(Paperback)
ISBN-10: 0-19-921559-6
ISBN-13: 978-0-19-921559-1
Estimated publication date: February 2007
320 pages, 234x156 mm
Series: Oxford Graduate Texts in Mathematics number 12
Description
Accessible to graduate students in both Mathematics and Physics
Surveys current research and states open problems, particularly
in calibrated geometry
Thorough coverage, major proofs such as the Calabi conjecture are
provided in full
Extensive, up-to-date bibliography
This graduate level text covers an exciting and active area of
research at the crossroads of several different fields in
Mathematics and Physics. In Mathematics it involves Differential
Geometry, Complex Algebraic Geometry, Symplectic Geometry, and in
Physics String Theory and Mirror Symmetry. Drawing extensively on
the author's previous work, the text explains the advanced
mathematics involved simply and clearly to both mathematicians
and physicists. Starting with the basic geometry of connections,
curvature, complex and Kahler structures suitable for beginning
graduate students, the text covers seminal results such as Yau's
proof of the Calabi Conjecture, and takes the reader all the way
to the frontiers of current research in calibrated geometry,
giving many open problems.
Readership: Graduates and researchers in Mathematics and Physics
Contents
Preface
1. Background material
2. Introduction to connections, curvature and holonomy groups
3. Riemannian holonomy groups
4. Calibrated geometry
5. Kahler manifolds
6. The Calabi Conjecture
7. Calabi-Yau manifolds
8. Special Lagrangian geometry
9. Mirror Symmetry and the SYZ Conjecture
10. Hyperkahler and quaternionic Kahler manifolds
11. The exceptional holonomy groups
12. Associative, coassociative and Cayley submanifolds
References
Index
(paper)
ISBN-10: 0-19-920522-1
ISBN-13: 978-0-19-920522-6
Estimated publication date: May 2007
472 pages, 234x156 mm
Series: Numerical Mathematics and Scientific Computation
Description
Authored by a leading researcher and established teacher
Aimed at a broad readership of advanced undergraduates and
graduates and researchers in Applied Mathematics, Engineering,
Computer Science, and the Physical Sciences.
Several exercises provided throughout
Provides a complete introduction to the analysis of partial
differential equations from the theoretical aspects to numerical
algorithms
This text, based on the author's teaching at Ecole Polytechnique,
introduces the reader to the world of mathematical modelling and
numerical simulation. Covering the finite difference method;
variational formulation of elliptic problems; Sobolev spaces;
elliptical problems; the finite element method; Eigenvalue
problems; evolution problems; optimality conditions and
algorithms and methods of operational research, and including a
several exercises throughout, this is an ideal text for advanced
undergraduate students and graduates in applied mathematics,
engineering, computer science, and the physical sciences.
(paper)
ISBN-10: 0-19-929660-X
ISBN-13: 978-0-19-929660-6
Estimated publication date: May 2007
528 pages, 130 b/w diagrams, 234x156 mm
Series: Oxford Statistical Science Series number 34
Description
Extremely timely
Experienced author team
Numerous figures
End of chapter notes on further reading
Ideal for students and researchers in Statistics, and
experimentalists in the Medical, Pharmaceutical and Chemical
Industries
Supporting website with SAS program codes, problems and
solutions, at http://www.oup.com/uk/academic/companion/mathematics/atkinson
Experiments in the field and in the laboratory cannot avoid
random error, and statistical methods are essential for their
efficient design and analysis. This book focuses on the use of
SAS, a powerful software package that provides a complete set of
statistical tools including analysis of variance, regression,
categorical data analysis, and multivariate analysis. Many
examples of SAS code, results, plots and tables are provided,
along with a fully supported website. The text contains numerous
figures, and end of chapter notes on further reading. Exercises
consolidating the material covered are given in the final chapter.
Authored by leading experts, this book is ideal for statisticians
in academia, research and the medical, pharmaceutical and
chemical industries.
Readership: Students and researchers in statistics, and
experimentalists in the medical, pharmaceutical and chemical
industries.
(hardback)
ISBN-10: 0-19-857008-2
ISBN-13: 978-0-19-857008-0
Estimated publication date: May 2007
352 pages, b/w illus., 234x156 mm
Series: Oxford Mathematical Monographs
Description
Authored by a leading name in the field
First book to unify recent developments in this important area
This unique reference, aimed at research topologists, gives an
exposition of the 'pseudo-Anosov' theory of foliations of 3-manifolds.
This theory generalizes Thurston's theory of surface
automorphisms and reveals an intimate connection between
dynamics, geometry and topology in 3 dimensions. Significant
themes returned to throughout the text include the importance of
geometry, especially the hyperbolic geometry of surfaces, the
importance of monotonicity, especially in 1-dimensional and co-dimensional
dynamics, and combinatorial approximation, using finite
combinatorical objects such as train-tracks, branched surfaces
and hierarchies to carry more complicated continuous objects.
Readership: Graduates and researchers in topology and geometry
NEW IN PAPERBACK
ISBN-10: 0-19-922807-8
ISBN-13: 978-0-19-922807-2
Estimated publication date: May 2007
400 pages, 234x156 mm
Description
The latest word from a senior philosopher of mathematics
Provides solutions to some vexing philosophical problems
Essential reading for anyone working in this field
Investigates how philosophy of maths applies to actual
mathematical and scientific practice
Charles Chihara's new book develops and defends a structural view
of the nature of mathematics, and uses it to explain a number of
striking features of mathematics that have puzzled philosophers
for centuries. The view is used to show that, in order to
understand how mathematical systems are applied in science and
everyday life, it is not necessary to assume that its theorems
either presuppose mathematical objects or are even true.
Chihara builds upon his previous work, in which he presented a
new system of mathematics, the constructibility theory, which did
not make reference to, or presuppose, mathematical objects. Now
he develops the project further by analysing mathematical systems
currently used by scientists to show how such systems are
compatible with this nominalistic outlook. He advances several
new ways of undermining the heavily discussed indispensability
argument for the existence of mathematical objects made famous by
W. V. Quine and Hilary Putnam. And Chihara presents a rationale
for the nominalistic outlook that is quite different from those
generally put forward, which he maintains have led to serious
misunderstandings.
A Structural Account of Mathematics will be required reading for
anyone working in this field.
Readership: Scholars and students of the philosophy of
mathematics; mathematicians interested in the foundations of
their subject.
Contents
Introduction
1. Five Puzzles in Search of an Explanation
2. Geometry and Mathematical Existence
3. The Van Inwagen Puzzle
4. Structuralism
5. Platonism
6. Minimal Anti-Nominalism
7. The Constructibility Theory
8. Constructible Structures
9. Applications
10. If-Thenism
11. Field's Account of Mathematics and Metalogic
Appendix A: Some Doubts about Hellman's Views
Appendix B: Balaguer's Fictionalism