Numbers: A Very Short Introduction


Author: Peter M. Higgins
Publisher: Oxford University Press
ISBN: 0199584052
Category: Mathematics
Page: 132
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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.

Algebra

A Very Short Introduction
Author: Peter M. Higgins
Publisher: Oxford University Press, USA
ISBN: 0198732821
Category: Algebra
Page: 144
View: 1144

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This introduction invites readers to revisit algebra and appreciate the elegance and power of equations and inequalities. Offering a clear explanation of algebra through theory and example, Higgins shows how equations lead to complex numbers, matrices, groups, rings, and fields.--

Mathematics: A Very Short Introduction


Author: Timothy Gowers
Publisher: OUP Oxford
ISBN: 9780191579417
Category: Mathematics
Page: 160
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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.

Statistics: A Very Short Introduction


Author: David J. Hand
Publisher: OUP Oxford
ISBN: 0191578924
Category: Mathematics
Page: 136
View: 9440

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Modern statistics is very different from the dry and dusty discipline of the popular imagination. In its place is an exciting subject which uses deep theory and powerful software tools to shed light and enable understanding. And it sheds this light on all aspects of our lives, enabling astronomers to explore the origins of the universe, archaeologists to investigate ancient civilisations, governments to understand how to benefit and improve society, and businesses to learn how best to provide goods and services. Aimed at readers with no prior mathematical knowledge, this Very Short Introduction explores and explains how statistics work, and how we can decipher them. 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


Author: Ian Stewart
Publisher: OUP Oxford
ISBN: 0199651981
Category: Mathematics
Page: 160
View: 1963

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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.

Probability: A Very Short Introduction


Author: John Haigh
Publisher: Oxford University Press
ISBN: 0199588481
Category: Mathematics
Page: 128
View: 2526

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Making good decisions under conditions of uncertainty requires an appreciation of the way random chance works. In this Very Short Introduction, John Haigh provides a brief account of probability theory; explaining the philosophical approaches, discussing probability distributions, and looking its applications in science and economics.

Logic: A Very Short Introduction


Author: Graham Priest
Publisher: Oxford University Press
ISBN: 0192539701
Category: Philosophy
Page: 152
View: 1750

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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.

Taxation: A Very Short Introduction


Author: Stephen Smith
Publisher: OUP Oxford
ISBN: 019150663X
Category: Law
Page: 144
View: 6173

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Taxation is crucial to the functioning of the modern state. Tax revenues pay for public services - roads, the courts, defence, welfare assistance to the poor and elderly, and in many countries much of health care and education too. More than one third of national income in the industrialized (OECD) countries is on average taken in taxation. Taxes affect individuals in many ways. Taxes paid on income and spending directly reduce taxpayer disposable income, taxpayers face the hassle of tax returns and making payments, and they may be anxious about the possibility of investigation and enforcement action. People also adapt their activities in various ways to reduce the impact of taxation - putting money into tax-free savings accounts, or making shopping trips to other countries where taxes are lower. Taxation is therefore central to politics and public debate. Politicians that make reckless campaign promises about taxation then have to live with the uncomfortable consequences if elected. Businesses lobby for tax breaks that they claim will create jobs and prosperity. In this Very Short Introduction Stephen Smith shows how taxes have real effects on citizens and the economy that tax policy-makers have to balance. Although tax policy will always be a highly political issue, he argues that public decisions about taxation would be improved by a better understanding of the role of taxation, and of the nature and effects of different taxes. 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.

Combinatorics

A Very Short Introduction
Author: Robin Wilson
Publisher: Oxford University Press
ISBN: 0198723490
Category: Mathematics
Page: 144
View: 904

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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.

Fractals: A Very Short Introduction


Author: K. J. Falconer
Publisher: Oxford University Press
ISBN: 0199675988
Category: Mathematics
Page: 132
View: 6624

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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.

Cryptography: A Very Short Introduction


Author: Fred Piper,Sean Murphy
Publisher: OUP Oxford
ISBN: 0191577758
Category: Mathematics
Page: 160
View: 1028

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This book is a clear and informative introduction to cryptography and data protection - subjects of considerable social and political importance. It explains what algorithms do, how they are used, the risks associated with using them, and why governments should be concerned. Important areas are highlighted, such as Stream Ciphers, block ciphers, public key algorithms, digital signatures, and applications such as e-commerce. This book highlights the explosive impact of cryptography on modern society, with, for example, the evolution of the internet and the introduction of more sophisticated banking methods. 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.

Applied Mathematics


Author: Alain Goriely
Publisher: Oxford University Press
ISBN: 0198754043
Category: Mathematics
Page: 168
View: 9852

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Mathematics is playing an increasingly important role in society and the sciences, enhancing our ability to use models and handle data. While pure mathematics is mostly interested in abstract structures, applied mathematics sits at the interface between this abstract world and the world in which we live. This area of mathematics takes its nourishment from society and science and, in turn, provides a unified way to understand problems arising in diverse fields. This Very Short Introduction presents a compact yet comprehensive view of the field of applied mathematics, and explores its relationships with (pure) mathematics, science, and engineering. Explaining the nature of applied mathematics, Alain Goriely discusses its early achievements in physics and engineering, and its development as a separate field after World War II. Using historical examples, current applications, and challenges, Goriely illustrates the particular role that mathematics plays in the modern sciences today and its far-reaching potential. 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.

