Drawing on many years'experience of teaching discrete mathem atics to students of all levels, Anderson introduces such as pects as enumeration, graph theory and configurations or arr angements. Starting with an introduction to counting and rel ated problems, he moves on to the basic ideas of graph theor y with particular emphasis on trees and planar graphs. He de scribes the inclusion-exclusion principle followed by partit ions of sets which in turn leads to a study of Stirling and Bell numbers. Then follows a treatment of Hamiltonian cycles, Eulerian circuits in graphs, and Latin squares as well as proof of Hall's theorem. He concludes with the constructions of schedules and a brief introduction to block designs. Each chapter is backed by a number of examples, with straightforw ard applications of ideas and more challenging problems.
This highly regarded work fills the need for a treatment of elementary discrete mathematics that provides a core of mathematical terminology and concepts as well as emphasizes computer applications. Includes numerous elementary applications to computing and examples with solutions.
an introductory approach : a first course in discrete mathematics
Author: Robin J. Wilson
Publisher: John Wiley & Sons Inc
The only text available on graph theory at the freshman/sophomore level, it covers properties of graphs, presents numerous algorithms, and describes actual applications to chemistry, genetics, music, linguistics, control theory and the social sciences. Illustrated.
Given the ease with which computers can do iteration it is now possible for almost anyone to generate beautiful images whose roots lie in discrete dynamical systems. Images of Mandelbrot and Julia sets abound in publications both mathematical and not. The mathematics behind the pictures are beautiful in their own right and are the subject of this text. Mathematica programs that illustrate the dynamics are included in an appendix.
Written by two prominent figures in the field, this comprehensive text provides a remarkably student-friendly approach. Its sound yet accessible treatment emphasizes the history of graph theory and offers unique examples and lucid proofs. 2004 edition.
Now with discrete mathematics, this edition makes it possible to organize an entire course without the use of calculus. However, if you wish to cover the chapters requiring calculus, the book's unique organization permits use to concurrently teach the introductory calculus course -- as early as the first semester of the freshman year. Plus, the book's rich choice of topics provide an introduction to the operations research and quantitative management science courses. This text gives students an opportunity to cover all phases of the mathematical modeling process, including creative and empirical model construction, model analysis, and model research using clearly defined techniques, such as modeling using graphs, modeling using proportionality, and modeling fitting.
Susanna Epp's DISCRETE MATHEMATICS: AN INTRODUCTION TO MATHEMATICAL REASONING, provides the same clear introduction to discrete mathematics and mathematical reasoning as her highly acclaimed DISCRETE MATHEMATICS WITH APPLICATIONS, but in a compact form that focuses on core topics and omits certain applications usually taught in other courses. The book is appropriate for use in a discrete mathematics course that emphasizes essential topics or in a mathematics major or minor course that serves as a transition to abstract mathematical thinking. The ideas of discrete mathematics underlie and are essential to the science and technology of the computer age. This book offers a synergistic union of the major themes of discrete mathematics together with the reasoning that underlies mathematical thought. Renowned for her lucid, accessible prose, Epp explains complex, abstract concepts with clarity and precision, helping students develop the ability to think abstractly as they study each topic. In doing so, the book provides students with a strong foundation both for computer science and for other upper-level mathematics courses. Important Notice: Media content referenced within the product description or the product text may not be available in the ebook version.
Explore real-world applications of selected mathematical theory,concepts, and methods Exploring related methods that can be utilized in various fieldsof practice from science and engineering to business, A FirstCourse in Applied Mathematics details how applied mathematicsinvolves predictions, interpretations, analysis, and mathematicalmodeling to solve real-world problems. Written at a level that is accessible to readers from a widerange of scientific and engineering fields, the book masterfullyblends standard topics with modern areas of application andprovides the needed foundation for transitioning to more advancedsubjects. The author utilizes MATLAB® to showcase thepresented theory and illustrate interesting real-world applicationsto Google's web page ranking algorithm, image compression,cryptography, chaos, and waste management systems. Additionaltopics covered include: Linear algebra Ranking web pages Matrix factorizations Least squares Image compression Ordinary differential equations Dynamical systems Mathematical models Throughout the book, theoretical and applications-orientedproblems and exercises allow readers to test their comprehension ofthe presented material. An accompanying website features relatedMATLAB® code and additional resources. A First Course in Applied Mathematics is an ideal book formathematics, computer science, and engineering courses at theupper-undergraduate level. The book also serves as a valuablereference for practitioners working with mathematical modeling,computational methods, and the applications of mathematics in theireveryday work.
A First Course in Combinatorial Optimization is a text for a one-semester introductory graduate-level course for students of operations research, mathematics, and computer science. It is a self-contained treatment of the subject, requiring only some mathematical maturity. Topics include: linear and integer programming, polytopes, matroids and matroid optimization, shortest paths, and network flows. Central to the exposition is the polyhedral viewpoint, which is the key principle underlying the successful integer-programming approach to combinatorial-optimization problems. Another key unifying topic is matroids. The author does not dwell on data structures and implementation details, preferring to focus on the key mathematical ideas that lead to useful models and algorithms. Problems and exercises are included throughout as well as references for further study.