Mathematics

Author: Timothy Gowers

Publisher: Sterling Publishing Company, Inc.

ISBN: 9781402768972

Category: Mathematics

Page: 180

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Mathematics is a subject we are all exposed to in our daily lives, but one that many of us fear. Timothy Gowers’s entertaining overview of the topic explains the differences between what we learn at school and advanced mathematics, and helps the math phobic emerge with a clearer understanding of such paradoxical-sounding concepts as “infinity,” “curved space,” and “imaginary numbers.” From basic ideas to philosophical queries to common sociological questions about the mathematical community, this book unravels the mysteries of space and numbers.

The History of Mathematics: A Very Short Introduction

Author: Jacqueline Stedall

Publisher: OUP Oxford

ISBN: 0191633968

Category: Mathematics

Page: 144

View: 3227

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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.

Applied Mathematics

Author: Alain Goriely

Publisher: Oxford University Press

ISBN: 0198754043

Category: Mathematics

Page: 168

View: 8202

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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.

Algebra

A Very Short Introduction

Author: Peter M. Higgins

Publisher: Oxford University Press, USA

ISBN: 0198732821

Category: Algebra

Page: 144

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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.--

Infinity: a Very Short Introduction

Author: Ian Stewart

Publisher: Oxford University Press

ISBN: 0198755236

Category: Mathematics

Page: 144

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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

View: 6435

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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.

Fractals: A Very Short Introduction

Author: K. J. Falconer

Publisher: Oxford University Press

ISBN: 0199675988

Category: Mathematics

Page: 132

View: 2895

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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.

Combinatorics

A Very Short Introduction

Author: Robin Wilson

Publisher: Oxford University Press

ISBN: 0198723490

Category: Mathematics

Page: 144

View: 519

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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.

Probability: A Very Short Introduction

Author: John Haigh

Publisher: Oxford University Press

ISBN: 0199588481

Category: Mathematics

Page: 128

View: 8597

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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.

Mathematical Finance: A Very Short Introduction

Author: Mark H. A. Davis

Publisher: Oxford University Press

ISBN: 0191092037

Category: Mathematics

Page: 144

View: 1605

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In recent years the finance industry has mushroomed to become an important part of modern economies, and many science and engineering graduates have joined the industry as quantitative analysts, with mathematical and computational skills that are needed to solve complex problems of asset valuation and risk management. An important parallel story exists of scientific endeavour. Between 1965-1995, insightful ideas in economics about asset valuation were turned into a mathematical 'theory of arbitrage', an enterprise whose first achievement was the famous 1973 Black-Scholes formula, followed by extensive investigations using all the resources of modern analysis and probability. The growth of the finance industry proceeded hand-in-hand with these developments. Now new challenges arise to deal with the fallout from the 2008 financial crisis and to take advantage of new technology, which has revolutionized the practice of trading. This Very Short Introduction introduces readers with no previous background in this area to arbitrage theory and why it works the way it does. Illuminating pricing theory, Mark Davis explains its applications to interest rates, credit trading, fund management and risk management. He concludes with a survey of the most pressing issues in mathematical finance 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.

Information: A Very Short Introduction

Author: Luciano Floridi

Publisher: Oxford University Press

ISBN: 0199551375

Category: Computers

Page: 130

View: 1513

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Luciano Floridi unpacks this fundamental concept - what information is, how it is measured, its value and meaning - cutting across the sciences and humanities, from DNA to the Internet, and the ethical issues related to privacy, copyright, and accessibility.

Measurement

Author: David J. Hand

Publisher: Oxford University Press

ISBN: 0198779569

Category: Mathematics

Page: 144

View: 4683

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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.

Erfahrung Mathematik

Author: P.J. Davis,R. Hersh

Publisher: Springer-Verlag

ISBN: 3034850409

Category: Science

Page: 466

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ie ältesten uns bekannten mathematischen Schriftta D feln stammen aus der Zeit um 2400 v. ehr. ; aber wir dürfen davon ausgehen, daß das Bedürfnis, Mathematik zu schaffen, ein Ausdruck der menschlichen Zivilisation an sich ist. In vier bis fünf Jahrtausenden hat sich ein gewalti ges System von Praktiken und Begriffen - die Mathematik herangebildet, die in vielfältiger Weise mit unserem Alltag verknüpft ist. Was ist Mathematik? Was bedeutet sie? Wo mit befaßt sie sich? Was sind ihre Methoden? Wie wird sie geschaffen und benützt? Wo ist ihr Platz in der Vielgestalt der menschlichen Erfahrung? Welchen Nutzen bringt sie? Was für Schaden richtet sie an? Welches Gewicht kommt ihr zu? Diese schwierigen Fragen werden noch zusätzlich kompliziert durch die Fülle des Materials und die weitver zweigten Querverbindungen, die es dem einzelnen verun möglichen, alles zu begreifen, geschweige denn, es in seiner Gesamtheit zu erfassen und zwischen den Deckeln eines normalen Buches unterzubringen. Um von dieser Material fülle nicht erdrückt zu werden, haben sich die Autoren für eine andere Betrachtungsweise entschieden. Die Mathema tik ist seit Tausenden von Jahren ein Feld menschlicher Ak tivität. In begrenztem Rahmen ist jeder von uns ein Mathe matiker und betreibt bewußt Mathematik, wenn er zum Beispiel auf dem Markt einkauft, Tapeten ausmißt oder ei nen Keramiktopf mit einem regelmäßigen Muster verziert. In bescheidenem Ausmaß versucht sich auch jeder von uns als mathematischer Denker. Schon mit dem Ausruf «Aber Zahlen lügen nicht!» befinden wir uns in der Gesellschaft von Plato oder Lakatos.

