Combinatorics A Very Short Introduction

Author : Robin J. Wilson
Publisher : Oxford University Press
ISBN 13 : 0198723490
Total Pages : 177 pages
Book Rating : 4.93/5 ( download)

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Download or read book Combinatorics written by Robin J. Wilson and published by Oxford University Press. This book was released on 2016 with total page 177 pages. Available in PDF, EPUB and Kindle. Book excerpt: 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.

Author : Robin Wilson
Publisher : Oxford University Press, USA
ISBN 13 : 0198798091
Total Pages : 177 pages
Book Rating : 4.95/5 ( download)

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Download or read book Number Theory written by Robin Wilson and published by Oxford University Press, USA. This book was released on 2020 with total page 177 pages. Available in PDF, EPUB and Kindle. Book excerpt: Number theory is the branch of mathematics primarily concerned with the counting numbers, especially primes. It dates back to the ancient Greeks, but today it has great practical importance in cryptography, from credit card security to national defence. This book introduces the main areas of number theory, and some of its most interesting problems.

Author : John Haigh
Publisher : OUP Oxford
ISBN 13 : 0191636835
Total Pages : 144 pages
Book Rating : 4.37/5 ( download)

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Download or read book Probability: A Very Short Introduction written by John Haigh and published by OUP Oxford. This book was released on 2012-04-26 with total page 144 pages. Available in PDF, EPUB and Kindle. Book excerpt: 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.

Author : Fred Piper
Publisher : OUP Oxford
ISBN 13 : 0191577758
Total Pages : 160 pages
Book Rating : 4.58/5 ( download)

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Download or read book Cryptography: A Very Short Introduction written by Fred Piper and published by OUP Oxford. This book was released on 2002-05-30 with total page 160 pages. Available in PDF, EPUB and Kindle. Book excerpt: 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.

Author : Robin Wilson
Publisher : OUP Oxford
ISBN 13 : 0191630624
Total Pages : 392 pages
Book Rating : 4.20/5 ( download)

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Download or read book Combinatorics: Ancient & Modern written by Robin Wilson and published by OUP Oxford. This book was released on 2013-06-27 with total page 392 pages. Available in PDF, EPUB and Kindle. Book excerpt: Who first presented Pascal's triangle? (It was not Pascal.) Who first presented Hamiltonian graphs? (It was not Hamilton.) Who first presented Steiner triple systems? (It was not Steiner.) The history of mathematics is a well-studied and vibrant area of research, with books and scholarly articles published on various aspects of the subject. Yet, the history of combinatorics seems to have been largely overlooked. This book goes some way to redress this and serves two main purposes: 1) it constitutes the first book-length survey of the history of combinatorics; and 2) it assembles, for the first time in a single source, researches on the history of combinatorics that would otherwise be inaccessible to the general reader. Individual chapters have been contributed by sixteen experts. The book opens with an introduction by Donald E. Knuth to two thousand years of combinatorics. This is followed by seven chapters on early combinatorics, leading from Indian and Chinese writings on permutations to late-Renaissance publications on the arithmetical triangle. The next seven chapters trace the subsequent story, from Euler's contributions to such wide-ranging topics as partitions, polyhedra, and latin squares to the 20th century advances in combinatorial set theory, enumeration, and graph theory. The book concludes with some combinatorial reflections by the distinguished combinatorialist, Peter J. Cameron. This book is not expected to be read from cover to cover, although it can be. Rather, it aims to serve as a valuable resource to a variety of audiences. Combinatorialists with little or no knowledge about the development of their subject will find the historical treatment stimulating. A historian of mathematics will view its assorted surveys as an encouragement for further research in combinatorics. The more general reader will discover an introduction to a fascinating and too little known subject that continues to stimulate and inspire the work of scholars today.

