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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.

This is a book written primarily for graduate students and early researchers in the fields of Analysis and Partial Differential Equations (PDEs). Coverage of the material is essentially self-contained, extensive and novel with great attention to details and rigour.

This text examines degree theory and some of its applications in analysis. Topics described include: degree theory for continuous functions; the multiplication theorem; Hopf's theorem; Brower's fixed point theorem; odd mappings; and Jordan's separation theorem.

Based on an established graduate course given at MIT that provides an introduction to the theory of the dynamical Yang-Baxter equation and its applications, which is an important area in representation theory and quantum groups. This book contains proofs and explicit calculations, and is useful for graduate students of mathematics.

This text provides a review of the consistent themes from Dominic Welsh's influential work in combinatorics and discrete probability. Original articles by key academics are set in a broader context by the inclusion of review material. The text will appeal to all those seeking an introduction to the relevant contemporary aspects of these fields.

The 'factorization method', discovered by Professor Kirsch, is a relatively new method for solving certain types of inverse scattering problems and problems in tomography. The text introduces the reader to this promising approach and discusses the wide applicability of this method by choosing typical examples.

The present book is the first one in the new subject area of non-integrable Hamiltonian partial differential equations, using the approach of analysis and geometry rather than algebra to study the equations. The book will be an invaluable source of information for postgraduate mathematics students and researchers working in analysis as well as for theoretical physicists interested in the topic.

Aimed at graduates and researchers in algebraic geometry, this collection of edited chapters provides a complete and essentially self-contained account of the construction of 3-fold and 4-fold klt flips.

Part of the OXFORD LECTURE SERIES IN MATHEMATICS AND ITS APPLICATIONS series, a comprehensive and straightforward introduction to the basic methods of designing efficient parallel algorithms for graph matching problems. Appropriate for students at undergraduate level.

An application-oriented introduction to the highly topical area of the development and analysis of efficient fixed-parameter algorithms for hard problems. Aimed at graduate and research mathematicians, algorithm designers, and computer scientists, it provides a fresh view on this highly innovative field of algorithmic research.

Aimed at graduate students and researchers in mathematics, engineering, oceanography, meteorology and mechanics, this text provides a detailed introduction to the physical theory of rotating fluids, a significant part of geophysical fluid dynamics. The Navier-Stokes equations are examined in both incompressible and rapidly rotating forms.

Based on lecture notes from the Scuola Normale this book presents the main mathematical prerequisites for analysis in metric spaces. Supplemented with exercises of varying difficulty it is ideal for a graduate-level short course for applied mathematicians and engineers.

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.

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.

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.

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.

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.

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.

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 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.

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.

Filling the gap between introductory and encyclopedic treatments, this book provides rich and appealing material for a second course in combinatorial optimization. This book is suitable for graduate students as well as a reference for established researchers.

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.

This text is concerned with quantitative aspects of the theory of nonlinear diffusion equations, which appear as mathematical models in different branches of Physics, Chemistry, Biology and Engineering.

This book is a unique introduction to graph theory, written by one of the founding fathers. It is not intended as a comprehensive treatise, but rather as an account of those parts of the theory that have been of special interest to the author. Professor Tutte details his experiences in the area, and provides a fascinating insight into the processes leading to his proofs.

This book provides a rapid introduction to the mathematical theory of compressible flow, giving a comprehensive account of the field and all important results up to the present day. The book is written in a clear, instructive and self-contained manner and will be accessible to a wide audience.

An international authorship of contributors from acknowledged experts in their field, this book provides a clear exposition on such topics as simplex algorithms, and interior point algorithms, both from a theoretical and a computational viewpoint.

This book combines the efforts of a distinguished team of authors, who are all renowned mathematicians and expositors, and provides a modern introduction to the calculus of variations. By focusing on the one-dimensional case it remains relatively free of technicalities, and therefore provides a useful overview of the theory at a level suitable for graduate students.

A rigorous mathematical description of the overall properties of fast-oscillating differential equations or integral functionals, which also includes an introduction to the theory of convergence and weak lower semicontinuous functionals. The text is volume number 12 in the OXFORD LECTURE SERIES IN MATHEMATICS AND ITS APPLICATIONS.

A second part of volume number 10 in the OXFORD LECTURE SERIES IN MATHEMATICS AND ITS APPLICATIONS, which describes compressible fluids-mechanics models and deals with problems associated with the compressible Navier-Stokes equations.