Book Description

The book is intended to be an introductory text for mathematics and computer science students at the second and third year level in universities. It gives an introduction to the subject with sufficient theory for that level of student, with emphasis on algorithms and applications. ... Read more

Reviews (2)

A suitable text for an undergraduate course
This book seems to be one of the best choices of the text for an undergraduate course. It covers all topics that can be included in such course. It contains many exercises. Some of the exercises are routine, some others are more challenging. Also the price of the paperback edition is quite reasonable for a text for a semester course.
I should mention that there are some misprints in this text. Also, there are some gaps in the proof of the Brooks' theorem (pp. 194-196). So a new corrected printing is desirable.

A First Look at Graph Theory
Deseo este libr ... Read more

Reviews (1)

Not much to it
The author makes an attempt to simplify math, but manages to overcomplicate the process. By switching from procedures for the 82/83 to the 85/86 to the 86 to all four to the 82, etc. If this book were to be broken into individual books for each model, or at least rearranged for each model, perhaps that might improve it, but that would reveal just how little meat there is to this book. You would probably be better served by reading the thin manual that comes with some of the models and then reading the thick manual for any additional needs you may have. Better yet, purchase Graphing Calculator Keystroke Guide by Karl Zilm at your local college bookstore. ... Read more

Book Description

The four-colour theorem is one of the famous problems of mathematics, that frustrated generations of mathematicians from its birth in 1852 to its solution (using substantial assistance from electronic computers) in 1976. The theorem asks whether four colours are sufficient to colour all conceivable maps, in such a way that countries with a common border are coloured with different colours. The book discusses various attempts to solve this problem, and some of the mathematics which developed out of these attempts. Much of this mathematics has developed a life of its own, and forms a fascinating part of the subject now known as graph theory. The book is designed to be self-contained, and develops all the graph-theoretical tools needed as it goes along. It includes all the elementary graph theory that should be included in an introduction to the subject, before concentrating on specific topics relevant to the four-colour problem. Part I covers basic graph theory, Euler's polyhedral formula, and the first published false proof of the four-colour theorem. Part II ranges widely through related topics, including map-colouring on surfaces with holes, the famous theorems of Kuratowski, Vizing, and Brooks, the conjectures of Hadwiger and Hajos, and much more besides. In Part II we return to the four-colour theorem, and study in detail the methods which finally cracked the problem. ... Read more

Book Description

Written by three internationally respected authorities in the field, this self-contained reference/text provides the first comprehensive treatment of theoretical, algorithmic, and application aspects of domination in graphs;discussing fundamental results and major research accomplishments in an easy-to-understand style.Includes chapters on domination algorithms and NP-completeness, as well as frameworks for domination that enable the researcher to approach and generalize graph domination from different mathematical perspectives.Appropriate for use at different levels, Fundamentals of Domination in Graphs reinforces the material with a host of learning and pedagogical features, such asbasic definitions and preliminary graph theoretic results consistent graph theory terminology throughout the work end-of-chapter exercises and problems as well as noteworthy open research problems real-world applications in fields from social sciences, optimization, and computer and communication networks to computational complexity and algorithm design nearly 400 examples, equations, drawings, and tables illustrating complex concepts an appendix listing all known domination-related parameters and notations and more!Containing the only comprehensive bibliography of more than 1200 published papers, Fundamentals of Domination in Graphs is a valuable reference for applied and discrete mathematicians, computer and systems engineers, communication network specialists, computer and social scientists, and operations researchers, as well as an excellent text for students taking courses, such as Advanced Topics in Graph Theory and Introduction to Graph Theory in departments of mathematics and computer science. ... Read more

Book Description

An exploration of regression graphics through computer graphics.

Recent developments in computer technology have stimulated new and exciting uses for graphics in statistical analyses. Regression Graphics, one of the first graduate-level textbooks on the subject, demonstrates how statisticians, both theoretical and applied, can use these exciting innovations. After developing a relatively new regression context that requires few scope-limiting conditions, Regression Graphics guides readers through the process of analyzing regressions graphically and assessing and selecting models. This innovative reference makes use of a wide range of graphical tools, including 2D and 3D scatterplots, 3D binary response plots, and scatterplot matrices. Supplemented by a companion ftp site, it features numerous data sets and applied examples that are used to elucidate the theory.

Other important features of this book include:
* Extensive coverage of a relatively new regression context based on dimension-reduction subspaces and sufficient summary plots
* Graphical regression, an iterative visualization process for constructing sufficient regression views
* Graphics for regressions with a binary response
* Graphics for model assessment, including residual plots
* Net-effects plots for assessing predictor contributions
* Graphics for predictor and response transformations
* Inverse regression methods
* Access to a Web site of supplemental plots, data sets, and 3D color displays.

