A First Course in Discrete Mathematics

Author: Ian Anderson

Publisher: Springer Science & Business Media

ISBN: 085729315X

Category: Mathematics

Page: 200

View: 1839

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.

A First Course in Discrete Mathematics

Author: John C. Molluzzo,Fred Buckley

Publisher: Waveland Press

ISBN: 1478634391

Category: Mathematics

Page: 507

View: 9500

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,John J. Watkins

Publisher: John Wiley & Sons Inc


Category: Mathematics

Page: 340

View: 1543

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.

A First Course in Discrete Dynamical Systems

Author: Richard A. Holmgren

Publisher: Springer Science & Business Media

ISBN: 1441987320

Category: Mathematics

Page: 223

View: 878

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.

A First Course in Mathematical Modeling

Author: Frank R. Giordano,Maurice D. Weir,William P. Fox

Publisher: Thomson Brooks/Cole


Category: Mathematical models

Page: 525

View: 5662

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.

A First Course in Graph Theory

Author: Gary Chartrand,Ping Zhang

Publisher: Courier Corporation

ISBN: 0486297306

Category: Mathematics

Page: 464

View: 3054

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.

A First Course in Probability

Author: Sheldon M. Ross

Publisher: Macmillan College


Category: Probabilities

Page: 473

View: 9802

This market leader is written as an elementary introduction to the mathematical theory of probability for readers in mathematics, engineering, and the sciences who possess the prerequisite knowledge of elementary calculus. A major thrust of the Fifth Edition has been to make the book more accessible to today's readers. The exercise sets have been revised to include more simple, "mechanical" problems and new section of Self-test Problems, with fully worked out solutions, conclude each chapter. In addition many new applications have been added to demonstrate the importance of probability in real situations. A software diskette, packaged with each copy of the book, provides an easy to use tool to derive probabilities for binomial, Poisson, and normal random variables. It also illustrates and explores the central limit theorem, works with the strong law of large numbers, and more.

Discrete Mathematics

Elementary and Beyond

Author: L. Lovász,J. Pelikán,K. Vesztergombi

Publisher: Springer Science & Business Media

ISBN: 9780387955858

Category: Mathematics

Page: 284

View: 5368

Aimed at undergraduate mathematics and computer science students, this book is an excellent introduction to a lot of problems of discrete mathematics. It discusses a number of selected results and methods, mostly from areas of combinatorics and graph theory, and it uses proofs and problem solving to help students understand the solutions to problems. Numerous examples, figures, and exercises are spread throughout the book.

A Beginner's Guide to Discrete Mathematics

Author: W.D. Wallis

Publisher: Springer Science & Business Media

ISBN: 9780817682866

Category: Mathematics

Page: 427

View: 5840

Wallis's book on discrete mathematics is a resource for an introductory course in a subject fundamental to both mathematics and computer science, a course that is expected not only to cover certain specific topics but also to introduce students to important modes of thought specific to each discipline . . . Lower-division undergraduates through graduate students. —Choice reviews (Review of the First Edition) Very appropriately entitled as a 'beginner's guide', this textbook presents itself as the first exposure to discrete mathematics and rigorous proof for the mathematics or computer science student. —Zentralblatt Math (Review of the First Edition) This second edition of A Beginner’s Guide to Discrete Mathematics presents a detailed guide to discrete mathematics and its relationship to other mathematical subjects including set theory, probability, cryptography, graph theory, and number theory. This textbook has a distinctly applied orientation and explores a variety of applications. Key Features of the second edition: * Includes a new chapter on the theory of voting as well as numerous new examples and exercises throughout the book * Introduces functions, vectors, matrices, number systems, scientific notations, and the representation of numbers in computers * Provides examples which then lead into easy practice problems throughout the text and full exercise at the end of each chapter * Full solutions for practice problems are provided at the end of the book This text is intended for undergraduates in mathematics and computer science, however, featured special topics and applications may also interest graduate students.

