NEW EDITION

Devinderjit Sivia and John Skilling

Data Analysis, Second Edition
A Bayesian Tutorial

(Hardback)
ISBN-10: 0-19-856831-2
(Paperback)
ISBN-10: 0-19-856832-0
Publication date: 25 May 2006
256 pages, 68 b+w line drawings + 1 halftone, 234mm x 156mm

Description

An easy to read tutorial introduction to data anlaysis.
Concise, being one of the slimmest books in the field!
Self-contained - assumes little or no previous statistical training.
Good illustrative examples where the basic concepts are explained with a series of examples that become progressively more advanced, but that are always kept as simple as possible to aid understanding.
A contribution from John Skilling, an expert in numerical techniques. He introduces the simple but powerful new 'nested sampling' technique for Bayesian computaton.
New to this edition
Completely updated graduate text.
Three new chapters, two of which are from new co-author, John Skilling.

Statistics lectures have been a source of much bewilderment and frustration for generations of students. This book attempts to remedy the situation by expounding a logical and unified approach to the whole subject of data analysis. This text is intended as a tutorial guide for senior undergraduates and research students in science and engineering. After explaining the basic principles of Bayesian probability theory, their use is illustrated with a variety of examples ranging from elementary parameter estimation to image processing. Other topics covered include reliability analysis, multivariate optimisation, least-squares and maximum likelihood, error-propagation, hypothesis testing, maximum entropy and experimental design. The Second Edition of this successful tutorial book contains a new chapter on extensions to the ubiquitous least-squares procedure, allowing for the straightforward handling of outliers and unknown correlated noise, and a cutting-edge contribution from John Skilling on a novel numerical technique for Bayesian computation called 'nested sampling'.

Readership: Senior undergraduate and graduate students in physics, chemistry, and engineering. Researchers across a broad spectrum of experimental scientific disciplines. Not for statisticians.

Contents

1 Sivia: The Basics
2 Sivia: Parameter Estimation I
3 Sivia: Parameter Estimation II
4 Sivia: Model Selection
5 Sivia: Assigning Probabilities
6 Sivia: Non-parametric Estimation
7 Sivia: Experimental Design
8 Sivia: Least-Squares Extensions
9 Skilling: Nested Sampling
10 Skilling: Quantification
Appendices
Bibliography

Giandomenico Boffi and David Buchsbaum

Threading Homology through Algebra
Selected patterns

(Hardback)
ISBN-10: 0-19-852499-4
ISBN-13: 978-0-19-852499-1
Publication date: 27 July 2006
Clarendon Press 264 pages, 234mm x 156mm
Series: Oxford Mathematical Monographs

Description

Updates well-known material
Discusses new techniques in more classical fields
Highlights further areas of exploration
Unified treatment of dispersed material
Extensive bibliography

Threading Homology through Algebra takes homological themes (Koszul complexes and their variations, resolutions in general) and shows how these affect the perception of certain problems in selected parts of algebra, as well as their success in solving a number of them. The text deals with regular local rings, depth-sensitive complexes, finite free resolutions, letter-place algebra, Schur and Weyl modules, Weyl-Schur complexes and determinantal ideals. Aimed at graduates and academics in mathematics, the book provides an overview of the developments that have taken place in these areas as well as an insight into some of the open problems which exist.

Readership: Graduates and researchers in mathematics

Contents

Preface
1 Recollections and perspectives
2 Local ring theory
3 Generalized Koszul complexes
4 Structure theorems for finite free resolutions
5 Exactness criteria at work
6 Weyl and Schur modules
7 Some applications of Weyl and Schur modules
Appendix for letter-place methods
References
Index

NEW IN PAPERBACK

Shmuel Kantorovitz

Introduction to Modern Analysis

(Paperback)
ISBN-10: 0-19-920315-6
ISBN-13: 978-0-19-920315-4
Publication date: 10 July 2006
448 pages, 234mm x 156mm
Series: Oxford Graduate Texts in Mathematics

Description

A comprehensive and lucid text covering the basic tools of modern analysis
Each chapter provides an ideal source for study and general reference
Contains over 120 end-of-chapter exercises
Solutions to exercises available on a companion website

This new-in-paperback text is based on lectures given by the author at the advanced undergraduate and graduate levels in Measure Theory, Functional Analysis, Banach Algebras, Spectral Theory (of bounded and unbounded operators), Semigroups of Operators, Probability and Mathematical Statistics, and Partial Differential Equations. The first 10 chapters discuss theoretical methods in Measure Theory and Functional Analysis, and contain over 120 end of chapter exercises. The final two chapters discuss applications in Probability Theory and Partial Differential Equations.

