Books in the Oxford Lecture Series in Mathematics and Its Applications series

A number of methods, from several areas of mathematics, have been used in the hope of finding a formula giving the Frobenius number and algorithms to calculate it. The main intention of this book is to highlight such methods, ideas, viewpoints and applications to a broader audience.

Written by the winner of the 1994 Fields Medal, this work sheds lights on a theoretical problem concerning the mathematical modelling of physical phenomena: the existence, uniqueness, and stability of solutions for large classes of nonlinear partial differential equations.

Fractal geometrics can arise in many different ways mathematically. This book proposes notions of coherent geometric structure, asking what exactly is a fractal "pattern"? A wide range of problems are dealt with, and examples given, which connect to other diverse areas of mathmatics.

This is a handbook of Gamma-convergence, which is a theoretical tool used to study problems in Applied Mathematics where varying parameters are present, with many applications that range from Mechanics to Computer Vision. The book is directed to Applied Mathematicians in all fields and to Engineers with a theoretical background.

Based on the authors' lecture notes, this book is concerned with an aspect of graph theory that has broad applications to complexity theory, graph colourings, channel assignment and statistical physics. Containing exercises, hints and references, it is ideal for graduate students and researchers alike.

This work provides a self-contained introduction to the mathematical theory of hyperbolic systems of conservation laws, with particular emphasis on the study of discontinuous solutions characterized by the appearance of shock waves.

This book presents in a self-contained form the typical basic properties of solutions to semilinear evolutionary partial differential equations, with special emphasis on global properties. It has a didactic ambition and will be useful for an applied readership as well as theoretical researchers.

Phylogenetic (evolutionary) trees and networks are widely used throughout evolutionary biology, epidemiology, and ecology to infer the historical relationships between species through inherited characteristics. Semple and Steel discuss the mathematics that underlies the reconstruction and analysis of these phylogenetic trees.

A timely research text by a leading academic on the mathematical theory of viscous compressible fluids. Containing the most recent results in the field, described in a clear self-contained manner, it is aimed at research mathematicians, theoretical physicists, engineers and graduate students.

The theory of homogenization replaces a real composite material with an imaginary homogeneous one, to describe the macroscopic properties of the composite using the properties of the microscopic structure. This work illustrates the relevant mathematics, logic and methodology with examples.

This is an updated and extended version of the last part of Dr Pretzel's successful book Error Correcting Codes and Finite Fields. It provides an introduction to the geometry of curves over finite fields. and uses the theory for a detailed investigation of geometric Goppa codes, a new and important area of coding theory.