This book contains detailed lecture notes on four topics at the forefront of current research in computational mathematics. Each set of notes presents a self-contained guide to a current research area and has an extensive bibliography. In addition, most of the notes contain detailed proofs of the key results. The notes start from a level suitable for first year graduate students in applied mathematics, mathematical analysis or numerical analysis, and proceed to current research topics. The reader should therefore be able to gain quickly an insight into the important results and techniques in each area without recourse to the large research literature. Current (unsolved) problems are also described and directions for future research are given. This book is also suitable for professional mathematicians who require a succint and accurate account of recent research in areas parallel to their own, and graduates in mathematical sciences.

This book contains detailed lecture notes on four topics at the forefront of current research in computational mathematics. Each set of notes presents a self-contained guide to a current research area and has an extensive bibliography. In addition, most of the notes contain detailed proofs of the key results. The notes start from a level suitable for first year graduate students in applied mathematics, mathematical analysis or numerical analysis, and proceed to current research topics. The reader should therefore be able to gain quickly an insight into the important results and techniques in each area without recourse to the large research literature. Current (unsolved) problems are also described and directions for future research are given. This book is also suitable for professional mathematicians who require a succint and accurate account of recent research in areas parallel to their own, and graduates in mathematical sciences.

TheEleventh LMS-EPSRCComputational MathematicsandScienti?cC- puting Summer School was held at the University of Durham, UK, from the 4th of July to the 9th of July 2004. This was the third of these schools to be held in Durham, having previously been hosted by the University of L- caster and the University of Leicester. The purpose of the summer school was to present high quality instructional courses on topics at the forefront of computational mathematics and scienti?c computing research to postgra- ate students. The main speakers were Emmanuel Candes, Markus Melenk, Joe Monaghan and Alex Schweitzer. This volume presents written contributions three of our speakers which are more comprehensive versions of the high quality lecture notes which were distributedtoparticipantsduringthemeeting.Wearealsoextremelypleased that Angela Kunoth was able to make an additional contribution from the ill-fated ?rst week. At the time of writing it is now more than two years since we ?rst contacted theguestspeakersandduringthatperiodtheyhavegivensigni?cantportions of their time to making the summer school, and this volume, a success. We wouldliketothankallofthemforthecarewhichtheytookinthepreparation and delivery of their material.

This book contains detailed lecture notes on six topics at the forefront of current research in numerical analysis and applied mathematics. Each set of notes presents a self-contained guide to a current research area and has an extensive bibliography. In addition, most of the notes contain detailed proofs of the key results. The notes start from a level suitable for first year graduate students in applied mathematics, mathematical analysis or numerical analysis, and proceed to current research topics. The reader should therefore be able to gain quickly an insight into the important results and techniques in each area without recourse to the large research literature. Current (unsolved) problems are also described and directions for future research are given. This book is also suitable for professional mathematicians who require a succinct and accurate account of recent research in areas parallel to their own, and graduates in mathematical sciences.