(Hardback)
0-19-856849-5
Publication date: 28 July 2005
208 pages, 34 b/w line drawings, 234mm x 156mm
Series: International Series of Monographs on Physics
Reviews
'... very carefully written ..., will inspire a wide range of
physicists and mathematicians for a long period of time.' -Albrecht
Klemm, University of Wisconsin
Description
Only existing book on exciting new developments
Pedagogical style, based on lectures
Attractive to both mathematicians and physicists
Covers well-established and important subjects
In recent years, the old idea that gauge theories and string
theories are equivalent has been implemented and developed in
various ways, and there are by now various models where the
string theory / gauge theory correspondence is at work. One of
the most important examples of this correspondence relates Chern-Simons
theory, a topological gauge theory in three dimensions which
describes knot and three-manifold invariants, to topological
string theory, which is deeply related to Gromov-Witten
invariants. This has led to some surprising relations between
three-manifold geometry and enumerative geometry. This book gives
the first coherent presentation of this and other related topics.
After an introduction to matrix models and Chern-Simons theory,
the book describes in detail the topological string theories that
correspond to these gauge theories and develops the mathematical
implications of this duality for the enumerative geometry of
Calabi-Yau manifolds and knot theory. It is written in a
pedagogical style and will be useful reading for graduate
students and researchers in both mathematics and physics willing
to learn about these developments.
Readership: Primary market: graduate students and academic
professionals in string theory, mathematical physics, algebraic
geometry and three-manifold topology. Secondary market: the
theoretical physics and pure mathematics community at large.
Contents
Part I: Matrix Models, Chern-Simons Theory, and the Large N
Expansion
1 Matrix Models
2 Chern-Simons Theory and Knot Invariants
Part II: Topological Strings
3 Topological Sigma Models
4 Topological Strings
5 Calabi-Yau Geometries
Part III: The Topological String / Gauge Theory Correspondence
6 String Theory and Gauge Theory
7 String Field Theory and Gauge Theories
8 Geometric Transitions
9 The Topological Vertex
10 Applications of the Topological String / Gauge Theory
Correspondence
A Symmetric Polynomials
(Hardback)
0-19-856651-4
Publication date: 27 October 2005
Clarendon Press 400 pages, 234mm x 156mm
Series: Oxford Logic Guides
Reviews
'Review from previous edition 'I am enthusiastic about this
proposal...[it is] very coherent. There has been a very wide
range of activity in constructive mathematics...aside from the
broad interest to computer science, there is certainly a lot to
interest category theorists, general topologists and proof
theorists.'' -Professor Angus Macintyre, Royal Society
''Regarding the need for a book in this area, I believe the
answer is a clear yes. The subject matter is indeed very topical.
The contributing authors are top quality.'' -Professor Achim Jung
(University of Birmingham)
''There is a niche for an up to date synthesis of current
developments. This has the potential to be a good reference book.
I very much recommend the book to be published.'' -Professor
Robin Knight (University of Oxford)
Description
Reference book covering the latest developments in the
practicable foundations for constructive mathematics
World-class contributors
Broad in scope and aimed at computer scientist, logicians and
philosophers
This edited collection bridges the foundations and practice of
constructive mathematics and focusses on the contrast between the
theoretical developments, which have been most useful for
computer science (eg constructive set and type theories), and
more specific efforts on constructive analysis, algebra and
topology. Aimed at academic logicians, mathematicians,
philosophers and computer scientistsIncluding, with contributions
from leading researchers, it is up-to-date, highly topical and
broad in scope.