Author : Timothy Gowers
Publisher : Oxford Paperbacks
ISBN 13 : 9780192853615
Total Pages : 172 pages
Book Rating : 4.19/5 ( download)

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Download or read book Mathematics: A Very Short Introduction written by Timothy Gowers and published by Oxford Paperbacks. This book was released on 2002-08-22 with total page 172 pages. Available in PDF, EPUB and Kindle. Book excerpt: The aim of this volume is to explain the differences between research-level mathematics and the maths taught at school. Most differences are philosophical and the first few chapters are about general aspects of mathematical thought.

Author : Guido Caldarelli
Publisher : OUP Oxford
ISBN 13 : 0191642738
Total Pages : 136 pages
Book Rating : 4.39/5 ( download)

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Download or read book Networks: A Very Short Introduction written by Guido Caldarelli and published by OUP Oxford. This book was released on 2012-10-25 with total page 136 pages. Available in PDF, EPUB and Kindle. Book excerpt: From ecosystems to Facebook, from the Internet to the global financial market, some of the most important and familiar natural systems and social phenomena are based on a networked structure. It is impossible to understand the spread of an epidemic, a computer virus, large-scale blackouts, or massive extinctions without taking into account the network structure that underlies all these phenomena. In this Very Short Introduction, Guido Caldarelli and Michele Catanzaro discuss the nature and variety of networks, using everyday examples from society, technology, nature, and history to explain and understand the science of network theory. They show the ubiquitous role of networks; how networks self-organize; why the rich get richer; and how networks can spontaneously collapse. They conclude by highlighting how the findings of complex network theory have very wide and important applications in genetics, ecology, communications, economics, and sociology. 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.

Author : Richard Earl
Publisher : Oxford University Press, USA
ISBN 13 : 0198832680
Total Pages : 169 pages
Book Rating : 4.83/5 ( download)

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Download or read book Topology written by Richard Earl and published by Oxford University Press, USA. This book was released on 2020-01-11 with total page 169 pages. Available in PDF, EPUB and Kindle. Book excerpt: How is a subway map different from other maps? What makes a knot knotted? What makes the M�bius strip one-sided? These are questions of topology, the mathematical study of properties preserved by twisting or stretching objects. In the 20th century topology became as broad and fundamental as algebra and geometry, with important implications for science, especially physics. In this Very Short Introduction Richard Earl gives a sense of the more visual elements of topology (looking at surfaces) as well as covering the formal definition of continuity. Considering some of the eye-opening examples that led mathematicians to recognize a need for studying topology, he pays homage to the historical people, problems, and surprises that have propelled the growth of this field. 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.

Author : Chuan-Chong Chen
Publisher : World Scientific
ISBN 13 : 9789810211394
Total Pages : 314 pages
Book Rating : 4.92/5 ( download)

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Download or read book Principles and Techniques in Combinatorics written by Chuan-Chong Chen and published by World Scientific. This book was released on 1992 with total page 314 pages. Available in PDF, EPUB and Kindle. Book excerpt: A textbook suitable for undergraduate courses. The materials are presented very explicitly so that students will find it very easy to read. A wide range of examples, about 500 combinatorial problems taken from various mathematical competitions and exercises are also included.

Author : Kenneth P. Bogart
Publisher : Harcourt Brace College Publishers
ISBN 13 :
Total Pages : 648 pages
Book Rating : 4.01/5 ( download)

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Download or read book Introductory Combinatorics written by Kenneth P. Bogart and published by Harcourt Brace College Publishers. This book was released on 1990 with total page 648 pages. Available in PDF, EPUB and Kindle. Book excerpt: Introductory, Combinatorics, Third Edition is designed for introductory courses in combinatorics, or more generally, discrete mathematics. The author, Kenneth Bogart, has chosen core material of value to students in a wide variety of disciplines: mathematics, computer science, statistics, operations research, physical sciences, and behavioral sciences. The rapid growth in the breadth and depth of the field of combinatorics in the last several decades, first in graph theory and designs and more recently in enumeration and ordered sets, has led to a recognition of combinatorics as a field with which the aspiring mathematician should become familiar. This long-overdue new edition of a popular set presents a broad comprehensive survey of modern combinatorics which is important to the various scientific fields of study.