This book covers new ground on Fibonacci
sequences and the
well-known Fibonacci numbers. It will appeal
to research
mathematicians wishing to advance the new
ideas themselves, and
to recreational mathematicians, who will
enjoy the various visual
approaches and the problems inherent in them.
There is a continuing emphasis on diagrams,
both geometric and
combinatorial, which helps to tie disparate
topics together,
weaving around the unifying themes of the
golden mean and various
generalizations of the Fibonacci recurrence
relation.
Very little prior mathematical knowledge is assumed, other than the rudiments of algebra and geometry, so the book may be used as a source of enrichment material and project work for college students. A chapter on games using goldpoint tiles is included at the end, and it can provide much material for stimulating mathematical activities involving geometric puzzles of a combinatoric nature.
Contents:
Number-Theoretic Perspectives ? Coupled Recurrence
Relations:
Introductory Remarks by the First Author
The 2-Fibonacci Sequences
Extensions of the Concepts of 2-Fibonacci
Sequences
Other Ideas for Modification of the Fibonacci
Sequences
Number-Theoretic Perspectives - Number Trees:
Introduction - Turner's Number Trees
Generalizations Using Tableaux
On Gray Codes and Coupled Recurrence Trees
Studies of Node Sums on Number Trees
Connections with Pascal-T Triangles
Geometric Perspectives - Finonacci Vector
Geometry:
Introduction and Elementary Results
Vector Sequences from Linear Recurrences
The Fibonacci Honeycomb Plane
Fibonacci and Lucas Vector Polygons
Trigonometry in the Honeycomb Plane
Vector Sequences Generated in Planes
Fibonacci Tracks, Groups, and Plus-Minus
Sequences
Geometric Perspectives - Goldpoint Geometry:
On Goldpoints and Golden-Mean Constructions
The Goldpoint Rings of a Line Segment
Some Fractals in Goldpoint Geometry
Triangles and Squares Marked with Goldpoints
Plane Tessellations with Goldpoint Triangles
Tessellations with Goldpoint Squares
Games with Goldpoint Tiles
Readership: Researchers, academics, college teachers and general readers interested in Fibonacci mathematics.
300pp (approx.) Pub. date: Scheduled Winter
2002
ISBN 981-238-114-7
ISBN 981-238-134-1(pbk)
This invaluable textbook is divided into
two parts. The first
part includes a detailed discussion on the
discrete
transformations for the Dirac equation, as
well as on the central
force problem for the Dirac equation. In
the second part, the
external field problem is examined; pair
production and vacuum
polarization leading to charge renormalization
are treated in
detail.
Relativistic Quantum Mechanics and Introduction
to Quantum Field
Theory has arisen from a graduate course
which the author taught
for several years at the University of Alberta
to students
interested in particle physics and field
theory.
Contents:
Relativistic Quantum Mechanics:
The Poincare Group
Spin 0: The Klein-Gordon Equation
The Dirac Equation
Structure of Dirac Particles
Dirac Equation: Central Potentials
The Weyl or Neutrino Equation
Relativistic Quantum Field Theory:
The Neutral Klein-Gordon Field
The Charged Klein-Gordon Field
The Dirac Field
Asymptotic Fields: LSZ Formulation
Perturbation Theory
Readership: Graduate students in high energy physics and quantum field theory.
190pp (approx.) Pub. date: Scheduled Spring
2003
ISBN 981-238-136-8
ISBN 981-238-137-6(pbk)
This book presents a general approach to
integration theory,
as well as some advanced topics. It includes
some new results,
but is also a self-contained introduction
suitable for a graduate
student doing self-study or for an advanced
course on integration
theory.
The book is divided into two parts. In the
first part,
integration theory is developed from the
start in a general
setting and immediately for vector-valued
functions. This
material can hardly be found in other textbooks.
The second part
covers various topics related to integration
theory, such as
spaces of measurable functions, convolutions,
famous paradoxes,
and extensions of formulae from elementary
calculus to the
setting of the Lebesgue integral.
Contents:
Basic Integration Theory:
Abstract Integration
Adding a Topological Structure: The Radon
Measure
Adding a Group Structure: The Haar Measure
Advanced Topics:
Spaces of Measurable Functions
Convolutions
Connections with Logic and Set Theory
Special Properties of the Lebesgue Measure
Miscellaneous
Readership: Graduate students, academics and researchers in analysis & differential equations, and stochastic theory.
