Algebra

A Very Short Introduction

Author: Peter M. Higgins

Publisher: Oxford University Press, USA

ISBN: 0198732821

Category: Algebra

Page: 144

View: 7206

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.--
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Mathematics: A Very Short Introduction

Author: Timothy Gowers

Publisher: Oxford Paperbacks

ISBN: 9780192853615

Category: Mathematics

Page: 143

View: 3577

This book aims to explain, in clear non-technical language,what it is that mathematicians do, and how that differs from and builds on the mathematics that most people are familiar with from school. It is the ideal introduction for anyone who wishes to deepen their understanding of mathematics.
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Numbers: A Very Short Introduction

Author: Peter M. Higgins

Publisher: Oxford University Press

ISBN: 0199584052

Category: Mathematics

Page: 132

View: 866

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.
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The History of Mathematics: A Very Short Introduction

Author: Jacqueline Stedall

Publisher: OUP Oxford

ISBN: 0191633968

Category: Mathematics

Page: 144

View: 6077

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.
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Statistics: A Very Short Introduction

Author: David J. Hand

Publisher: OUP Oxford

ISBN: 0191578924

Category: Mathematics

Page: 136

View: 4618

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.
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Symmetry: A Very Short Introduction

Author: Ian Stewart

Publisher: OUP Oxford

ISBN: 0199651981

Category: Mathematics

Page: 160

View: 7172

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.
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Probability: A Very Short Introduction

Author: John Haigh

Publisher: OUP Oxford

ISBN: 0191636835

Category: Mathematics

Page: 144

View: 8431

Making good decisions under conditions of uncertainty - which is the norm - requires a sound appreciation of the way random chance works. As analysis and modelling of most aspects of the world, and all measurement, are necessarily imprecise and involve uncertainties of varying degrees, the understanding and management of probabilities is central to much work in the sciences and economics. In this Very Short Introduction, John Haigh introduces the ideas of probability and different philosophical approaches to probability, and gives a brief account of the history of development of probability theory, from Galileo and Pascal to Bayes, Laplace, Poisson, and Markov. He describes the basic probability distributions, and goes on to discuss a wide range of applications in science, economics, and a variety of other contexts such as games and betting. He concludes with an intriguing discussion of coincidences and some curious paradoxes. 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.
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Combinatorics

A Very Short Introduction

Author: Robin Wilson

Publisher: Oxford University Press

ISBN: 0198723490

Category: Mathematics

Page: 144

View: 8608

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.
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Logic: A Very Short Introduction

Author: Graham Priest

Publisher: Oxford University Press

ISBN: 0192539701

Category: Philosophy

Page: 152

View: 972

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.
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Applied Mathematics

Author: Alain Goriely

Publisher: Oxford University Press

ISBN: 0198754043

Category: Mathematics

Page: 168

View: 2177

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.
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Cryptography: A Very Short Introduction

Author: Fred Piper,Sean Murphy

Publisher: OUP Oxford

ISBN: 0191577758

Category: Mathematics

Page: 160

View: 3780

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.
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Infinity: a Very Short Introduction

Author: Ian Stewart

Publisher: Oxford University Press

ISBN: 0198755236

Category: Mathematics

Page: 144

View: 9811

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.
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Economics: A Very Short Introduction

Author: Partha Dasgupta

Publisher: OUP Oxford

ISBN: 9780191578281

Category: Business & Economics

Page: 192

View: 2371

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.
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Introduction to Algebraic Geometry

Author: Brendan Hassett

Publisher: Cambridge University Press

ISBN: 1139464590

Category: Mathematics

Page: N.A

View: 9215

Algebraic geometry, central to pure mathematics, has important applications in such fields as engineering, computer science, statistics and computational biology, which exploit the computational algorithms that the theory provides. Users get the full benefit, however, when they know something of the underlying theory, as well as basic procedures and facts. This book is a systematic introduction to the central concepts of algebraic geometry most useful for computation. Written for advanced undergraduate and graduate students in mathematics and researchers in application areas, it focuses on specific examples and restricts development of formalism to what is needed to address these examples. In particular, it introduces the notion of Gröbner bases early on and develops algorithms for almost everything covered. It is based on courses given over the past five years in a large interdisciplinary programme in computational algebraic geometry at Rice University, spanning mathematics, computer science, biomathematics and bioinformatics.
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The U. S. Constitution: a Very Short Introduction

