(Hardback)
0-19-856664-6
Publication date: 1 July 2005
400 pages, 39 line figures, 234mm x 156mm
Series: Numerical Mathematics and Scientific Computation
Description
Timely text from world- class researchers
Broad in scope, highlighting recent and important results
Ideal as a graduate text for mathematicians and engineers
Inverse eigenvalue problems arise in a remarkable variety of
applications and associated with any inverse eigenvalue problem
are two fundamental questions--the theoretic issue on solvability
and the practical issue on computability. Both questions are
difficult and challenging. In this text, the authors discuss the
fundamental questions, some known results, many applications,
mathematical properties, a variety of numerical techniques, as
well as several open problems.
Readership: Aimed at graduates and researchers in applied
mathematics, engineering and computer science;
an ideal graduate text
Contents
Preface
1 Introduction
2 Applications
3 Parameterized Inverse Eigenvalue Problems
4 Structured Inverse Eigenvalue Problems
5 Partially Described Inverse Eigenvalue Problems
6 Least Squares Inverse Eigenvalue Problems
7 Spectrally Constrained Approximation
8 Structured Low Rank Approximation
9 Group Orbitally Constrained Approximation
Index
(Hardback (cloth))
0-19-851174-4
Publication date: 12 May 2005
Clarendon Press 512 pages, 234mm x 156mm
Series: Oxford Logic Guides
Description
Excellent expository monograph by experts in the field
Aimed at a broad audience of mathematicians, computer scientists
and philosophers
This book is a specialized monograph on interpolation and
definability, a notion central in pure logic and with significant
meaning and applicability in all areas where logic is applied,
especially computer science, artificial intelligence, logic
programming, philosophy of science and natural language.
Suitable for researchers and graduate students in mathematics,
computer science and philosophy, this is the latest in the
prestigous world-renowned Oxford Logic Guides, which contains
Michael Dummet's Elements of intuitionism (second edition), J. M.
Dunn and G. Hardegree's Algebraic Methods in Philosophical Logic,
H. Rott's Change, Choice and Inference: A Study of Belief
Revision and Nonmonotonic Reasoning, P. T. Johnstone's Sketches
of an Elephant: A Topos Theory Compendium: Volumes 1 and 2, and
David J. Pym and Eike Ritter's Reductive Logic and Proof Search:
Proof theory, semantics and control.
Readership: Researchers and graduate students in mathematics,
computer science and philosophy
Contents
1 Introduction and Discussion
2 Modal and Superintuitionistic Logics: Basic Concepts
3 Superintuitionistic Logics and Normal Extensions of the Modal
Logics S4
4 The Interpolation Theorem in Intuitionistic Predicate Calculus
5 Interpolation and Definability in Quantified Logics
6 Craig's Theorem in Superintuitionistic Logics and Amalgamable
Varieties of Pseudoboolean Algebras
7 Interpolation, Definability, Amalgamation
8 Interpolation in Normal Extensions of the Modal Logic S4
9 Complexity of Some Problems in Modal and Intuitionistic Calculi
10 Interpolation in Modal Infinite Slice Logics Containing the
Logic K4
11 An Analog of Beth's Theorem in Normal Extensions of the Modal
Logic K4
12 Extensions of the Provability Logic
13 Syntactic Proof of Interpolation for the Intuitionistic
Predicate Logic
14 Interpolation by Translation
15 Interpolation in (Intuitionistic) Logic Programming
16 Interpolation in Goal-directed Proof Systems
17 Further Results and Discussion
Appendix
References
Index
(Hardback (laminated boards))/0-19-856813-4
(Paperback)/0-19-856814-2
Publication date: 29 September 2005
370 pages, 246mm x 171mm
Description
A concise and lucid introduction to simple stochastic processes
and models
Includes numerous exercises, problems and solutions
Ideal for an undergraduate second course in probability
Stochastic Processes and Models provides a concise and lucid
introduction to simple stochastic processes and moddels.
Including numerous exercises, problems and solutions, it covers
the key concepts and tools.
Readership: Undergraduates and graduates in probability,
statistics, mathematics, finance and operational research.
Contents
Probability and Random Variables
Introduction to Stochastic Processes
Markov Chains
Markov Chains in Continuous Time
Diffusions
Hints and solutions to selected exercises
(Hardback)
0-19-856852-5
Publication date: 12 May 2005
Clarendon Press 272 pages, 234mm x 156mm
Series: Oxford Logic Guides
Description
A clear exposition of independence proofs in set theory presented
in its most elegant form--Boolean-valued models
With a foreword by Dana Scott--an illuminating historical account
by one of the creators of the subject
Numerous exercises, along with the enlarged and entirely updated
background material, make this an ideal text for students in
logic and set theory
New to this edition
30% new material on recent developments
Expanded background material
A new appendix on category theory
This monograph is a follow up to the author's classic text
Boolean-Valued Models and Independence Proofs in Set Theory,
providing an exposition of some of the most important results in
set theory obtained in the 20th century--the independence of the
continuum hypothesis and the axiom of choice. Aimed at research
students and academics in mathematics, mathematical logic,
philosophy, and computer science, the text has been extensively
updated with expanded introductory material, new chapters, and a
new appendix on category theory, and includes recent developments
in the field. Numerous exercises, along with the enlarged and
entirely updated background material, make this an ideal text for
students in logic and set theory.
