Book Description

The Petersen graph occupies an important position in the development of several areas of modern graph theory, because it often appears as a counter-example to important conjectures. In this account, the authors examine those areas, using the prominent role of the Petersen graph as a unifying feature. Topics covered include: vertex and edge colorability (including snarks), factors, flows, projective geometry, cages, hypohamiltonian graphs, and "symmetry" properties such as distance transitivity. The final chapter contains a potpourri of other topics in which the Petersen graph has played its part. ... Read more

Reviews (1)

A fascinating survey of topics in graph theory
The Petersen graph is a small graph which shows up amazingly often as a counterexample in graph theory. Holton and Sheehan use it as a starting point to discuss several topics, such as the four-color problem and "snarks", cages, symmetry conditions on graphs, and hypohamiltonian graphs. Graph theory is kind of a hobby of mine, and I find this book an absorbing mishmash of introductory material. It's very accessible, and gives a real sense of a live field, full of conjectures.

The level is probably appropriate for a smart math undergrad. A little knowledge of graphs would be good, and you should know what groups are, and be able to read a proof. The presentation is often a bit sloppy (I had to rewrite some of the proofs to understand them). But still, I definitely want this in my library. ... Read more

Book Description

An effort has been made to present the various topics in the theory of graphs in a logical order, to indicate the historical background, and to clarify the exposition by including figures to illustrate concepts and results. In addition, there are three appendices which provide diagrams of graphs, directed graphs, and trees. The emphasis throughout is on theorems rather than algorithms or applications, which however are occaisionally mentioned. ... Read more

Reviews (4)

A class for theoretical math, but not applied math
I used this text in school, as a computer science student in a theoretical math class.

If you are looking for examples of computer algorithms, look elsewhere; the closest this will get you is to "existence proofs", which is showing that something (such as a hamiltonian cycle) exists in a graph that has thus-and-such number of points or edges, but not tell you which sequence of points/edges make up that something. (For example, a graph can be embedded in a plane unless there's a subgraph that looks like K(5) or K(3,3) inside it - this is in about chapter 5, and an important theorem. The text proves this, but doesn't tell you HOW to embed the graph in a plane.)

That said, this is an excellent book for theoretical mathematics. I understand that the first two chapters can be used as a high school math text, as an introduction to proofs, and agree that it would work well.

As a formal introduction to proving theorems, especially in a self-contained world (you don't need many prerequisites for this, like you do for a topology or analysis text), this is pretty swell.

So, to the person who said that he didn't like this because there weren't algorithms in the book: you can find those in the semiliterate computer science textbooks. (I would insist that the last four words of the previous sentence are redundant.)

Look here for mathematics.

missing solution
This book was not published in 1995, but in 1969.

i was looking for some algorithms that solve the classical problems like shortest path and they were not even mentioned

Clasical and Excellent
Good

The absolute classic!
This is the abslolute classic in the field and a great introduction to this fascinating area of the discrete mathematics. ... Read more

Book Description

This book presents mathematical models that arise in current photographic science. The book contains seventeen chapters, each dealing with one area of photographic science, and a final chapter containing exercises. Each chapter, except the two introductory chapters and the last one, begins with general background information at a level understandable by graduate and undergraduate students. It then proceeds to develop a mathematical model, using mathematical tools such as ordinary differential equations, partial differential equations, and stochastic processes. Next, some mathematical results are mentioned, often providing a partial solution to problems raised by the model. Finally, most chapters include open problems. The last chapter of the book contains ôModeling and Applied Mathematicsö exercises based on the material presented in the earlier chapters.These exercises are intended primarily for graduate students and advanced undergraduates. ... Read more

Book Description

Hardbound. Threshold graphs have a beautiful structure and possess many important mathematical properties. They have applications in many areas including computer science and psychology. Over the last 20 years the interest in threshold graphs has increased significantly, and the subject continues to attract much attention.