Author: David J. Bodenhamer

Publisher: Oxford University Press

ISBN: 0195378326

Category: Law

Page: 168

View: 5289

"Though the U.S. Constitution was ratified in 1788, its impact on our lives is as recent as today's news. Claims and counterclaims about the constitutionality of governmental actions are a habit of American politics. This document, which its framers designed to limit power, often has made political conflict inevitable. It also has accommodated and legitimized the political and social changes of a vibrant, powerful democratic nation. A product of history's first modern revolution, the Constitution embraced a new formula for government: it restrained power on behalf of liberty, but it also granted power to promote and protect liberty. The U.S. Constitution: A Very Short Introduction explores the major themes that have shaped American constitutional history-- federalism, the balance of powers, property, representation, equality, rights, and security. Informed by the latest scholarship, this book places constitutional history within the context of American political and social history. We do not operate today under the same Constitution created by our founding fathers or the Constitution as completed by the Bill of Rights in 1791 or even the one revised by the Reconstruction amendments. Nor are we the same nation. As our circumstances have changed, so has our Constitution.Today we face serious challenges to the nation's constitutional legacy. Endless wars, a sharply divided electorate and deadlocked government, economic inequality, immigration, cybersecurity and privacy, and foreign interference in the nation's democratic processes, among a host of other issues, have placed demands on government and on society that test our constitutional values. Understanding how the Constitution has evolved will help us adapt its principles to the challenges of our age"--
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Metaphysics: A Very Short Introduction

Author: Stephen Mumford

Publisher: OUP Oxford

ISBN: 0191640263

Category: Philosophy

Page: 128

View: 4761

Metaphysics is one of the traditional four main branches of philosophy, alongside ethics, logic and epistemology. It is also an area that continues to attract and hold a fascination for many people yet it is associated with being complex and abstract. For some it is associated with the mystical or religious. For others it is known through the metaphysical poets who talk of love and spirituality. This Very Short Introduction goes right to the heart of the matter, getting to the basic and most important questions of metaphysical thought in order to understand the theory: What are objects? Do colours and shapes have some form of existence? What is it for one thing to cause another rather than just being associated with it? What is possible? Does time pass? By using these questions to initiate thought about the basic issues around substance, properties, changes, causes, possibilities, time, personal identity, nothingness and emergentism, Stephen Mumford provides a clear and simple path through this analytical tradition at the core of philosophical thought. 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.
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Measurement: A Very Short Introduction

Author: David J. Hand

Publisher: Oxford University Press

ISBN: 0191085022

Category: Mathematics

Page: 144

View: 9258

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.
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Leadership: A Very Short Introduction

Author: Keith Grint

Publisher: OUP Oxford

ISBN: 0191614327

Category: Business & Economics

Page: 160

View: 4633

The subject of leadership raises many questions: What is it? How does it differ from management and command? Are leaders born or bred? Who are the leaders? Do we actually need leaders? Inevitably, the answers are provocative and partial; leadership is a hugely important topic of debate. There are constant calls for 'greater' or 'stronger' leadership, but what this actually means, how we can evaluate it, and why it's important are not very clear. In this Very Short Introduction Keith Grint prompts the reader to rethink their understanding of what leadership is. He examines the way leadership has evolved from its earliest manifestations in ancient societies, highlighting the beginnings of leadership writings through Plato, Sun Tzu, Machiavelli and others, to consider the role of the social, economic, and political context undermining particular modes of leadership. Exploring the idea that leaders cannot exist without followers, and recognising that we all have diverse experiences and assumptions of leadership, Grint looks at the practice of management, its history, future, and influence on all aspects of society. 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.
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Concepts of Modern Mathematics

Author: Ian Stewart

Publisher: Courier Corporation

ISBN: 0486134954

Category: Mathematics

Page: 368

View: 6886

In this charming volume, a noted English mathematician uses humor and anecdote to illuminate the concepts of groups, sets, subsets, topology, Boolean algebra, and other mathematical subjects. 200 illustrations.
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Wittgenstein: A Very Short Introduction

Author: A. C. Grayling

Publisher: OUP Oxford

ISBN: 0191540382

Category: Philosophy

Page: 160

View: 7058

Ludwig Wittgenstein (1889-1951) was an extraordinarily original philospher, whose influence on twentieth-century thinking goes well beyond philosophy itself. In this book, which aims to make Wittgenstein's thought accessible to the general non-specialist reader, A. C. Grayling explains the nature and impact of Wittgenstein's views. He describes both his early and later philosophy, the differences and connections between them, and gives a fresh assessment of Wittgenstein's continuing influence on contemporary thought. 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.
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