Readership: Aimed at research students and academics in
mathematics, mathematical logic, philosophy, and computer science.
Contents
Dana Scott: Foreword
Preface
List of Problems
0 Boolean and Heyting Algebras: The Essentials
1 Boolean-Valued Models: First Steps
2 Forcing and Some Independece Proofs
3 Group Actions on V(B) and the Independence of the Axiom of
Choice
4 Generic Ultrafilters and Transitive Models of ZFC
5 Cardinal Collapsing, Boolean Isomorphism and Applications to
the Theory of Boolean Algebras
6 Iterated Boolean Extensions, Martin's Axiom and Souslin's
Hypothesis
7 Boolean-Valued Analysis
8 Intuitionistic Set Theory and Heyting-Algebra-Valued Models
Appendix. Boolean- and Heyting-Algebra-Valued Models as
Categories
Historical Notes
Bibliography
Index of Symbols
Index of Terms
(Hardback)
0-19-856726-X
Publication date: 28 July 2005
576 pages, 66 line drawings, 240mm x 168mm
Series: Oxford Graduate Texts
Description
Modern graduate text on analytical mechanics
Treats time as a transformable coordinate integrating special
relativity with other, more traditional topics
Introduces notations and methods directly transferrable to
quantum mechanics
Highlights the interface between classical and quantum mechanics
Pedagogic style, including many exercises, while maintaining
mathematical precision for deeper understanding
This book provides an innovative and mathematically sound
treatment of the foundations of analytical mechanics and the
relation of classical mechanics to relativity and quantum theory.
It is intended for use at the graduate level.
A distinguishing feature of the book is its integration of
special relativity into the teaching of classical mechanics.
Extended Lagrangian and Hamiltonian methods are introduced that
treat time as a transformable coordinate rather than the fixed
parameter of Newtonian physics. Advanced topics such as covariant
Lagrangians and Hamiltonians, canonical transformations, and the
Hamilton-Jacobi equation are developed using this extended theory.
This permits the Lorentz transformation of special relativity to
become a canonical transformation.
This is also a book for those who study analytical mechanics as a
preliminary to a critical exploration of quantum mechanics.
Comparisons to quantum mechanics appear throughout the text, and
classical mechanics itself is presented in a way that will aid
the reader in the study of quantum theory. A chapter is devoted
to linear vector operators and dyadics, including a comparison to
the bra-ket notation of quantum mechanics. Rotations are
presented using an operator formalism similar to that used in
quantum theory, and the definition of the Euler angles follows
the quantum mechanical convention. The extended Hamiltonian
theory with time as a coordinate is compared to Dirac's formalism
of primary phase space constraints. The chapter on relativistic
mechanics shows how to use covariant Hamiltonian theory to write
the Klein-Gordon and Dirac equations. The chapter on Hamilton-Jacobi
theory includes a discussion of the closely related Bohm hidden
variable model of quantum mechanics.
The book provides a necessary bridge to carry graduate students
from their previous undergraduate classical mechanics courses to
the future study of advanced relativity and quantum theory.
Several of the current fundamental problems in theoretical
physics---the development of quantum information technology, and
the problem of quantizing the gravitational field, to name two---require
a rethinking of the quantum-classical connection. This text is
intended to encourage the retention or restoration of
introductory graduate analytical mechanics courses. It is written
for the intellectually curious graduate student, and the teacher
who values mathematical precision in addition to accessibility.
Readership: Graduate students and lecturers considering adoption
as the textbook in a graduate course in Analytical Mechanics, at
universities worldwide. Graduate students embarking on research
in string theory or quantum gravity.
Contents
Part I: The Classical Theory
1 Basic Dynamics of Point Particles and Collections
2 Introduction to Lagrangian Mechanics
3 Lagrangian Theory of Constraints
4 Introduction to Hamiltonian Mechanics
5 The Calculus of Variations
6 Hamilton's Principle
7 Linear Operators and Dyadics
8 Kinematics of Rotation
9 Rotational Dynamics
10 Small Vibrations about Equilibrium
Part II: Mechanics with Time as a Coordinate
11 Lagrangian Mechanics with Time as a Coordinate
12 Hamiltonian Mechanics with Time as a Coordinate
13 Hamilton's Principle and Noether's Theorem
14 Relativity and Spacetime
15 Fourvectors and Operators
16 Relativistic Mechanics
17 Canonical Transformations with Time as a Coordinate
18 Generating Functions
19 Hamilton-Jacobi Theory
Part III: Mathematical References
A Vector Fundamentals
B Matrices and Determinants
C Eigenvalue Problem with General Metric
D The Calculus of Many Variables
E Geometry of Phase Space