The Art of Mathematics: Coffee Time in Memphis

Bela Bollobás

Cambridge University Press  | 2006 | 374 Páginas  | PDF | 8,2 Mb

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Can a Christian escape from a lion? How quickly can a rumor spread? Can you fool an airline into accepting oversize baggage? Recreational mathematics is full of frivolous questions where the mathematician's art can be brought to bear. But play often has a purpose. In mathematics, it can sharpen skills, provide amusement, or simply surprise, and books of problems have been the stock-in-trade of mathematicians for centuries. This collection is designed to be sipped from, rather than consumed in one sitting. The questions range in difficulty: the most challenging offer a glimpse of deep results that engage mathematicians today; even the easiest prompt readers to think about mathematics. All come with solutions, many with hints, and most with illustrations. Whether you are an expert, or a beginner or an amateur mathematician, this book will delight for a lifetime.

Revisão: plus.maths.org

How to Guard an Art Gallery and Other Discrete Mathematical Adventures

T.S. Michael

The Johns Hopkins University | 2009 | 272 páginas | PDF | 1,18 Mb

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What is the maximum number of pizza slices one can get by making four straight cuts through a circular pizza? How does a computer determine the best set of pixels to represent a straight line on a computer screen? How many people at a minimum does it take to guard an art gallery?

Discrete mathematics has the answer to these -- and many other -- questions of picking, choosing, and shuffling. T. S. Michael's gem of a book brings this vital but tough-to-teach subject to life using examples from real life and popular culture. Each chapter uses one problem -- such as slicing a pizza -- to detail key concepts about counting numbers and arranging finite sets. Michael takes a different perspective in tackling each of eight problems and explains them in differing degrees of generality, showing in the process how the same mathematical concepts appear in varied guises and contexts. In doing so, he imparts a broader understanding of the ideas underlying discrete mathematics and helps readers appreciate and understand mathematical thinking and discovery.

This book explains the basic concepts of discrete mathematics and demonstrates how to apply them in largely nontechnical language. The explanations and formulas can be grasped with a basic understanding of linear equations.

Graphs and their Uses

Martin Gardner

The Mathematical Association of America | 1996 | 160 páginas | PDF | 4,04 Mb

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In 1963 Oystein Ore wrote this classic volume, which was published in the New Mathematical Library Series. This elegant book has provided students and teachers with an excellent introduction to the field of graph theory for close to thirty years. Robin Wilson's revision adds strength to the book by updating the terminology and notation, bringing them in line with contemporary usage. Wilson has added new material on interval graphs, the traveling salesman problem, bracing frameworks, shortest route problems, and coloring maps on surfaces. Most of the diagrams in the book have been redrawn.

Introduction to Graph Theory

2.ª Edição

Douglas B. West

Prentice Hall | 2000 | 589 páginas | Djvu | 7 Mb

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This book fills a need for a thorough introduction to graph theory that features both the understanding and writing of proofs about graphs. Verification that algorithms work is emphasized more than their complexity. An effective use of examples, and huge number of interesting exercises, demonstrate the topics of trees and distance, matchings and factors, connectivity and paths, graph coloring, edges and cycles, and planar graphs. For those who need to learn to make coherent arguments in the fields of mathematics and computer science.

Graph Edge Coloring: Vizing's Theorem and Goldberg's Conjecture

(Wiley Series in Discrete Mathematics and Optimization)

Michael Stiebitz

Wiley | 2012 | 344 páginas | PDF | 12,69 Mb

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Features recent advances and new applications in graph edge coloring

Reviewing recent advances in the Edge Coloring Problem, Graph Edge Coloring: Vizing's Theorem and Goldberg's Conjecture provides an overview of the current state of the science, explaining the interconnections among the results obtained from important graph theory studies. The authors introduce many new improved proofs of known results to identify and point to possible solutions for open problems in edge coloring.

The book begins with an introduction to graph theory and the concept of edge coloring. Subsequent chapters explore important topics such as:

• Use of Tashkinov trees to obtain an asymptotic positive solution to Goldberg's conjecture
• Application of Vizing fans to obtain both known and new results
• Kierstead paths as an alternative to Vizing fans
• Classification problem of simple graphs
• Generalized edge coloring in which a color may appear more than once at a vertex

This book also features first-time English translations of two groundbreaking papers written by Vadim Vizing on an estimate of the chromatic class of a p-graph and the critical graphs within a given chromatic class.

Written by leading experts who have reinvigorated research in the field, Graph Edge Coloring is an excellent book for mathematics, optimization, and computer science courses at the graduate level. The book also serves as a valuable reference for researchers interested in discrete mathematics, graph theory, operations research, theoretical computer science, and combinatorial optimization.

Discrete mathematics and its applications

Kenneth Rosen

7.ª edição

McGraw-Hill Science | 2011 | 1072 páginas | PDF | 36 Mb

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Discrete Mathematics and its Applications, Seventh Edition, is intended for one- or two-term introductory discrete mathematics courses taken by students from a wide variety of majors, including computer science, mathematics, and engineering. This renowned best-selling text, which has been used at over 500 institutions around the world, gives a focused introduction to the primary themes in a discrete mathematics course and demonstrates the relevance and practicality of discrete mathematics to a wide a wide variety of real-world applications…from computer science to data networking, to psychology, to chemistry, to engineering, to linguistics, to biology, to business, and to many other important fields.

Graph Theory 1736-1936

Norman L. Biggs, E. Keith Lloyd, Robin J. Wilson

Oxford University Press, USA | 240 páginas | 1999 |

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Descrição: First published in 1976, this book has been widely acclaimed as a major and enlivening contribution to the history of mathematics. The updated and corrected paperback contains extracts from the original writings of mathematicians who contributed to the foundations of graph theory. The author's commentary links each piece historically and frames the whole with explanations of the relevant mathematical terminology and notation.

Geometry and Discrete Mathematics

Harcourt Mathematics 12
Peter Crippin, Donald J. Curran, Neal E. Reid, Ronald G. Dunkley, Jock MacKay

McGraw-Hill | zip-pdf | 4,7 Mb

Ano de escolaridade: 12.º ano

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Discrete Mathematics and its Applications

4 Ed.
Kenneth H. Rosen

McGraw-Hill | 1998 | 824 páginas | PDF | 14,5 MB

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6.ª edição

Kenneth H. Rosen

McGraw-Hill | 2006 | 1006 páginas | djvu | 20 MB

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Manual de soluções: 4shared.com

"Discrete Mathematics and its Applications, Sixth Edition", is intended for one- or two-term introductory discrete mathematics courses taken by students from a wide variety of majors, including computer science, mathematics, and engineering. This renowned best-selling text, which has been used at over 500 institutions around the world, gives a focused introduction to the primary themes in a discrete mathematics course and demonstrates the relevance and practicality of discrete mathematics to a wide variety of real-world applications...from computer science to data networking, to psychology, to chemistry, to engineering, to linguistics, to biology, to business, and to many other important fields.