History: A Very Short Introduction


Author: John Arnold
Publisher: Oxford Paperbacks
ISBN: 019285352X
Category: History
Page: 134
View: 5864

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Starting with an examination of how historians work, this "Very Short Introduction" aims to explore history in a general, pithy, and accessible manner, rather than to delve into specific periods.

Infinity: a Very Short Introduction


Author: Ian Stewart
Publisher: Oxford University Press
ISBN: 0198755236
Category: Mathematics
Page: 144
View: 2299

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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.

Particle Physics: A Very Short Introduction


Author: Frank Close
Publisher: OUP Oxford
ISBN: 0191516856
Category: Science
Page: 160
View: 7648

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In this compelling introduction to the fundamental particles that make up the universe, Frank Close takes us on a journey into the atom to examine known particles such as quarks, electrons, and the ghostly neutrino. Along the way he provides fascinating insights into how discoveries in particle physics have actually been made, and discusses how our picture of the world has been radically revised in the light of these developments. He concludes by looking ahead to new ideas about the mystery of antimatter, the number of dimensions that there might be in the universe, and to what the next 50 years of research might reveal. 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 Palestinian-Israeli Conflict: A Very Short Introduction


Author: Martin Bunton,Martin P. Bunton
Publisher: Oxford University Press
ISBN: 0199603936
Category: History
Page: 132
View: 9292

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"The conflict between Palestine and Israel is one of the most highly publicized and bitter struggles of modern times, a dangerous tinderbox always poised to set the Middle East aflame, and to draw the United States into the fire. In this volume the author illuminates the history of the problem, reducing it to its very essence. He explores the Palestinian-Israeli dispute in twenty-year segments, to highlight the historical complexity of the conflict throughout successive decades. Each chapter starts with an examination of the relationships among people and events that marked particular years as historical stepping stones in the evolution of the conflict, including the 1897 Basel Congress, the 1917 Balfour Declaration and British occupation of Palestine, and the 1947 U.N. Partition Plan and the war for Palestine. Providing an exploration of the main issues, the author explores not only the historical basis of the conflict, but also looks at how and why partition has been so difficult and how efforts to restore peace continue today"--OCLC

The History of Mathematics: A Very Short Introduction


Author: Jacqueline Stedall
Publisher: OUP Oxford
ISBN: 0191633968
Category: Mathematics
Page: 144
View: 5693

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Mathematics is a fundamental human activity that can be practised and understood in a multitude of ways; indeed, mathematical ideas themselves are far from being fixed, but are adapted and changed by their passage across periods and cultures. In this Very Short Introduction, Jacqueline Stedall explores the rich historical and cultural diversity of mathematical endeavour from the distant past to the present day. Arranged thematically, to exemplify the varied contexts in which people have learned, used, and handed on mathematics, she also includes illustrative case studies drawn from a range of times and places, including early imperial China, the medieval Islamic world, and nineteenth-century Britain. 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.

International Migration: A Very Short Introduction


Author: Khalid Koser
Publisher: Oxford University Press
ISBN: 0191068268
Category: Social Science
Page: 152
View: 2347

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In recent years, global migration has transformed in terms of its numbers and reach, its political significance, and its impact. The rising rates of international migration have been matched by growing public and media interest around the world. Today, the political and media attention on migration and greater public interest and concern feed into an international debate that is all too often poorly informed and one-sided. This Very Short Introduction looks at the phenomenon of international human migration - both legal and illegal - and offers an objective stance on the topic, and its benefits and challenges. Khalid Koser reveals the opportunities migration presents that must be taken advantage of in the current economic climate, and debunks common myths to demonstrate that society, as we now know it, cannot function without migrants. Using interviews with migrants from around the world, Koser presents the human side of issues such as asylum, human trafficking, migrant smuggling, and the international labour force, inviting readers to come to their own conclusions on the international migration situation today. 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.

Objectivity: A Very Short Introduction


Author: Stephen Gaukroger
Publisher: Oxford University Press
ISBN: 0199606692
Category: Philosophy
Page: 112
View: 1964

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Objectivity is both an essential and elusive philosophical concept. This Very Short Introduction explores the theoretical and practical problems raised by objectivity, and also deals with the way in which particular understandings of objectivity impinge on social research, science, and art.

Measurement


Author: David J. Hand
Publisher: Oxford University Press
ISBN: 0198779569
Category: Mathematics
Page: 144
View: 2355

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Measurement is a fundamental concept that underpins almost every aspect of the modern world. It is central to the sciences, social sciences, medicine, and economics, but it affects everyday life. We measure everything - from the distance of far-off galaxies to the temperature of the air, levels of risk, political majorities, taxes, blood pressure, IQ, and weight. The history of measurement goes back to the ancient world, and its story has been one of gradual standardization. Today there are different types of measurement, levels of accuracy, and systems of units, applied in different contexts. Measurement involves notions of variability, accuracy, reliability, and error, and challenges such as the measurement of extreme values. In this Very Short Introduction, David Hand explains the common mathematical framework underlying all measurement, the main approaches to measurement, and the challenges involved. Following a brief historical account of measurement, he discusses measurement as used in the physical sciences and engineering, the life sciences and medicine, the social and behavioural sciences, economics, business, and public policy. 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.