ISBN: 0-471-69098-8
Paperback
408 pages
July 2005
A smorgasbord of math puzzles, factoids, quotations, trivia,
formulas, and much more
Are you fascinated by numbers and want to learn more? Does the
vast world of math problems that humans have solved?and the ones
we have yet to begin to comprehend?give you goose bumps? If so,
this is the book for you. A Passion for Mathematics is an
educational, entertaining trip through the curiosities of the
math world, blending an eclectic mix of history, biography,
philosophy, number theory, geometry, probability, huge numbers,
and mind-bending problems into a delightfully compelling
collection that is sure to please math buffs, students, and
experienced mathematicians alike.
In each chapter, Clifford Pickover provides factoids, anecdotes,
definitions, quotations, and captivating challenges that range
from fun, quirky puzzles to insanely difficult problems. You'll
encounter mad mathematicians, strange number sequences, obstinate
numbers, curious constants, magic squares, fractal geese, monkeys
typing Hamlet, infinity, and much, much more.
If you love all things mathematical, A Passion for Mathematics
will feed your fascination while giving your problem-solving
skills a great workout!
"Pickover has published nearly a book a year in which he
stretches the limits of computers, art, and thought."
-Los Angeles Times
"A perpetual idea machine, Clifford Pickover is one of the
most creative, original thinkers in the world today."
-Journal of Recreational Mathematics
ISBN: 0-471-73579-5
Hardcover
288 pages
July 2005
Learn to write programs to solve linear algebraic problems
The Second Edition of this popular textbook provides a highly
accessible introduction to the numerical solution of linear
algebraic problems. Readers gain a solid theoretical foundation
for all the methods discussed in the text and learn to write
FORTRAN90 and MATLAB(r) programs to solve problems. This new
edition is enhanced with new material and pedagogical tools,
reflecting the author's hands-on teaching experience, including:
* A new chapter covering modern supercomputing and parallel
programming
* Fifty percent more examples and exercises that help clarify
theory and demonstrate real-world applications
* MATLAB(r) versions of all the FORTRAN90 programs
* An appendix with answers to selected problems
The book starts with basic definitions and results from linear
algebra that are used as a foundation for later chapters. The
following four chapters present and analyze direct and iterative
methods for the solution of linear systems of equations, linear
least-squares problems, linear eigenvalue problems, and linear
programming problems. Next, a chapter is devoted to the fast
Fourier transform, a topic not often covered by comparable texts.
The final chapter features a practical introduction to writing
computational linear algebra software to run on today's vector
and parallel supercomputers.
Highlighted are double-precision FORTRAN90 subroutines that solve
the problems presented in the text. The subroutines are carefully
documented and readable, allowing students to follow the program
logic from start to finish. MATLAB(r) versions of the codes are
listed in an appendix. Machine-readable copies of the FORTRAN90
and MATLAB(r) codes can be downloaded from the text's
accompanying Web site.
With its clear style and emphasis on problem solving, this is a
superior textbook for upper-level undergraduates and graduate
students
Series: The New Synthese Historical Library, Vol. 58
2005, XV, 293 p., Hardcover
ISBN: 1-4020-3400-8
About this book
In the present book, Pauline Phemister argues against traditional
Anglo-American interpretations of Leibniz as an idealist who
conceives ultimate reality as a plurality of mind-like immaterial
beings and for whom physical bodies are ultimately unreal and our
perceptions of them illusory. Re-reading the texts without the
prior assumption of idealism allows the more material aspects of
Leibniz's metaphysics to emerge. Leibniz is found to advance a
synthesis of idealism and materialism. His ontology posits
indivisible, living, animal-like corporeal substances as the real
metaphysical constituents of the universe; his epistemology
combines sense-experience and reason; and his ethics fuses
confused perceptions and insensible appetites with distinct
perceptions and rational choice. In the light of his sustained
commitment to the reality of bodies, Phemister re-examines his
dynamics, the doctrine of pre-established harmony and his views
on freedom. The image of Leibniz as a rationalist philosopher who
recognises that, in the created world, there can only be activity
if there is also passivity; minds, souls and forms if there is
also matter; good if there is evil; perfection if there is
imperfection.
Table of contents
Preface. Abbreviations. Introduction.
1. Substances: Public and Private. The public monad. Monads and
Cartesian minds: the French connection. Disagreement with
Descartes. First entelechies.
2. Primary Matter. Substantial form and primary matter. Complete
and incomplete substances. Completion of the active and the
passive. Naturally necessary extension.
3. Extension. Continuity. Plurality and discrete repetition. Co-existence.
Completion of the entelechy. Complete corporeal substances.
4. The Composition of Bodies. Aggregates of substances. Metaphors
and similes. The Fardella Notes. Parts and wholes.
5. The Composition of the Continuum. The real versus the ideal.
The Cartesian continuum and alternatives. Reality and ideality of
corporeal substances.
6. Perceptions and Perceivers. Perceptions and perceivers.
Perceptual multiplicity. Independence and solipsism.
7. Phenomenal Bodies. Spiritual phenomenalism. Monadological
phenomenalism. Corporeal substance phenomenalism. Real Phenomena.
Rainbows. First and third person perspectives.
8. Derivative Forces. Derivative active force. Modifications.
Derivative passive force. Pre-established Harmony. Derivative
forces and perceptions. Harmony of mind and body. Alleged
priority of internal modifications. Multiple harmonies. Final and
efficient causes. Nature and grace.
9. Freedom. The perfection of the world. Evil. Passivity and
freedom. Appetition. Body. Moral evil.
Bibliography. Index of Names. Index of Subjects.
Series: NATO Science Series II: Mathematics, Physics and Chemistry, Vol. 205
2005, X, 580 p.,
Hardcover / ISBN: 1-4020-3645-0
Softcover / ISBN: 1-4020-3646-9
Table of contents
List of figures. Preface. Contributing Authors. Introduction.-
1. History of Delay Equations; J.K. Hale.-
Part I General Results and Linear Theory of Delay Equations in
Finite Dimensional Spaces.
2. Some General Results and Remarks on Delay Differential
Equations; E. Ait Dads. 3. Linear Autonomous Functional
Differential Equations; F. Kappel.-
Part II Hopf Bifurcation, Centre Manifolds and Normal Forms for
Delay Differential Equations.
4. