Using theory and example, he renews the reader's aquaintance with school mathematics, before taking them progressively further and deeper into the subject. 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.

Navigation

Author: Jim Bennett

Publisher: Oxford University Press

ISBN: 0198733712

Category: History

Page: 144

View: 3756

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From the Bronze Age mariners of the Mediterranean to contemporary sailors using satellite-based technologies, the history of navigation at sea, the art of finding a position and setting a course, is fascinating. The scientific and technological developments that have enabled accurate measurements of position were central to exploration, trade, and the opening up of new continents, and the resulting journeys taken under their influence have had a profound influence on world history. In this Very Short Introduction Jim Bennett looks at the history of navigation, starting with the distinctive cultures of navigation that are defined geographically - the Mediterranean Sea, and the Pacific, Indian, and Atlantic Oceans. He shows how the adoption of mathematical methods, the use of instruments, the writing of textbooks and the publication of charts all combined to create a more standardized practice. Methods such as longitude-finding by chronometer and lunar distance were complemented by the routine business of recording courses and reckoning position 'by account'. Bennett also introduces the incredible array of instruments relied on by sailors, from astrolabes, sextants, and chronometers, to our more modern radio receivers, electronic equipment, and charts, and highlights the crucial role played by the individual qualities of endeavor and resourcefulness from mathematicians, scientists, and seamen in finding their way at sea. The story of navigation combines the societal, the technical, and the human, and it was vital for shaping the modern world.

Nothing: A Very Short Introduction

Author: Frank Close

Publisher: Oxford University Press

ISBN: 0199225869

Category: History

Page: 157

View: 5385

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An exploration of the concept of "nothing" journeys from ancient ideas and cultural traditions to the latest scientific research, discussing the history of the vacuum, theories on the nature of time and space, and other discoveries.

Philosophy in the Islamic World

A Very Short Introduction

Author: Peter Adamson

Publisher: Oxford University Press, USA

ISBN: 0199683670

Category: Philosophy

Page: 144

View: 421

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In the history of philosophy, few topics are so relevant to today's cultural and political landscape as philosophy in the Islamic world. Yet, this remains one of the lesser-known philosophical traditions. In this Very Short Introduction, Peter Adamson explores the history of philosophy among Muslims, Jews, and Christians living in Islamic lands, from its historical background to thinkers in the twentieth century. Introducing the main philosophical themes of the Islamic world, Adamson integrates ideas from the Islamic and Abrahamic faiths to consider the broad philosophical questions that continue to invite debate: What is the relationship between reason and religious belief? What is the possibility of proving God's existence? What is the nature of knowledge? Drawing on the most recent research in the field, this book challenges the assumption of the cultural decline of philosophy and science in the Islamic world by demonstrating its rich heritage and overlap with other faiths and philosophies. 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 History of Time: A Very Short Introduction

Author: Leofranc Holford-Strevens

Publisher: OUP Oxford

ISBN: 0191578002

Category: History

Page: 160

View: 7007

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Why do we measure time in the way that we do? Why is a week seven days long? At what point did minutes and seconds come into being? Why are some calendars lunar and some solar? The organisation of time into hours, days, months and years seems immutable and universal, but is actually far more artificial than most people realise. The French Revolution resulted in a restructuring of the French calendar, and the Soviet Union experimented with five and then six-day weeks. Leofranc Holford-Strevens explores these questions using a range of fascinating examples from Ancient Rome and Julius Caesar's imposition of the Leap Year, to the 1920s' project for a fixed Easter. 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.

Economics: A Very Short Introduction

Author: Partha Dasgupta

Publisher: OUP Oxford

ISBN: 9780191578281

Category: Business & Economics

Page: 192

View: 3130

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Economics has the capacity to offer us deep insights into some of the most formidable problems of life, and offer solutions to them too. Combining a global approach with examples from everyday life, Partha Dasgupta describes the lives of two children who live very different lives in different parts of the world: in the Mid-West USA and in Ethiopia. He compares the obstacles facing them, and the processes that shape their lives, their families, and their futures. He shows how economics uncovers these processes, finds explanations for them, and how it forms policies and solutions. Along the way, Dasgupta provides an intelligent and accessible introduction to key economic factors and concepts such as individual choices, national policies, efficiency, equity, development, sustainability, dynamic equilibrium, property rights, markets, and public goods. 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.