Discrete Mathematics in the Schools

Author: Joseph G. Rosenstein

Publisher: American Mathematical Soc.

ISBN: 9780821885789

Category: Mathematics

Page: 452

View: 6000

This book provides teachers of all levels with a great deal of valuable material to help them introduce discrete mathematics into their classrooms.

Discrete Mathematics: Introduction to Mathematical Reasoning

Author: Susanna S. Epp

Publisher: Cengage Learning

ISBN: 0495826170

Category: Mathematics

Page: 648

View: 9615

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.

A First Course in Information Theory

Author: Raymond W. Yeung

Publisher: Springer Science & Business Media

ISBN: 1441986081

Category: Technology & Engineering

Page: 412

View: 6988

This book provides an up-to-date introduction to information theory. In addition to the classical topics discussed, it provides the first comprehensive treatment of the theory of I-Measure, network coding theory, Shannon and non-Shannon type information inequalities, and a relation between entropy and group theory. ITIP, a software package for proving information inequalities, is also included. With a large number of examples, illustrations, and original problems, this book is excellent as a textbook or reference book for a senior or graduate level course on the subject, as well as a reference for researchers in related fields.

Option Valuation

A First Course in Financial Mathematics

Author: Hugo D. Junghenn

Publisher: CRC Press

ISBN: 1439889112

Category: Business & Economics

Page: 266

View: 9994

Option Valuation: A First Course in Financial Mathematics provides a straightforward introduction to the mathematics and models used in the valuation of financial derivatives. It examines the principles of option pricing in detail via standard binomial and stochastic calculus models. Developing the requisite mathematical background as needed, the text presents an introduction to probability theory and stochastic calculus suitable for undergraduate students in mathematics, economics, and finance. The first nine chapters of the book describe option valuation techniques in discrete time, focusing on the binomial model. The author shows how the binomial model offers a practical method for pricing options using relatively elementary mathematical tools. The binomial model also enables a clear, concrete exposition of fundamental principles of finance, such as arbitrage and hedging, without the distraction of complex mathematical constructs. The remaining chapters illustrate the theory in continuous time, with an emphasis on the more mathematically sophisticated Black-Scholes-Merton model. Largely self-contained, this classroom-tested text offers a sound introduction to applied probability through a mathematical finance perspective. Numerous examples and exercises help students gain expertise with financial calculus methods and increase their general mathematical sophistication. The exercises range from routine applications to spreadsheet projects to the pricing of a variety of complex financial instruments. Hints and solutions to odd-numbered problems are given in an appendix and a full solutions manual is available for qualifying instructors.

Discrete Mathematics for Computing

Author: Peter Grossman

Publisher: Macmillan International Higher Education

ISBN: 0230374050

Category: Computers

Page: 328

View: 9054

Discrete Mathematics for Computing presents the essential mathematics needed for the study of computing and information systems. The subject is covered in a gentle and informal style, but without compromising the need for correct methodology. It is perfect for students with a limited background in mathematics. This new edition includes: • An expanded section on encryption • Additional examples of the ways in which theory can be applied to problems in computing • Many more exercises covering a range of levels, from the basic to the more advanced This book is ideal for students taking a one-semester introductory course in discrete mathematics - particularly for first year undergraduates studying Computing and Information Systems. PETER GROSSMAN has worked in both MA26 and industrial roles as a mathematician and computing professional. As a lecturer in mathematics, he was responsible for coordinating and developing mathematics courses for Computing students. He has also applied his skills in areas as diverse as calculator design, irrigation systems and underground mine layouts. He lives and works in Melbourne, Australia.

A First Course in Combinatorial Optimization

Author: Jon Lee

Publisher: Cambridge University Press

ISBN: 9780521010122

Category: Business & Economics

Page: 211

View: 3569

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.