An ideal text for students in graduate-level courses on statistical analysis, Regression Graphics is also an excellent reference for professional statisticians. ... Read more

Reviews (1)

graphical methods for regression
This is one of a series of books Dennis Cook has written on regression graphics. This is the most theoretical of the three. It is a companion to the recent book with Sandy Weisberg. The other book emphasizes applications while this provides some theory to support a complete regression analysis through graphical methods. It provides a modern and up-to-date treatment. This work was summarized in a recent tutorial I attended that Cook gave at the Deming Conference last year. It includes several examples and covers asymptotic theory for such topics as sliced inverse regression. It is a great reference source also. ... Read more

Book Description

Bipartite graphs are perhaps the most basic of objects in graph theory, both from a theoretical and practical point of view. Until now, they have been considered only as a special class in some wider context. This work deals solely with bipartite graphs, providing traditional material as well as many new and unusual results. The authors illustrate the theory with many applications, especially to problems in timetabling, chemistry, communication networks and computer science. The material is accessible to any reader with a graduate understanding of mathematics and will be of interest to specialists in combinatorics and graph theory. ... Read more

Book Description

This is a textbook for an introductory combinatorics course that can take up one or two semesters. An extensive list of exercises, ranging in difficulty from "routine" to "worthy of independent publication", is included. In each section, there are also exercises that contain material not explicitly discussed in the text before, so as to provide instructors with extra choices if they want to shift the emphasis of their course.

It goes without saying that the text covers the classic areas, i.e. combinatorial choice problems and graph theory. What is unusual, for an undergraduate textbook, is that the author has included a number of more elaborate concepts, such as Ramsey theory, the probabilistic method and - probably the first of its kind - pattern avoidance. While the reader can only skim the surface of these areas, the author believes that they are interesting enough to catch the attention of some students. As the goal of the book is to encourage students to learn more combinatorics, every effort has been made to provide them with a not only useful, but also enjoyable and engaging reading. ... Read more

Reviews (1)

A Stroll Through the Old and New
Combinatorics often, but not always, involves finite sets, and the ideas of counting. But the subject of combinatorics has indeed become very large, and it has worked its way into many others parts of mathematics, computer science, science, and engineering. Bona's book, `A Walk Through Combinatorics', is a text designed for an introductory course in combinatorics. It covers the traditional areas of combinatorics like enumeration and graph theory, but also makes a real effort to introduce some more sophisticated ideas in combinatorics like Ramsey Theory and the probabilistic method.

The book is very exciting to read, and the author has a wonderful sense of humor: in Chapter 3 he introduces the idea of a permutation by the example of n people arriving at a dentist's office at the same time. They must decide the order in which they will be served. How many orders are possible?

The problems are a great strength of this text. Each chapter ends with a set of exercises with solutions. These tend to be very interesting and often quite challenging. A set of supplementary exercises follows. These tend to be a little easier, though not always, and make good homework assignments. The supplementary exercises do not have solutions, but a solutions manual is available to instructors.

The book walks through four parts: I. Basic Methods; II. Enumerative Combinatorics; III. Graph Theory; IV. Horizons. I particularly like the fourth part which includes Ramsey Theory, subsequence conditions on permutations, the probabilistic method, and partial orders and lattices. A glimpse of these subjects can whet the walker's appetite for more challenging terrain.

I would have liked to give this book 5 stars, but it suffers from a lack of clarity in some places. For example, the discussion of example 2.2 in Chapter 2 on induction just does not read clearly or make sense as it is written. Though an instructor can figure out what is missing, it would be much harder for a student to do so. And figure 13.1 on the colors of the edge of a triangle in Chapter 13 on Ramsey Theory is mislabeled. Again, this could steer an unwary student off the path of understanding. But these defects are minor compared to the riches contained in this text. The author has chosen his subjects carefully, illustrated them well and provided a wealth of wonderful exercises. And he has given the reader a glimpse of some of the less traditional and newer areas of combinatorics at the end of the book. ... Read more

Book Description

This new edition of Matrix Methods emphasizes applications to Jordan-canonical forms, differential equations, and least squares. The revision now includes an entire new chapter on inner products, additional material on elementary row applications, and hundreds of new exercises.

* Provides an introduction to the functional approach to programming
* Emphasizes the problem to be solved, not the programming language
* Takes the view that all computer programs are a definition of a function
* Includes exercises for each chapter
* Requires at least a high school algebra level of mathematical sophistication
* A self-contained work
* Can be used as a pre-programming language introduction to the mathematics of computing ... Read more

Reviews (1)

Matrices revealed
This is the best book on matrix algebra I ever read. It so thoroughly unraveled the mysteries of inverting and transposing matrices that I saw the world in a whole new light. I look forward to the movie!! ... Read more

Book Description

With over 10,000 diagrams and extensive tables of properties, this atlas is comprehensive and unique. Never before has so much visual information about graphs been collected in a single volume, making it an invaluable source for researchers in graph theory, operations research and computer science. ... Read more