The book contains many open problems and research ideas which will appeal to graduate students and researchers interested in graph theory. But above all Threshold Graphs and Related Topics provides a valuable source of information for all those working in this field. ... Read more

Book Description

Emphasizing graphing technology and business applications, this user-friendly book is the perfect reference for everyday and business mathematics.Solves problems using both algebra and a graphing utility, with the benefits of each illustrated. Uses real data to help readers make connections between the mathematics learned and familiar situations.Uses up-to-date technology including the more powerful features of ZERO(ROOT) and INTERSECT, with minimal use of TRACE. Helps readers quickly identify key points in the book with a vivid new full-color design.For anyone who needs to brush up on everyday or business-related mathematics. ... Read more

Book Description

This book, suitable for graduate students and professional mathematicians alike, didactically introduces methodologies due to Furstenberg and others for attacking problems in chromatic and density Ramsey theory via recurrence in topological dynamics and ergodic theory, respectively. Many standard results are proved, including the classical theorems of van der Waerden, Hindman, and Szemerdi. More importantly, the presentation strives to reflect the extent to which the field has been streamlined since breaking onto the scene around twenty years ago. Potential readers who were previously intrigued by the subject matter but found it daunting may want to give a second look. ... Read more

Book Description

This book constitutes the strictly refereed post-conference proceedings of the 6th International Symposium on Graph Drawing, GD '98, held in Montreal, Canada in August 1998. The 23 revised full papers presented were carefully selected for inclusion in the book from a total of 57 submissions. Also included are nine system demonstrations and abstracts of 14 selected posters. The papers presented cover the whole range of graph drawing, ranging from theoretical aspects in graph theory to graph drawing systems design and evaluation, graph layout and diagram design. ... Read more

Book Description

This essay collection focuses on the relationship between continuous time models and Autoregressive Conditionally Heteroskedastic (ARCH) models and applications. For the first time, Modelling Stock Market Volatility provides new insights about the links between these two models and new work on practical estimation methods for continuous time models. Featuring the pioneering scholarship of Daniel Nelson, the text presents research about the discrete time model, continuous time limits and optimal filtering of ARCH models, and the specification and estimation of continuous time processes. This work will lead to a rapid growth in their empirical application as they are increasingly subjected to routine specification testing.

Key Features
* Provides for the first time new insights on the links between continuous time and ARCH models
* Collects seminal scholarship by some of the most renowned researchers in finance and econometrics
* Captures complex arguments underlying the approximation and proper statistical modelling of continuous time volatility dynamics ... Read more

Reviews (1)

Clear and easy to follow.
I read this book as a refresher of the high school algebra I'd forgotten (or slept through). This book flows well from one topic to the next. Unlike my high school textbooks, this book carefully covers everything you need to know before the practice questions - I never felt lost or hopelessly confused. ... Read more

Book Description

This book constitutes the refereed proceedings of the 25th International Workshop on Graph-Theorie Concepts in Computer Science WG'99, held at the Centre Stefano Frascini on Monte Verita, Ascona, Switzerland in June 1999. The 33 revised full papers presented together with four invited contributions were carefully reviewed and selected from 64 papers submitted. The papers provide a wealth of new results for various graph classes, graph computations, graph algorithms and graph-theoretical applications in a variety of fields. ... Read more

Book Description

Markov process theory is basically an extension of ordinary calculus to accommodate functions whos time evolutions are not entirely deterministic. It is a subject that is becoming increasingly important for many fields of science. This book develops the single-variable theory of both continuous and jump Markov processes in a way that should appeal especially to physicists and chemists at the senior and graduate level.

Key Features
* A self-contained, prgamatic exposition of the needed elements of random variable theory
* Logically integrated derviations of the Chapman-Kolmogorov equation, the Kramers-Moyal equations, the Fokker-Planck equations, the Langevin equation, the master equations, and the moment equations
* Detailed exposition of Monte Carlo simulation methods, with plots of many numerical examples
* Clear treatments of first passages, first exits, and stable state fluctuations and transitions
* Carefully drawn applications to Brownian motion, molecular diffusion, and chemical kinetics ... Read more

Reviews (1)

Good Introduction
This is the most readable introduction to Markov processes I have found. ... Read more

Book Description

This book is the result of 18 years of research into Steiner's problem and its relatives in theory and application. Starting with investigations of shortest networks for VLSI layout and, on the other hand, for certain facility location problems, the author has found many common properties for Steiner's problem in various spaces. The purpose of the book is to sum up and generalize many of these results for arbitrary finite-dimensional Banach spaces. It shows that we can create a homogeneous and general theory when we consider two dimensions of such spaces, and that we can find many facts which are helpful in attacking Steiner's problem in the higher-dimensional cases. The author examines the underlying mathematical properties of this network design problem and demonstrates how it can be attacked by various methods of geometry, graph theory, calculus, optimization and theoretical computer science.Audience: All mathematicians and users of applied graph theory. ... Read more

Book Description

A lively invitation to the flavor, elegance, and power of graph theory

This mathematically rigorous introduction is tempered and enlivened by numerous illustrations, revealing examples, seductive applications, and historical references. An award-winning teacher, Russ Merris has crafted a book designed to attract and engage through its spirited exposition, a rich assortment of well-chosen exercises, and a selection of topics that emphasizes the kinds of things that can be manipulated, counted, and pictured. Intended neither to be a comprehensive overview nor an encyclopedic reference, this focused treatment goes deeply enough into a sufficiently wide variety of topics to illustrate the flavor, elegance, and power of graph theory.

