*I. S. Duff, A. M. Erisman, and J. K. Reid*

- Published in print:
- 2017
- Published Online:
- April 2017
- ISBN:
- 9780198508380
- eISBN:
- 9780191746420
- Item type:
- book

- Publisher:
- Oxford University Press
- DOI:
- 10.1093/acprof:oso/9780198508380.001.0001
- Subject:
- Mathematics, Numerical Analysis

Direct Methods for Sparse Matrices, second edition, is a complete rewrite of the first edition published 30 years ago. Much has changed since that time. Problems have grown greatly in size and ...
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Direct Methods for Sparse Matrices, second edition, is a complete rewrite of the first edition published 30 years ago. Much has changed since that time. Problems have grown greatly in size and complexity; nearly all our examples were of order less than 5,000 in the first edition, and are often more than a million in the second edition. Computer architectures are now much more complex, requiring new ways of adapting algorithms to parallel environments with memory hierarchies. Because the area is such an important one to all of computational science and engineering, a huge amount of research has been done since the first edition, some of it by the authors. This new research is integrated into the text with a clear explanation of the underlying mathematics and algorithms. New research that is described includes new techniques for scaling and error control, new orderings, new combinatorial techniques for partitioning both symmetric and unsymmetric problems, and a detailed description of the multifrontal approach to solving systems that was pioneered by the research of the authors and colleagues. This includes a discussion of techniques for exploiting parallel architectures and new work for indefinite and unsymmetric systems.Less

Direct Methods for Sparse Matrices, second edition, is a complete rewrite of the first edition published 30 years ago. Much has changed since that time. Problems have grown greatly in size and complexity; nearly all our examples were of order less than 5,000 in the first edition, and are often more than a million in the second edition. Computer architectures are now much more complex, requiring new ways of adapting algorithms to parallel environments with memory hierarchies. Because the area is such an important one to all of computational science and engineering, a huge amount of research has been done since the first edition, some of it by the authors. This new research is integrated into the text with a clear explanation of the underlying mathematics and algorithms. New research that is described includes new techniques for scaling and error control, new orderings, new combinatorial techniques for partitioning both symmetric and unsymmetric problems, and a detailed description of the multifrontal approach to solving systems that was pioneered by the research of the authors and colleagues. This includes a discussion of techniques for exploiting parallel architectures and new work for indefinite and unsymmetric systems.

*Dusa McDuff and Dietmar Salamon*

- Published in print:
- 2017
- Published Online:
- June 2017
- ISBN:
- 9780198794899
- eISBN:
- 9780191836411
- Item type:
- book

- Publisher:
- Oxford University Press
- DOI:
- 10.1093/oso/9780198794899.001.0001
- Subject:
- Mathematics, Analysis, Geometry / Topology

Over the past number of years powerful new methods in analysis and topology have led to the development of the modern global theory of symplectic topology, including several striking and important ...
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Over the past number of years powerful new methods in analysis and topology have led to the development of the modern global theory of symplectic topology, including several striking and important results. The first edition of Introduction to Symplectic Topology was published in 1995. The book was the first comprehensive introduction to the subject and became a key text in the area. In 1998, a significantly revised second edition contained new sections and updates. This third edition includes both further updates and new material on this fast-developing area. All chapters have been revised to improve the exposition, new material has been added in many places, and various proofs have been tightened up. Copious new references to key papers have been added to the bibliography. In particular, the material on contact geometry has been significantly expanded, many more details on linear complex structures and on the symplectic blowup and blowdown have been added, the section on J-holomorphic curves in Chapter 4 has been thoroughly revised, there are new sections on GIT and on the topology of symplectomorphism groups, and the section on Floer homology has been revised and updated. Chapter 13 has been completely rewritten and has a new title (Questions of Existence and Uniqueness). It now contains an introduction to existence and uniqueness problems in symplectic topology, a section describing various examples, an overview of Taubes–Seiberg–Witten theory and its applications to symplectic topology, and a section on symplectic 4-manifolds. Chapter 14 on open problems has been added.Less

Over the past number of years powerful new methods in analysis and topology have led to the development of the modern global theory of symplectic topology, including several striking and important results. The first edition of *Introduction to Symplectic Topology* was published in 1995. The book was the first comprehensive introduction to the subject and became a key text in the area. In 1998, a significantly revised second edition contained new sections and updates. This third edition includes both further updates and new material on this fast-developing area. All chapters have been revised to improve the exposition, new material has been added in many places, and various proofs have been tightened up. Copious new references to key papers have been added to the bibliography. In particular, the material on contact geometry has been significantly expanded, many more details on linear complex structures and on the symplectic blowup and blowdown have been added, the section on *J*-holomorphic curves in Chapter 4 has been thoroughly revised, there are new sections on GIT and on the topology of symplectomorphism groups, and the section on Floer homology has been revised and updated. Chapter 13 has been completely rewritten and has a new title (Questions of Existence and Uniqueness). It now contains an introduction to existence and uniqueness problems in symplectic topology, a section describing various examples, an overview of Taubes–Seiberg–Witten theory and its applications to symplectic topology, and a section on symplectic 4-manifolds. Chapter 14 on open problems has been added.

