This book leads the reader from simple graphs through planar graphs, Euler's formula, Platonic graphs, coloring, the genus of a graph, Euler walks, Hamilton walks, more. Includes exercises. 1976 edition.

     -Byte, September 1995 I can't begin to tell you how many pleasurable hours of study and recreation they have afforded me! I have pored over them in cars, restaurants, at work, at home... and even at a Little League game when my son wasn't in the line-up. -Charles Long If you think you're a really good programmer... read [Knuth's] Art of Computer Programming... You should definitely send me a resume if you can read the whole thing. -Bill Gates It's always a pleasure when a problem is hard enough that you have to get the Knuths off the shelf. I find that merely opening one has a very useful terrorizing effect on computers. -Jonathan Laventhol This first volume in the series begins with basic programming concepts and techniques, then focuses more particularly on information structures-the representation of information inside a computer, the structural relationships between data elements and how to deal with them efficiently. Elementary applications are given to simulation, numerical methods, symbolic computing, software and system design. Dozens of simple and important algorithms and techniques have been added to those of the previous edition. The section on mathematical preliminaries has been extensively revised to match present trends in research. Ebook (PDF version) produced by Mathematical Sciences Publishers (MSP), http: //msp.org

    Practical Algebra is an easy andfun-to-use workout program that quickly puts you in command of allthe basic concepts and tools of algebra. With the aid of practical, real-life examples and applications, you'll learn: * The basic approach and application of algebra to problemsolving * The number system (in a much broader way than you have known itfrom arithmetic) * Monomials and polynomials; factoring algebraic expressions; howto handle algebraic fractions; exponents, roots, and radicals;linear and fractional equations * Functions and graphs; quadratic equations; inequalities; ratio, proportion, and variation; how to solve word problems, andmore Authors Peter Selby and Steve Slavin emphasize practical algebrathroughout by providing you with techniques for solving problems ina wide range of disciplines--from engineering, biology, chemistry, and the physical sciences, to psychology and even sociology andbusiness administration. Step by step, Practical Algebra shows youhow to solve algebraic problems in each of these areas, then allowsyou to tackle similar problems on your own, at your own pace.Self-tests are provided at the end of each chapter so you canmeasure your mastery.

    Seeking to address the various challenges of off-camera lighting, professional photographers and advanced amateurs alike will find a range of confidence-building instruction, beginning with basic how’s and why’s of lighting for creative effect, the types of equipment available and instruction about their proper use, clear definitions of various technical concepts such as managing shutter speed and controlling flash exposure, using ambient light as well as natural sunlight during a shoot, and incorporating off-camera flash into a portrait session. Concluding this lesson plan is a look at five different real-life photo sessions, each employing a different flash technique. Here, photographers get a deeper understanding of each concept put into practice, marrying the elements of lighting with the natural elements presented by the shoot.

    Introductory Graph Theory presents a nontechnical introduction to this exciting field in a clear, lively, and informative style. Author Gary Chartrand covers the important elementary topics of graph theory and its applications. In addition, he presents a large variety of proofs designed to strengthen mathematical techniques and offers challenging opportunities to have fun with mathematics. Ten major topics — profusely illustrated — include: Mathematical Models, Elementary Concepts of Graph Theory, Transportation Problems, Connection Problems, Party Problems, Digraphs and Mathematical Models, Games and Puzzles, Graphs and Social Psychology, Planar Graphs and Coloring Problems, and Graphs and Other Mathematics. A useful Appendix covers Sets, Relations, Functions, and Proofs, and a section devoted to exercises — with answers, hints, and solutions — is especially valuable to anyone encountering graph theory for the first time. Undergraduate mathematics students at every level, puzzlists, and mathematical hobbyists will find well-organized coverage of the fundamentals of graph theory in this highly readable and thoroughly enjoyable book.

    A Key Strength Of This Text Is Zill'S Emphasis On Differential Equations As Mathematical Models, Discussing The Constructs And Pitfalls Of Each. The Third Edition Is Comprehensive, Yet Flexible, To Meet The Unique Needs Of Various Course Offerings Ranging From Ordinary Differential Equations To Vector Calculus. Numerous New Projects Contributed By Esteemed Mathematicians Have Been Added. Key Features O The Entire Text Has Been Modernized To Prepare Engineers And Scientists With The Mathematical Skills Required To Meet Current Technological Challenges. O The New Larger Trim Size And 2-Color Design Make The Text A Pleasure To Read And Learn From. O Numerous NEW Engineering And Science Projects Contributed By Top Mathematicians Have Been Added, And Are Tied To Key Mathematical Topics In The Text. O Divided Into Five Major Parts, The Text'S Flexibility Allows Instructors To Customize The Text To Fit Their Needs. The First Eight Chapters Are Ideal For A Complete Short Course In Ordinary Differential Equations. O The Gram-Schmidt Orthogonalization Process Has Been Added In Chapter 7 And Is Used In Subsequent Chapters. O All Figures Now Have Explanatory Captions. Supplements O Complete Instructor'S Solutions: Includes All Solutions To The Exercises Found In The Text. Powerpoint Lecture Slides And Additional Instructor'S Resources Are Available Online. O Student Solutions To Accompany Advanced Engineering Mathematics, Third Edition: This Student Supplement Contains The Answers To Every Third Problem In The Textbook, Allowing Students To Assess Their Progress And Review Key Ideas And Concepts Discussed Throughout The Text. ISBN: 0-7637-4095-0