Readership: Researchers and academics in logic, computer science
and philosophy
Contents
Introduction
Douglas Bridges: Errett Bishop
1 Michael Rathjen: Generalized Inductive Definitions in
Constructive Set Theory
2 Alex Simpson: Constructive Set Theories and their Category-theoretic
Models
3 Nicola Gambino: Presheaf models for Constructive Set Theories
4 Thomas Streicher: Universes in Toposes
5 Maria Emilia Maietti & Giovanni Sambin: Toward a
minimalistic foundation for constructive mathematics
6 Peter Hancock & Anton Setzer: Interactive Programs and
Weakly Final Coalgebras in Dependent Type Theory
7 Ulrich Berger and Monika Seisenberger: Applications of
inductive definitions and choice principles to program synthesis
8 Sara Negri and Jan von Plato: The duality of lcassical and
constructive notions and proofs
9 Erik Palmgren: Continuity on the real line and in formal spaces
10 Peter Aczel & Christopher Fox: Separation Properties in
Constructive Topology
11 A. Bucalo & G. Rosolini: Spaces as comonoids
12 Maria Emilia Maietti: Predicative exponentiation of locally
compact formal topologies over inductively generated ones
13 Stephen Vickers: Some constructive roads to Tychonoff
14 Thierry Coquand, Henri Lombardi & Marie-Francoise Roy: An
elementary characterisation of Krull dimension
15 Hajime Ishihara: Constructive reverse mathematics: compactness
properties
16 Bas Spitters: Approximating integrable sets by compacts
constructively
17 Hiroki Takamura: An introduction to the theory of c*-algegras
in constructive mathematics
18 Douglas Bridges & Robin Havea: Approximations to the
numerical range of an element of a Banach algebra
19 Douglas Bridges & Luminita Vita: The constructive
uniqueness of the locally convex topology on rn
20 Vasco Brattka: Computability on Non-Separable Banach Spaces
and Landau's Theorem
ISBN: 0-13-186137-9
Copyright: 2006
Format: Cloth; 448 pp
Description
For courses in Elementary Number Theory for math majors, for
mathematics education students, and for Computer Science students.
This introductory undergraduate text is designed to entice a wide
variety of majors into learning some mathematics, while teaching
them to think mathematically at the same time. Starting with
nothing more than basic high school algebra, the reader is
gradually led from basic algebra to the point of actively
performing mathematical research while getting a glimpse of
current mathematical frontiers. The writing style is informal and
includes many numerical examples, which are analyzed for patterns
and used to make conjectures. Emphasis is on the methods used for
proving theorems rather than on specific results.
New To This Edition
? A new chapter that introduces the theory of continued fractions
? Includes the recursion formula for convergents and the
difference of successive convergents (Ch. 39, “The Topsy-Turvy
World of Continued Fractions”)
? New chapter on big-Oh notation and how it is used to describe
the growth rate of number theoretic functions and to describe the
complexity of algorithms (Ch. 38, “Oh, What a Beautiful
Function”).
? A new chapter on “Continued Fractions, Square Roots and Pell’s
Equation” (Ch. 40) ? A continuation of the previous chapter,
inlcuding a discussion of periodicity of continued fractions for
quadratic irrationalities and the relationship between such
continued fraction and solutions to Pell’s equation.
? Additional historical material ? Includes material on Pell’s
equation and the Chinese Remainder Theorem.
? New exercises added to existing chapters.
? Some proofs have been rewritten for added clarity.
2005, VI, 308 p. 98 illus., Hardcover
ISBN: 0-387-23045-9
About this book
Practical quantum computing still seems more than a decade away,
and researchers have not even identified what the best physical
implementation of a quantum bit will be. There is a real need in
the scientific literature for a dialogue on the topic of lessons
learned and looming roadblocks. This reprint from Quantum
Information Processing is dedicated to the experimental aspects
of quantum computing and includes articles that 1) highlight the
lessons learned over the last 10 years, and 2) outline the
challenges over the next 10 years. The special issue includes a
series of invited articles that discuss the most promising
physical implementations of quantum computing. The invited
articles were to draw grand conclusions about the past and
speculate about the future, not just report results from the
present.
Table of contents
Progress in Quantum Algorithms.- NMR Quantum Information
Processing.- Quantum Computing with Trapped Ion Hyperfine Qubits.-
Ion Trap Quantum Computing with Ca+ Ions.- Quantum Information
Processing in Cavity.- QED.- Quantum Information Processing with
Trapped Neutral Atoms.- The Road to a Silicon Quantum Computer.-
Controlling Spin Qubits in Quantum Dots.- Spin-based Quantum Dot
Quantum Computing in Silicon.- Optically driven quantum computing
devices based on semiconductor quantum dots.- Superconducting
Qubits.- Towards Linear Optical Quantum Computers.- Photonic
Technologies for Quantum Information Processing.- Quantum
computer development with single ion implantation.- Bang-bang
refocusing of a qubit exposed to telegraph noise.- Quantum
computing and information extraction for a dynamic quantum system.-
One dimensional continuous time quantum walks.