Another unique feature of the book is its user-friendly modular format. Following a basic foundation in Chapters 1-3, the remainder of the book is organized into four strands that can be explored independently of each other. These strands center, respectively, around matching theory; planar graphs and hamiltonian cycles; topics involving chordal graphs and oriented graphs that naturally emerge from recent developments in the theory of graphic sequences; and an edge coloring strand that embraces both Ramsey theory and a self-contained introduction to Pólya's enumeration of nonisomorphic graphs. In the edge coloring strand, the reader is presumed to be familiar with the disjoint cycle factorization of a permutation. Otherwise, all prerequisites for the book can be found in a standard sophomore course in linear algebra.

The independence of strands also makes Graph Theory an excellent resource for mathematicians who require access to specific topics without wanting to read an entire book on the subject. ... Read more

Reviews (1)

Mediocre text with some potential
Merris has tried to write a text suitable for a one-semester introduction to graph theory for undergraduates with little background required (merely standard proof techniques). He has succeeded in writing a text that can be covered in one term, if you rush, rush, and rush some more. However, he has relegated some important topics to poorly-written exercises (e.g., Euler tours and such). The text also lacks cohesiveness. The Preface makes it clear that Merris wants the book to lead to four independent strands after the initial three chapters. However, a single chapter does not constitute a "strand" to be followed, and the only set of chapters that becomes cohesive at the end is 7, 8, and 9. Regarding chapter 9, don't let the title "Oriented Graphs" mislead you. A tiny portion of the chapter deals with oriented graphs as an excuse to introduce the vertex-edge incidence matrix and then the Laplacian matrix, and the rest of the chapter is devoted to properties of the Laplacian spectrum.

Another complaint is that this text brushes over multigraphs and doesn't even think of talked about digraphs beyond the dumbing-down of digraphs to oriented graphs in chapter 9.

The author's writing style is clear and student-friendly, and the chapters have a good selection of exercises. However, instructors should do the exercises before assigning them, as we encountered at least one unprovable proposition that was simply stated as "Show that ..." There is also at least one statement that is much more difficult than Merris intended.

I think that future editions of this text could have some promise, but it needs work. ... Read more

Book Description

Line graphs have the property that their least eigenvalue is greater than, or equal to, -2, a property shared by generalized line graphs and a finite number of so-called exceptional graphs. This book deals with all these families of graphs in the context of their spectral properties. Technical descriptions of these graphs are included in the appendices, while the bibliography provides over 250 references.It will be an important resource for all researchers with an interest in algebraic graph theory. ... Read more

Book Description

This book motivates students by highlighting real people facing real challenges finding real solutions. This series features real workers at Motorola, along with hundreds of applications and real data sets highlighting the relevance and scope of activities a reader may encounter in life.Covers such topics as graphs, functions, polynomial and rational functions, the zeros of a polynomial function, exponential and logarithmic functions, trigonometric functions, analytic trigonometry, applications of trigonometric functions, polar coordinates, vectors, analytic geometry, systems of equations and inequalities, sequence, induction, the binomial theorem, counting and probability, and more.For anyone interested in Precalculus. ... Read more

Reviews (1)

Consider other books first
If you already know precalculus at the level of a college professor, this may be the book for you. Vital steps for completing problems are omitted, explanations are not given for processes that must be understood. Definitions of new terms are not given, forcing the student to reference another book or go to the web. ... Read more

Book Description

Emphasizing graphing technology and business applications, this user-friendly book is the perfect reference for everyday and business mathematics.Solves problems using both algebra and a graphing utility, with the benefits of each illustrated. Uses real data to help readers make connections between the mathematics learned and familiar situations.Uses up-to-date technology including the more powerful features of ZERO(ROOT) and INTERSECT, with minimal use of TRACE. Helps readers quickly identify key points in the book with a vivid new full-color design.For anyone who needs to brush up on everyday or business-related mathematics. ... Read more

Reviews (1)

What can you say it's a math book?
I did use this book for two semesters and I did pass my classes with good enough grades to go on to calculus. I didn't like how it was missing any practical applications for most of the material. isn't college about the time to reveal hou you are going to USE all this math you've learned? Oh well many challenging problems but I would not buy this book for my personal library. ... Read more