Invitation to Discrete Mathematics

Author: Ji%rí Matousek,Jaroslav Ne%set%ril

Publisher: Oxford University Press

ISBN: 0198570430

Category: Mathematics

Page: 443

View: 9643

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Invitation to Discrete Mathematics is an introduction and a thoroughly comprehensive text at the same time. A lively and entertaining style with mathematical precision and maturity uniquely combine into an intellectual happening and should delight the interested reader. A master example of teaching contemporary discrete mathematics, and of teaching science in general.
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Invitation to Discrete Mathematics

Author: Jiří Matoušek,Jaroslav Nešetřil

Publisher: Oxford University Press

ISBN: 9780198502081

Category: Mathematics

Page: 410

View: 2543

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This book is a clear and self-contained introduction to discrete mathematics, and in particular to combinatorics and graph theory. Aimed at undergraduates and early graduate students in mathematics and computer science, it is written with the goal of stimulating interest in mathematics and encourages an active, problem-solving approach to the material. The reader is led to an understanding of the basic principles and methods of actually doing mathematics. It is more narrowly focused than many discrete mathematics textbooks and treats selected topics in unusual depth and from several points of view. The book reflects the conviction of the authors, active and internationally renowned mathematicians, that the most important gain from studying mathematics is the cultivation of clear and logical thinking and habits, invariably useful for attacking new problems. More than 400 exercises, ranging widely in difficulty, and many accompanied by hints for solution, support this approach to teaching. Readers will appreciate the lively and informal style of the text, accompanied by more than 200 drawings and diagrams. Specialists in various parts of science ( with a basic mathematical education) wishing to apply discrete mathematics in their field will find the book a useful source, and even experts in combinatorics may occasionally learn from pointers to research literature or from the presentation of recent results. Invitation to Discrete Mathematics should make delightful readingboth for beginners and mathematical professionals.
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Invitation to Discrete Mathematics

Author: Jiří Matoušek,Jaroslav Nešetřil

Publisher: Oxford University Press

ISBN: 9780198502074

Category: Mathematics

Page: 410

View: 9281

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This book is a clear and self-contained introduction to discrete mathematics, and in particular to combinatorics and graph theory. Aimed at undergraduate and early graduate students in mathematics and computer science, it is written with the goal of stimulating interest in mathematics and provides an active, problem-solving approach to the material. The reader is led to an understanding of the basic principles and methods of actually doing mathematics. It is more narrowly focused than many discrete mathematics textbooks and treats selected topics in unusual depth and from several points of view. The book reflects the conviction of the authors, active and internationally renowned mathematicians, that the most important gain from studying mathematics is the cultivation of clear and logical thinking and habits, invariably useful for attacking new problem. More than 400 exercises, ranging widely in difficulty and many accompanied by hints for solution, support this approach to teaching. Readers will appreciate the lively and informal style of the text, accompanied by more than 200 drawings and diagrams. Specialists in various parts of science with a basic mathematical education wishing to apply discrete mathematics in their field can use the book as a useful source, and even experts in combinatorics may occasionally learn from pointers to research literature or from the presentation of recent results. Invitation to Discrete Mathematics should make delightful reading both for beginners and for mathematical professionals. The main topics include: elementary counting problems, asymptotic estimates, basic graph theory and graph algorithms, finite projective planes, elementary probability and the probabilistic method, generating functions, and combinatorial applications of linear algebra. General mathematical notions beyond high-school level are thouroughly explained in the introductory chapter. An appendix summarizes the undergraduate algebra needed in some of the more advanced sections of the book.
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The Heart of Mathematics

An invitation to effective thinking

Author: Edward B. Burger,Michael Starbird

Publisher: Springer Science & Business Media

ISBN: 9781931914413

Category: Mathematics

Page: 760

View: 4887

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Hallmark features include: * A focus on the important ideas of mathematics that students will retain long after their formal studies are complete. * An engaging and humorous style, written to be read and enjoyed. * Ten Life Lessons that readers will apply beyond their study of mathematics. * Use of a variety of visualization techniques that direct students to model their thinking and to actively explore the world around them. New to this Edition: * A new chapter, Deciding Wisely: Applications of Rigorous Thought, provides a thought-provoking capstone. * Expanded and improved statistics and probability content in Chapter 7, Taming Uncertainty. * Enhanced Mindscapes at the end of each section which ask the reader to review, apply and think deeply about the ideas presented in the chapter. * Radically superior ancillary package.
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An Invitation to the Rogers-Ramanujan Identities

Author: Andrew V. Sills

Publisher: CRC Press

ISBN: 1351647962

Category: Mathematics

Page: 234

View: 2122

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The Rogers--Ramanujan identities are a pair of infinite series—infinite product identities that were first discovered in 1894. Over the past several decades these identities, and identities of similar type, have found applications in number theory, combinatorics, Lie algebra and vertex operator algebra theory, physics (especially statistical mechanics), and computer science (especially algorithmic proof theory). Presented in a coherant and clear way, this will be the first book entirely devoted to the Rogers—Ramanujan identities and will include related historical material that is unavailable elsewhere.
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An Invitation to Computational Homotopy

Author: Graham Ellis

Publisher: Oxford University Press

ISBN: 0192569414

Category: Mathematics

Page: 640

View: 9549

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An Invitation to Computational Homotopy is an introduction to elementary algebraic topology for those with an interest in computers and computer programming. It expertly illustrates how the basics of the subject can be implemented on a computer through its focus on fully-worked examples designed to develop problem solving techniques. The transition from basic theory to practical computation raises a range of non-trivial algorithmic issues which will appeal to readers already familiar with basic theory and who are interested in developing computational aspects. The book covers a subset of standard introductory material on fundamental groups, covering spaces, homology, cohomology and classifying spaces as well as some less standard material on crossed modules. These topics are covered in a way that hints at potential applications of topology in areas of computer science and engineering outside the usual territory of pure mathematics, and also in a way that demonstrates how computers can be used to perform explicit calculations within the domain of pure algebraic topology itself. The initial chapters include in-depth examples from data mining, biology and digital image analysis, while the later chapters cover a range of computational examples on the cohomology of classifying spaces that are likely beyond the reach of a purely paper-and-pen approach to the subject. An Invitation to Computational Homotopy serves as a self-contained and informal introduction to these topics and their implementation in the sphere of computer science. Written in a dynamic and engaging style, it skilfully showcases a range of useful machine computations, and will serve as an invaluable aid to graduate students working with algebraic topology.
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Concrete mathematics

a foundation for computer science

Author: Ronald L. Graham,Donald Ervin Knuth,Oren Patashnik

Publisher: Addison Wesley Publishing Company

ISBN: N.A

Category: Mathematics

Page: 625

View: 1325

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The Foundations of Mathematics

Author: Ian Stewart,Professor of Math and Gresham Professor of Geometry Ian Stewart,David Tall,David Orme Tall

Publisher: Oxford University Press on Demand

ISBN: 9780198531654

Category: Fiction

Page: 263

View: 2340

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"There are many textbooks available for a so-called transition course from calculus to abstract mathematics. I have taught this course several times and always find it problematic. The Foundations of Mathematics (Stewart and Tall) is a horse of a different color. The writing is excellent and there is actually some useful mathematics. I definitely like this book."--The Bulletin of Mathematics Books
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Mathematics: A Very Short Introduction

Author: Timothy Gowers

Publisher: Oxford Paperbacks

ISBN: 9780192853615

Category: Mathematics

Page: 143

View: 3550

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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.
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