Book Description

This comprehensive, detailed reference for symbolic computation with Mathematica provides the reader with a working knowledge of Mathematica in general and a detailed knowledge of key aspects of Mathematica needed to create the fastest, shortest and most elegant implementations to solve symbolic problems from the natural and physical sciences. The Guidebook gives the user a deeper understanding of Mathematica by instructive implementations, explanations, and examples at varying levels of complexity. ... Read more

Book Description

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. ... Read more

Book Description

This well-organized reference is a definitive encyclopedia for the literature on graph classes. It contains a survey of more than 200 classes of graphs, organized by types of properties used to define and characterize the classes, citing key theorems and literature references for each. The authors state results without proof, providing readers with easy access to far more key theorems than are commonly found in other mathematical texts. Interconnections between graph classes are also provided to make the book useful to a variety of readers. ... Read more

Book Description

An emphasis on the practical applications of algebra motivates readers and encourages them to see algebra as an important part of their daily lives. Strongly emphasizes good problem-solving skills, uses real-world applications. For anyone interested in Algebra. ... Read more

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Elementary Algebra
Great book! I have used this book for class and and it had proven to be very efficiant. The lessons are easy to follow and it provides adequate examples for algebra. ... Read more

Reviews (1)

Knuth's eccentricity discourages beginners
I found that Knuth's reputation for eccenctricity gets in the way of actually getting to the meat of the book. For example, getting the programs to compile under Windows was not as straightforward as it could be (although not that difficult). Much harder was to get used to the idea of using CTANGLE and CWEB in order to get Graphbase to a state where you can actually compile it.

It does not help at all that Chapter 3 of the book is when how to install Graphbase is actually discussed. Just for these alone I have to give the book a 3 star rating. Perhaps I will change this once I have had the opportunity peruse the _real_ contents of the book. ... Read more

Book Description

Graph theory has experienced a tremendous growth during the 20th century. One of the main reasons for this phenomenon is the applicability of graph theory in other disciplines such as physics, chemistry, psychology, sociology, and theoretical computer science. This book aims to provide a solid background in the basic topics of graph theory. It covers Dirac's theorem on k-connected graphs, Harary-Nashwilliam's theorem on the hamiltonicity of line graphs, Toida-McKee's characterization of Eulerian graphs, the Tutte matrix of a graph, Fournier's proof of Kuratowski's theorem on planar graphs, the proof of the nonhamiltonicity of the Tutte graph on 46 vertices and a concrete application of triangulated graphs. The book does not presuppose deep knowledge of any branch of mathematics, but requires only the basics of mathematics. It can be used in an advanced undergraduate course or a beginning graduate course in graph theory. ... Read more

Book Description

This book evolved from several courses in combinatorics and graph theory given at Appalachian State University and UCLA. Chapter 1 focuses on finite graph theory, including trees, planarity, coloring, matchings, and Ramsey Theory.Chapter 2 studies combinatorics, including the principle of inclusion and exclusion, generating functions, recurrence relations, Pólya Theory, the stable marriage problem, and several important classes of numbers.Chapter 3 presents infinite pigeonhole principles, König's lemma, and Ramsey's theorem, and discusses their connections to axiomatic set theory. The text is written in an enthusiastic and lively style.It includes results and problems that cross subdisciplines, emphasizing relationships between different areas of mathematics.In addition, recent results appear in the text, illustrating the fact that mathematics is a living discipline. The text is primarily directed toward upper-division undergraduate students, but lower-division undergraduates with a penchant for proof and graduate students seeking an introduction to these subjects will also find much of interest. John Harris did his undergraduate work at Furman University, and he received his Ph.D. from Emory University. He has taught at Appalachian State University and at Furman. His primary mathematical interest is finite graph theory, focusing mainly on subgraphs, paths, and cycles. Jeff Hirst is a mathematical logician and has published a number of papers analyzing the logical strength of theorems of infinite graph theory and combinatorics. He received his B.A. and M.A. from the University of Kansas, and his Ph.D. from the Pennsylvania State University.He has taught at the Ohio State University and Appalachian State University.Michael Mossinghoff received his undergraduate degree from Texas A & M University, his M.S. in computer science from Stanford University, and his Ph.D. in mathematics from the University of Texas at Austin. He has taught at Appalachian State University and UCLA. His research concerns analytic and algorithmic problems in number theory and combinatorics. ... Read more

Reviews (1)

What an introductory book on combinatorics should be
Little did I expect of a book that has seemingly not garnered that much attention among professors and students (at least the lack of reviews in Amazon.com might serve as a confirming instance of that speculation), but come exam time, the book proved that such prejudice is outright foolish.

The authors must really love both the field and writing about it, for their overflowing exuberance readily transfers to the pages. Pictures and humor are never a scarcity here: the authors took no shame providing both; a curious but pleasurably fresh anomaly in the often dry and coldly serious world that is mathematics writing. ... Read more