    Today, unfortunately, the traditional place of mathematics in education is in grave danger. The teaching and learning of mathematics has degenerated into the realm of rote memorization, the outcome of which leads to satisfactory formal ability but does not lead to real understanding or to greater intellectual independence. This new edition of Richard Courant's and Herbert Robbins's classic work seeks to address this problem. Its goal is to put the meaning back into mathematics.Written for beginners and scholars, for students and teachers, for philosophers and engineers, What is Mathematics? Second Edition is a sparkling collection of mathematical gems that offers an entertaining and accessible portrait of the mathematical world. Covering everything from natural numbers and the number system to geometrical constructions and projective geometry, from topology and calculus to matters of principle and the Continuum Hypothesis, this fascinating survey allows readers to delve into mathematics as an organic whole rather than an empty drill in problem solving. With chapters largely independent of one another and sections that lead upward from basic to more advanced discussions, readers can easily pick and choose areas of particular interest without impairing their understanding of subsequent parts.Brought up to date with a new chapter by Ian Stewart, What is Mathematics? Second Edition offers new insights into recent mathematical developments and describes proofs of the Four-Color Theorem and Fermat's Last Theorem, problems that were still open when Courant and Robbins wrote this masterpiece, but ones that have since been solved.Formal mathematics is like spelling and grammar - a matter of the correct application of local rules. Meaningful mathematics is like journalism - it tells an interesting story. But unlike some journalism, the story has to be true. The best mathematics is like literature - it brings a story to life before your eyes and involves you in it, intellectually and emotionally. What is Mathematics is like a fine piece of literature - it opens a window onto the world of mathematics for anyone interested to view.

    

    

    As well as lucid descriptions of all the topics and many worked examples, it contains over 800 exercises. New stand-alone chapters give a systematic account of the 'special functions' of physical science, cover an extended range of practical applications of complex variables, and give an introduction to quantum operators. Further tabulations, of relevance in statistics and numerical integration, have been added. In this edition, half of the exercises are provided with hints and answers and, in a separate manual available to both students and their teachers, complete worked solutions. The remaining exercises have no hints, answers or worked solutions and can be used for unaided homework; full solutions are available to instructors on a password-protected web site, www.cambridge.org/9780521679718.

    With this astonishing guidebook, Surfing Through Hyperspace, you need not be a mathematician or an astrophysicist to explore the all-but-unfathomable concepts of hyperspace and higher-dimensional geometry.No subject in mathematics has intrigued both children and adults as much as the idea of a fourth dimension. Philosophers and parapsychologists have meditated on this mysterious space that no one can point to but may be all around us. Yet this extra dimension has a very real, practical value to mathematicians and physicists who use it every day in their calculations. In the tradtion of Flatland, and with an infectious enthusiasm, Clifford Pickover tackles the problems inherent in our 3-D brains trying to visualize a 4-D world, muses on the religious implications of the existence of higher-dimensional consciousness, and urges all curious readers to venture into the unexplored territory lying beyond the prison of the obvious. Pickover alternates sections that explain the science of hyperspace with sections that dramatize mind-expanding concepts through a fictional dialogue between two futuristic FBI agents who dabble in the fourth dimension as a matter of national security. This highly accessible and entertaining approach turns an intimidating subject into a scientific game open to all dreamers.Surfing Through Hyperspace concludes with a number of puzzles, computer experiments and formulas for further exploration, inviting readers to extend their minds across this inexhaustibly intriguing scientific terrain.

    

    Intuition and computational abilities are stressed. Original material on DE and multiple integrals has been expanded.

    Book is unique in its emphasis on the frequency approach and its use in the solution of problems. Contents include: Fundamentals and Algorithms; Polynomial Approximation — Classical Theory; Fourier Approximation — Modern Theory; and Exponential Approximation.

    Essentially, you make an initial guess, and then get more data to improve it. Bayes Theorem, or Bayes Rule, has a ton of real world applications, from estimating your risk of a heart attack to making recommendations on Netflix But It Isn't That Complicated This book is a short introduction to Bayes Theorem. It is only 15 pages long, and is intended to show you how Bayes Theorem works as quickly as possible. The examples are intentionally kept simple to focus solely on Bayes Theorem without requiring that the reader know complicated probability distributions. If you want to learn the basics of Bayes Theorem as quickly as possible, with some easy to duplicate examples, this is a good book for you.