Norman Biggs

In this substantial revision of his excellent book, Professor Biggs has clarified and updated the text, whilst leaving the structure unchanged. The two major changes are: bringing the notation in line with current practice; the inclusion of 'Additional Results' at the end of each chapter, intending thereby to cover most of the major advances in the last twenty years. His basic aim remains algebraically to interpret properties of graphs, then to deduce theorems about them. Like the first edition, this will be essential reading for a wide range of mathematicians, computer scientists and theoretical physicists.

San Ling, Chaoping Xing

Coding theory is concerned with successfully transmitting data through a noisy channel and correcting errors in corrupted messages. It is of central importance for many applications in computer science or engineering. This book gives a comprehensive introduction to coding theory whilst only assuming basic linear algebra. It is based on the authors' teaching experiences and provides a thoroughly modern introduction to the subject. There are numerous examples and exercises, some of which introduce students to novel or more advanced material.

Sriram Pemmaraju, Steven Skiena

Experimenting with Combinatorica, a widely used software package for teaching and research in discrete mathematics, provides an exciting new way to learn combinatorics and graph theory. With examples of all 450 functions in action plus tutorial text on the mathematics, this book is the definitive guide to Combinatorica. The Combinatorica user community ranges from students to engineers to researchers in mathematics, computer science, physics, economics, and the humanities. Combinatorica, which has received the EDUCOM Higher Education Software Award, is included with every copy of the popular computer algebra system Mathematica.

Randall J. LeVeque

This book contains an introduction to hyperbolic partial differential equations and a powerful class of numerical methods for approximating their solution, including both linear problems and nonlinear conservation laws. These equations describe a wide range of wave propagation and transport phenomena arising in nearly every scientific and engineering discipline. Several applications are described in a self-contained manner, along with much of the mathematical theory of hyperbolic problems. The methods studied are implemented in the CLAWPACK software package and source code for all the examples presented can be found on the web, along with animations of many of the simulations. This provides an excellent learning environment for understanding wave propagation phenomena and finite volume methods.

Glenn R. Fulford, Philip Broadbridge

The focus in this text is on mathematical modelling stimulated by contemporary industrial problems involving heat conduction and mass diffusion. These include continuous metal casting, laser drilling, spontaneous combustion of industrial waste, water filtration and crop irrigation. The industrial problems prove to be an excellent setting for the introduction and reinforcement of modelling skills, equation solving techniques, qualitative understanding of partial differential equations and their dynamical properties. For students of mathematics, engineering, or any other related discipline, this will be a great introduction to modelling the real world.

James C. Robinson

This book treats the theory of global attractors, a recent development in the theory of partial differential equations, in a way that also includes much of the traditional elements of the subject. As such it gives a quick but directed introduction to some fundamental concepts, and by the end proceeds to current research problems. Since the subject is relatively new, this is the first book to attempt to treat these various topics in a unified and didactic way. It is intended to be suitable for first year graduate students.

Brian J. Cantwell

Symmetry analysis based on Lie group theory is the most important method for solving nonlinear problems aside from numerical computation. This is a broad, self-contained, introduction to the basics of symmetry analysis and is for first and second year graduate students in science, engineering and applied mathematics. Applications are emphasised, with numerous worked examples to illustrate basic concepts. Mathematica-based software is included on a CD along with more than forty sample notebooks illustrating applications ranging from simple, low order, ordinary differential equations to complex systems of partial differential equations.

John G. Harris

Wave propagation and scattering are often very complex processes. One way to begin to understand them is to study wave propagation in the linear approximation. This is a book describing such propagation using, as a context, the equations of elasticity. The topics covered include reflection, refraction, the propagation of interfacial waves, integral representations, radiation and diffraction, and propagation in closed and open waveguides. Linear Elastic Waves is an advanced level textbook directed at applied mathematicians, seismologists, and engineers.

Elizabeth S. Allman, John A. Rhodes

This introductory textbook focuses on discrete models across a variety of biological subdisciplines, including linear and non-linear models of populations, Markov models of molecular evolution, phylogenetic tree construction from DNA sequence data, genetics, and infectious disease models. The book is suitable for students at a calculus level, but assumes no calculus. Self-contained development of mathematical topics, such as matrix algebra and basic probability, is motivated by the biological models. Computer investigations with MATLAB are incorporated throughout, in both exercises and more extensive projects, to give readers hands-on experience with the mathematical models developed.

Jerome K. Percus

The massive research effort known as the Human Genome Project is an attempt to record the sequence of the three trillion nucleotides that make up the human genome and to identify individual genes within this sequence. While the basic effort is of course a biological one, the description and classification of sequences also lend themselves naturally to mathematical and statistical modeling. This short textbook on the mathematics of genome analysis presents a brief description of several ways in which mathematics and statistics are being used in genome analysis and sequencing. It will be of interest not only to students but also to professional mathematicians curious about the subject.

Avram Sidi

This book is concerned with the coherent treatment, including the derivation, analysis, and applications, of the most useful scalar extrapolation methods. Its importance is rooted in the fact that the methods it discusses are geared towards problems that arise commonly in scientific and engineering disciplines. It differs from existing books on the subject in that it concentrates on the most powerful nonlinear methods, presents in-depth treatments of them, and shows which methods are most effective for different classes of practical nontrivial problems, and also shows how to apply these methods to obtain best results.

Grigory Isaakovich Barenblatt

The author describes and teaches the art of discovering scaling laws, starting from dimensional analysis and physical similarity, which are here given a modern treatment. He demonstrates the concepts of intermediate asymptotics and the renormalisation group as natural consequences of self-similarity and shows how and when these notions and tools can be used to tackle the task at hand, and when they cannot. Based on courses taught to undergraduate and graduate students, the book can also be used for self-study by biologists, chemists, astronomers, engineers and geoscientists.

Tobin A. Driscoll, Lloyd N. Trefethen

Written by the world's two leading experts in the field, this practical guide will have broad appeal. The topic is a subset of 'conformal mapping' and is most closely associated with Laplace's equation on polygonal geometries in two dimensions. The applications of Schwarz-Christoffel mapping have yet to be thoroughly explored, but through the use of numerous figures and extensive referencing, the authors have made this exciting techique accessible. Electrical engineers as well as applied researchers will find particular interest in this book.

Theodore Frankel

This book provides a working knowledge of those parts of exterior differential forms, differential geometry, algebraic and differential topology, Lie groups, vector bundles and Chern forms that are essential for a deeper understanding of both classical and modern physics and engineering. Geometric intuition is developed through a rather extensive introduction to the study of surfaces in ordinary space; consequently, the book should be of interest also to mathematics students. Ideal for graduate and advanced undergraduate students of physics, engineering and mathematics as a course text or for self study.