Logic: A Very Short Introduction

Author: Graham Priest

Publisher: Oxford University Press

ISBN: 0192539701

Category: Philosophy

Page: 152

View: 439

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Logic is often perceived as having little to do with the rest of philosophy, and even less to do with real life. In this lively and accessible introduction, Graham Priest shows how wrong this conception is. He explores the philosophical roots of the subject, explaining how modern formal logic deals with issues ranging from the existence of God and the reality of time to paradoxes of probability and decision theory. Along the way, the basics of formal logic are explained in simple, non-technical terms, showing that logic is a powerful and exciting part of modern philosophy. In this new edition Graham Priest expands his discussion to cover the subjects of algorithms and axioms, and proofs in mathematics. 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 Great Mathematical Problems

Author: Ian Stewart

Publisher: Profile Books

ISBN: 1847653510

Category: Mathematics

Page: 340

View: 9864

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There are some mathematical problems whose significance goes beyond the ordinary - like Fermat's Last Theorem or Goldbach's Conjecture - they are the enigmas which define mathematics. The Great Mathematical Problems explains why these problems exist, why they matter, what drives mathematicians to incredible lengths to solve them and where they stand in the context of mathematics and science as a whole. It contains solved problems - like the Poincar Conjecture, cracked by the eccentric genius Grigori Perelman, who refused academic honours and a million-dollar prize for his work, and ones which, like the Riemann Hypothesis, remain baffling after centuries. Stewart is the guide to this mysterious and exciting world, showing how modern mathematicians constantly rise to the challenges set by their predecessors, as the great mathematical problems of the past succumb to the new techniques and ideas of the present.

From Here to Infinity

Author: Ian Stewart

Publisher: Oxford Paperbacks

ISBN: 9780192832023

Category: Literary Criticism

Page: 310

View: 4633

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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.

A Brief History of Mathematical Thought

Author: Luke Heaton

Publisher: Oxford University Press

ISBN: 0190621761

Category: Math anxiety

Page: 336

View: 4822

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Emblazoned on many advertisements for the wildly popular game of Sudoku are the reassuring words, "no mathematical knowledge required." Anxiety about math plagues many of us, and school memories can still summon intense loathing. In A Brief History of Mathematical Thought, Luke Heaton shows that much of what many think-and fear-about mathematics is misplaced, and to overcome our insecurities we need to understand its history. To help, he offers a lively guide into and through the world of mathematics and mathematicians, one in which patterns and arguments are traced through logic in a language grounded in concrete experience. Heaton reveals how Greek and Roman mathematicians like Pythagoras, Euclid, and Archimedes helped shaped the early logic of mathematics; how the Fibonacci sequence, the rise of algebra, and the invention of calculus are connected; how clocks, coordinates, and logical padlocks work mathematically; and how, in the twentieth century, Alan Turing's revolutionary work on the concept of computation laid the groundwork for the modern world. A Brief History of Mathematical Thought situates mathematics as part of, and essential to, lived experience. Understanding it requires not abstract thought or numbing memorization but an historical imagination and a view to its origins. --

Combinatorics

A Very Short Introduction

Author: Robin Wilson

Publisher: Oxford University Press

ISBN: 0198723490

Category: Mathematics

Page: 144

View: 3107

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How many possible sudoku puzzles are there? In the lottery, what is the chance that two winning balls have consecutive numbers? Who invented Pascal's triangle? (it was not Pascal) Combinatorics, the branch of mathematics concerned with selecting, arranging, and listing or counting collections of objects, works to answer all these questions. Dating back some 3000 years, and initially consisting mainly of the study of permutations and combinations, its scope has broadened to include topics such as graph theory, partitions of numbers, block designs, design of codes, and latin squares. In this Very Short Introduction Robin Wilson gives an overview of the field and its applications in mathematics and computer theory, considering problems from the shortest routes covering certain stops to the minimum number of colours needed to colour a map with different colours for neighbouring countries. 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

Author: Ken Binmore

Publisher: Oxford University Press

ISBN: 0199218463

Category: Business & Economics

Page: 184

View: 9888

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Games are everywhere: Drivers maneuvering in heavy traffic are playing a driving game. Bargain hunters bidding on eBay are playing an auctioning game. The supermarket's price for corn flakes is decided by playing an economic game. This Very Short Introduction offers a succinct tour of the fascinating world of game theory, a ground-breaking field that analyzes how to play games in a rational way. Ken Binmore, a renowned game theorist, explains the theory in a way that is both entertaining and non-mathematical yet also deeply insightful, revealing how game theory can shed light on everything from social gatherings, to ethical decision-making, to successful card-playing strategies, to calculating the sex ratio among bees. With mini-biographies of many fascinating, and occasionally eccentric, founders of the subject--including John Nash, subject of the movie A Beautiful Mind--this book offers a concise overview of a cutting-edge field that has seen spectacular successes in evolutionary biology and economics, and is beginning to revolutionize other disciplines from psychology to political science. About the Series: Oxford's Very Short Introductions offers concise and original introductions to a wide range of subjects--from Islam to Sociology, Politics to Classics, and Literary Theory to History. Not simply a textbook of definitions, each volume provides trenchant and provocative--yet always balanced and complete--discussions of the central issues in a given topic. Every Very Short Introduction gives a readable evolution of the subject in question, demonstrating how it has developed and influenced society. Whatever the area of study, whatever the topic that fascinates the reader, the series has a handy and affordable guide that will likely prove indispensable.