2005, XVI, 264 p. 31 illus., Hardcover
ISBN: 0-387-25591-5
About this book
Graph theory is very much tied to the geometric properties of
optimization and combinatorial optimization. Moreover, graph
theory's geometric properties are at the core of many research
interests in operations research and applied mathematics. Its
techniques have been used in solving many classical problems
including maximum flow problems, independent set problems, and
the traveling salesman problem.
GRAPH THEORY AND COMBINATORIAL OPTIMIZATION explores the field's
classical foundations and its developing theories, ideas and
applications to new problems. Belhaiza et al (Chapter 1) study
several conjectures on the algebraic connecticity of graphs.
Brass and Pach (Chapter 2) survey the results in the theory of
geometric patterns. Fukuda and Rosta (Chapter 3) discuss various
data depth measures that were first introduced in nonparametric
statistics. Hertz and Lozin (Chapter 4) examine the method of
augmenting graphs for solving the maximum independent set problem.
Krishnan and Terlaky (Chapter 5) present a survey of semidefinite
and interior point methods for solving NP-hard combinatorial
optimization problems to optimality and designing approximation
algorithms for some of these problems. Kubiak (Chapter 6)
presents a study of balancing mixed-model supply chains. Marcotte
and Savard (chapter 7) outline and overview two classes of
bilevel programs. Shepherd and Vetta (Chapter 8) present a study
of disjoins, and de Werra (Chapter 9) generalizes a coloring
property of unimodular hypergraphs.
The book examines the geometric properties of graph theory and
its widening uses in combinatorial optimization theory and
application. The field's leading researchers have contributed
chapters in their areas of expertise.
Table of contents
Foreword.- Avant-propos.- Contributing Authors.- Preface.-
Variable Neighborhood Search for Extremal Graphs ? XI Bounds on
Algebraic Connectivity.- Problems and Results on Geometric
Patterns.- Data Depth and Maximum Feasible Subsystems.- The
Maximum Independent Set Problem and Augmenting Graphs.- Interior
Point and Semidefinite Approaches in Combinatorial Optimization.-
Balancing Mixed-Model Supply Chains.- Bilevel Programming: A
Combinatorial Perspective.- Visualizing, Finding and Packing
Dijoins.- Hypergraph Coloring by Bichromatic Exchanges
Series: Springer Monographs in Mathematics,
2005, Approx. 300 p., Hardcover
ISBN: 3-540-24133-7
About this book
This book contains the basic theories and methods with many
interesting problems from PDE, ODE, differential geometry and
mathematical physics as applications, and covers the necessary
preparations to almost all important aspects in contemporary
studies. There are five chapters: Linearizations, Fixed Point
Theorems, Degree theory and applications, Minimizations, and
Topological and Variational Methods. Each chapter is a very nice
combination of abstract analysis, classical analysis and applied
analysis. Chapter 1 emphasizes on the applications of the
Implicit Function Theorem, including the continuation method,
bifurcation theory, perturbation technique, gluing method and the
transversality. Chapter 2 contains fixed point theorem obtained
by compactness and convexity. All theorems are based on Ky Fan’s
inequality. Besides the basic theory and standard applications of
the degree theory, the following topics are studied in Chapter 3:
Positive solutions for semilinear elliptic BVP, Multiple
solutions problems, Bifurcation at infinity etc. Chapters 4 and 5
consist of an overall view of modern calculus of variations:
Direct Method (constraint problem, Legendre transformation, quasi-convexity
and Morrey Theorem, Young measure, relaxing method, BV space,
Hardy space and compensation compactness, concentration
compactness and best constants, and the segmentation in the image
processing), Infinite dimensional Morse theory, Minimax
Principles and the Conley theory on metric spaces.
Table of contents
Linearization. - Fixed Point Theorems.- Degree Theory and
Applications.- Minimization Methods.-Topological Methods.