*Edward Witten, Martin Bridson, Helmut Hofer, Marc Lackenby, and Rahul Pandharipande*

*N M J Woodhouse (ed.)*

- Published in print:
- 2017
- Published Online:
- May 2017
- ISBN:
- 9780198784913
- eISBN:
- 9780191827150
- Item type:
- book

- Publisher:
- Oxford University Press
- DOI:
- 10.1093/oso/9780198784913.001.0001
- Subject:
- Mathematics, Geometry / Topology

This volume contains a collection of papers based on lectures delivered by distinguished mathematicians at Clay Mathematics Institute events over the past few years. Although not explicitly linked, ...
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This volume contains a collection of papers based on lectures delivered by distinguished mathematicians at Clay Mathematics Institute events over the past few years. Although not explicitly linked, the topics in this volume have a common flavour and a common appeal to all who are interested in recent developments in geometry. They are intended to be accessible to all who work in this general area, regardless of their own particular research interests.Less

This volume contains a collection of papers based on lectures delivered by distinguished mathematicians at Clay Mathematics Institute events over the past few years. Although not explicitly linked, the topics in this volume have a common flavour and a common appeal to all who are interested in recent developments in geometry. They are intended to be accessible to all who work in this general area, regardless of their own particular research interests.

*Jon Williamson*

- Published in print:
- 2017
- Published Online:
- March 2017
- ISBN:
- 9780199666478
- eISBN:
- 9780191749292
- Item type:
- book

- Publisher:
- Oxford University Press
- DOI:
- 10.1093/acprof:oso/9780199666478.001.0001
- Subject:
- Mathematics, Logic / Computer Science / Mathematical Philosophy

Inductive logic (also known as confirmation theory) seeks to determine the extent to which the premisses of an argument entail its conclusion. This book offers an introduction to the field of ...
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Inductive logic (also known as confirmation theory) seeks to determine the extent to which the premisses of an argument entail its conclusion. This book offers an introduction to the field of inductive logic and develops a new Bayesian inductive logic. Chapter 1 introduces perhaps the simplest and most natural account of inductive logic, classical inductive logic, which is attributable to Ludwig Wittgenstein. Classical inductive logic is seen to fail in a crucial way, so there is a need to develop more sophisticated inductive logics. Chapter 2 presents enough logic and probability theory for the reader to begin to study inductive logic, while Chapter 3 introduces the ways in which logic and probability can be combined in an inductive logic. Chapter 4 analyses the most influential approach to inductive logic, due to W.E. Johnson and Rudolf Carnap. Again, this logic is seen to be inadequate. Chapter 5 shows how an alternative approach to inductive logic follows naturally from the philosophical theory of objective Bayesian epistemology. This approach preserves the inferences that classical inductive logic gets right (Chapter 6). On the other hand, it also offers a way out of the problems that beset classical inductive logic (Chapter 7). Chapter 8 defends the approach by tackling several key criticisms that are often levelled at inductive logic. Chapter 9 presents a formal justification of the version of objective Bayesianism which underpins the approach. Chapter 10 explains what has been achieved and poses some open questions.Less

Inductive logic (also known as confirmation theory) seeks to determine the extent to which the premisses of an argument entail its conclusion. This book offers an introduction to the field of inductive logic and develops a new Bayesian inductive logic. Chapter 1 introduces perhaps the simplest and most natural account of inductive logic, classical inductive logic, which is attributable to Ludwig Wittgenstein. Classical inductive logic is seen to fail in a crucial way, so there is a need to develop more sophisticated inductive logics. Chapter 2 presents enough logic and probability theory for the reader to begin to study inductive logic, while Chapter 3 introduces the ways in which logic and probability can be combined in an inductive logic. Chapter 4 analyses the most influential approach to inductive logic, due to W.E. Johnson and Rudolf Carnap. Again, this logic is seen to be inadequate. Chapter 5 shows how an alternative approach to inductive logic follows naturally from the philosophical theory of objective Bayesian epistemology. This approach preserves the inferences that classical inductive logic gets right (Chapter 6). On the other hand, it also offers a way out of the problems that beset classical inductive logic (Chapter 7). Chapter 8 defends the approach by tackling several key criticisms that are often levelled at inductive logic. Chapter 9 presents a formal justification of the version of objective Bayesianism which underpins the approach. Chapter 10 explains what has been achieved and poses some open questions.