300pp (approx.) Pub. date: Scheduled Fall
2002
ISBN 981-238-115-5
Series on Knots and Everything - Vol. 32
This book is intended as a reference on links and on the invariants derived via algebraic topology from covering spaces of link exteriors. It emphasizes features of the multicomponent case not normally considered by knot theorists, such as longitudes, the homological complexity of many-variable Laurent polynomial rings, free coverings of homology boundary links, the fact that links are not usually boundary links, the lower central series as a source of invariants, nilpotent completion and algebraic closure of the link group, and disc links. Invariants of the types considered here play an essential role in many applications of knot theory to other areas of topology.
Contents:
Abelian Covers:
Links
Homology and Duality in Covers
Determinantal Invariants
The Maximal Abelian Cover
Sublinks and Other Abelian Covers
Applications: Special Cases and Symmetries:
Knot Modules
Links with Two Components
Symmetries
Free Covers, Nilpotent Quotients and Completion:
Free Covers
Nilpotent Quotients
Algebraic Closure
Disc Links
Readership: Graduate students and academics in geometry and topology.
300pp (approx.) Pub. date: Scheduled Fall
2002
ISBN 981-238-154-6
Complexity has become a central topic in certain sectors of theoretical physics and chemistry (for example, in connection with nonlinearity and deterministic chaos). Also, mathematical measurements of complexity and formal characterizations of this notion have been proposed. The question of how complex systems can show properties that are different from those of their constituent parts has nurtured philosophical debates about emergence and reductionism, which are particularly important in the study of the relationship between physics, chemistry, biology and psychology. This book offers a good presentation of those topics through a truly interdisciplinary approach in which the philosophy of science and the specialized topics of certain sciences are put in a dialogue.
Contents:
The Notions of Complexity and Emergence:
What Is Complexity? (E Agazzi)
Levels and Types of Complexity and Emergence
(H Lenk & A
Stephan)
Formal Metatheoretical Criteria of Complexity
and Emergence (C U
Moulines)
Beyond Reductionism and Holism. The Approach
of Synergetics (B
Kanitscheider)
Kolmogorov Complexity (J Mosterin)
Models of Emerging Structure in Complex Systems
(J Petitot)
Complexity and Emergence in Natural Science:
Emergence in Physics: The Case of Classical
Physics (R Omnes)
Classical Properties in a Quantum-Mechanical
World (A Cordero)
Biological Information, Complexity and Emergence
(J Ricard)
The Emergence of the Mind:
Complexity and the Emergence of Meaning:
Toward a Semiophysics (F
Tito Arecchi)
Complexity and the Emergence of Intentionality:
Some
Misconceptions (M Casartelli)
Can Supervenience Save the Mental? (L Montecucco)
From Complexity to the Separate Soul (G D
Re)
Readership: Graduate students, academics and researchers.
232pp (approx.) Pub. date: Scheduled Winter
2002
ISBN 981-238-158-9
This volume introduces some mathematical
and physical tools
and methods required to follow the recent
developments, and
provides insight in various active areas
of mathematical physics,
including duality, gauge field theory, conformal
field theory,
topological field theory, noncommutative
geometry, and geometry
of low-dimensional manifolds. It comprises
seven self-contained
lectures, which should progressively give
the reader a precise
idea of some of the techniques used in these
areas, as well as a
few short communications presented by young
participants at the
school and two appendices recalling some
basic notions in
differential geometry and quantum field theory.
Contents:
Lectures:
Introduction to the AdS/CFT Correspondence
(S Theisen)
Chern-Simons Supergravity (J Zanelli)
Introduction to Quantum Invariants of 3-Manifolds,
Topological
Quantum Field Theories and Modular Categories
(C Blanchet)
An Introduction to Donaldson-Witten Theory
(M Marino)
Noncommutative Geometry and Abstract Integration
Theory (M
Benameur)
Hopf Algebras in Noncommutative Geometry
(J Varilly)
The Noncommutative Geometry of Aperiodic
Solids (J Bellissard)
Short Communications:
OSp(N|4) Group Contractions and Its Consequences
on
Representations of Different Spatial Symmetry
Groups (M Ayala)
Gauge Anomalies, Weighted Traces and Index
Theorem (A Cardona)
Deligne Cohomology for Orbifolds, Discrete
Torsion and B-Fields (B
Uribe)
Appendices:
Mathematical Prerequisites (S Paycha)
Prerequisites in Physics (H Ocampo)
Readership: Graduate students and researchers
in theoretical and
mathematical physics, as well as geometry
and topology.
450pp (approx.) Pub. date: Scheduled Winter
2002
ISBN 981-238-131-7