Solutions to the end of chapter exercises may be found on the companion website for this text.

Readership: Advanced undergraduate and graduate students and researchers in mathematics.

Contents

Preface
1 Measures
2 Construction of measures
3 Measure and topology
4 Continuous linear functionals
5 Duality
6 Bounded operators
7 Banach algebras
8 Hilbert spaces
9 Integral representation
10 Unbounded operators
Application I:Probability
Application II: Distributions
Bibliography
Index

NEW IN PAPERBACK

Terry Lawson

Topology: A Geometric Approach

(Paperback)
ISBN-10: 0-19-920248-6
ISBN-13: 978-0-19-920248-5
Publication date: 10 August 2006
408 pages, numerous b/w line drawings, 234mm x 156mm
Series: Oxford Graduate Texts in Mathematics

Description

Fosters learning via guided exercises and projects, along with extensive coverage of basic material
Flexible set of topics, allowing independent assignments for students at different levels
Over 750 extensive and carefully developed exercises and projects
Contains selected solutions to problems as an appendix
A full set of solutions are available to lecturers on a companion website

This new-in-paperback introduction to topology emphasizes a geometric approach with a focus on surfaces. A primary feature is a large collection of exercises and projects, which fosters a teaching style that encourages the student to be an active class participant. A wide range of material at different levels supports flexible use of the book for a variety of students. Part I is appropriate for a one-semester or two-quarter course, and Part II (which is problem based) allows the book to be used for a year-long course which supports a variety of syllabuses.

The over 750 exercises range from simple checks of omitted details in arguments, to reinforce the material and increase student involvement, to the development of substantial theorems that have been broken into many steps. The style encourages an active student role. Solutions to selected exercises are included as an appendix, with solutions to all exercises available to the instructor on a companion website.

Readership: Advanced undergraduates and beginning graduate students in pure mathematics and topology.

Contents

Part I: A Geometric Introduction to Topology
1 Basic point set topology
2 The classification of surfaces
3 The fundamental group and its applications
Part II: Covering Spaces, CW Complexes and Homology
4 Covering spaces
5 CW complexes
6 Homology
Selected solutions
References
Index

NEW IN PAPERBACK

Qing Liu

Algebraic Geometry and Arithmetic Curves

(Paperback)
ISBN-10: 0-19-920249-4
ISBN-13: 978-0-19-920249-2
Publication date: 10 July 2006
592 pages, 234mm x 156mm
Series: Oxford Graduate Texts in Mathematics

Description

Includes essential background methods
Nearly 600 exercises included throughout the text
Lucid, rigorous, coherent and comprehensive exposition
Includes a rich bibliography with nearly 100 references

This new-in-paperback edition provides a general introduction to algebraic and arithmetic geometry, starting with the theory of schemes, followed by applications to arithmetic surfaces and to the theory of reduction of algebraic curves.

The first part introduces basic objects such as schemes, morphisms, base change, local properties (normality, regularity, Zariski's Main Theorem). This is followed by the more global aspect: coherent sheaves and a finiteness theorem for their cohomology groups. Then follows a chapter on sheaves of differentials, dualizing sheaves, and Grothendieck's duality theory. The first part ends with the theorem of Riemann-Roch and its application to the study of smooth projective curves over a field. Singular curves are treated through a detailed study of the Picard group.

The second part starts with blowing-ups and desingularisation (embedded or not) of fibered surfaces over a Dedekind ring that leads on to intersection theory on arithmetic surfaces. Castelnuovo's criterion is proved and also the existence of the minimal regular model. This leads to the study of reduction of algebraic curves. The case of elliptic curves is studied in detail. The book concludes with the fundamental theorem of stable reduction of Deligne-Mumford.

This book is essentially self-contained, including the necessary material on commutative algebra. The prerequisites are few, and including many examples and approximately 600 exercises, the book is ideal for graduate students.

Readership: Graduate students in algebraic geometry and number theory

Contents

Introduction
1 Some topics in commutative algebra
2 General Properties of schemes
3 Morphisms and base change
4 Some local properties
5 Coherent sheaves and Cech cohmology
6 Sheaves of differentials
7 Divisors and applications to curves
8 Birational geometry of surfaces
9 Regular surfaces
10 Reduction of algebraic curves
Bibilography
Index