A Short Course in Discrete Mathematics

Author: Edward A. Bender,S. Gill Williamson

Publisher: Courier Corporation

ISBN: 0486439461

Category: Mathematics

Page: 240

View: 3452

What sort of mathematics do I need for computer science? In response to this frequently asked question, a pair of professors at the University of California at San Diego created this text. Its sources are two of the university's most basic courses: Discrete Mathematics, and Mathematics for Algorithm and System Analysis. Intended for use by sophomores in the first of a two-quarter sequence, the text assumes some familiarity with calculus. Topics include Boolean functions and computer arithmetic; logic; number theory and cryptography; sets and functions; equivalence and order; and induction, sequences, and series. Multiple choice questions for review appear throughout the text. Original 2005 edition. Notation Index. Subject Index.

A First Course in Probability and Markov Chains

Author: Giuseppe Modica,Laura Poggiolini

Publisher: John Wiley & Sons

ISBN: 111847774X

Category: Mathematics

Page: 352

View: 1418

Provides an introduction to basic structures of probabilitywith a view towards applications in information technology A First Course in Probability and Markov Chains presentsan introduction to the basic elements in probability and focuses ontwo main areas. The first part explores notions and structures inprobability, including combinatorics, probability measures,probability distributions, conditional probability,inclusion-exclusion formulas, random variables, dispersion indexes,independent random variables as well as weak and strong laws oflarge numbers and central limit theorem. In the second part of thebook, focus is given to Discrete Time Discrete Markov Chains whichis addressed together with an introduction to Poisson processes andContinuous Time Discrete Markov Chains. This book also looks atmaking use of measure theory notations that unify all thepresentation, in particular avoiding the separate treatment ofcontinuous and discrete distributions. A First Course in Probability and Markov Chains: Presents the basic elements of probability. Explores elementary probability with combinatorics, uniformprobability, the inclusion-exclusion principle, independence andconvergence of random variables. Features applications of Law of Large Numbers. Introduces Bernoulli and Poisson processes as well as discreteand continuous time Markov Chains with discrete states. Includes illustrations and examples throughout, along withsolutions to problems featured in this book. The authors present a unified and comprehensive overview ofprobability and Markov Chains aimed at educating engineers workingwith probability and statistics as well as advanced undergraduatestudents in sciences and engineering with a basic background inmathematical analysis and linear algebra.

A First Course in Scientific Computing

Symbolic, Graphic, and Numeric Modeling Using Maple, Java, Mathematica, and Fortran90

Author: Rubin H. Landau

Publisher: Princeton University Press

ISBN: 1400841178

Category: Computers

Page: 512

View: 6570

This book offers a new approach to introductory scientific computing. It aims to make students comfortable using computers to do science, to provide them with the computational tools and knowledge they need throughout their college careers and into their professional careers, and to show how all the pieces can work together. Rubin Landau introduces the requisite mathematics and computer science in the course of realistic problems, from energy use to the building of skyscrapers to projectile motion with drag. He is attentive to how each discipline uses its own language to describe the same concepts and how computations are concrete instances of the abstract. Landau covers the basics of computation, numerical analysis, and programming from a computational science perspective. The first part of the printed book uses the problem-solving environment Maple as its context, with the same material covered on the accompanying CD as both Maple and Mathematica programs; the second part uses the compiled language Java, with equivalent materials in Fortran90 on the CD; and the final part presents an introduction to LaTeX replete with sample files. Providing the essentials of computing, with practical examples, A First Course in Scientific Computing adheres to the principle that science and engineering students learn computation best while sitting in front of a computer, book in hand, in trial-and-error mode. Not only is it an invaluable learning text and an essential reference for students of mathematics, engineering, physics, and other sciences, but it is also a consummate model for future textbooks in computational science and engineering courses. A broad spectrum of computing tools and examples that can be used throughout an academic career Practical computing aimed at solving realistic problems Both symbolic and numerical computations A multidisciplinary approach: science + math + computer science Maple and Java in the book itself; Mathematica, Fortran90, Maple and Java on the accompanying CD in an interactive workbook format