Newton

A Very Short Introduction

Author: Rob Iliffe

Publisher: Oxford University Press

ISBN: 0199298033

Category: History

Page: 141

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Newton's contributions to an understanding of the heavens and the earth are considered to be unparalleled. This very short introduction explains his scientific theories, and uses Newton's unpublished writings to paint a picture of an extremely complex man whose beliefs had a huge impact on Europe's political, intellectual, and religious landscape.

Statistics: A Very Short Introduction

Author: David J. Hand

Publisher: OUP Oxford

ISBN: 0191578924

Category: Mathematics

Page: 136

View: 598

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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.

The Ancient Near East: A Very Short Introduction

Author: Amanda H. Podany

Publisher: Oxford University Press

ISBN: 019970323X

Category: History

Page: 168

View: 1351

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The ancient Near East is known as the "cradle of civilization"--and for good reason. Mesopotamia, Syria, and Anatolia were home to an extraordinarily rich and successful culture. Indeed, it was a time and place of earth-shaking changes for humankind: the beginnings of writing and law, kingship and bureaucracy, diplomacy and state-sponsored warfare, mathematics and literature. This Very Short Introduction offers a fascinating account of this momentous time in human history. The three thousand years covered here--from around 3500 BCE, with the founding of the first Mesopotamian cities, to the conquest of the Near East by the Persian king Cyrus the Great in 539 BCE-represent a period of incredible innovation, from the invention of the wheel and the plow, to early achievements in astronomy, law, and diplomacy. As historian Amanda Podany explores this era, she overturns the popular image of the ancient world as a primitive, violent place. We discover that women had many rights and freedoms: they could own property, run businesses, and represent themselves in court. Diplomats traveled between the capital cities of major powers ensuring peace and friendship between the kings. Scribes and scholars studied the stars and could predict eclipses and the movements of the planets. Every chapter introduces the reader to a particular moment in ancient Near Eastern history, illuminating such aspects as trade, religion, diplomacy, law, warfare, kingship, and agriculture. Each discussion focuses on evidence provided in two or three cuneiform texts from that time. These documents, the cities in which they were found, the people and gods named in them, the events they recount or reflect, all provide vivid testimony of the era in which they were written. About the Series: Oxford's Very Short Introductions series offers concise and original introductions to a wide range of subjects--from Islam to Sociology, Politics to Classics, Literary Theory to History, and Archaeology to the Bible. Not simply a textbook of definitions, each volume in this series provides trenchant and provocative--yet always balanced and complete--discussions of the central issues in a given discipline or field. Every Very Short Introduction gives a readable evolution of the subject in question, demonstrating how the subject has developed and how it has influenced society. Eventually, the series will encompass every major academic discipline, offering all students an accessible and abundant reference library. Whatever the area of study that one deems important or appealing, whatever the topic that fascinates the general reader, the Very Short Introductions series has a handy and affordable guide that will likely prove indispensable.

Astrophysics: A Very Short Introduction

Author: James Binney

Publisher: Oxford University Press

ISBN: 0198752857

Category: Science

Page: 144

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Astrophysics is the physics of the stars, and more widely the physics of the Universe. It enables us to understand the structure and evolution of planetary systems, stars, galaxies, interstellar gas, and the cosmos as a whole. In this Very Short Introduction, the leading astrophysicist James Binney shows how the field of astrophysics has expanded rapidly in the past century, with vast quantities of data gathered by telescopes exploiting all parts of the electromagnetic spectrum, combined with the rapid advance of computing power, which has allowed increasingly effective mathematical modelling. He illustrates how the application of fundamental principles of physics - the consideration of energy and mass, and momentum - and the two pillars of relativity and quantum mechanics, has provided insights into phenomena ranging from rapidly spinning millisecond pulsars to the collision of giant spiral galaxies. This is a clear, rigorous introduction to astrophysics for those keen to cut their teeth on a conceptual treatment involving some 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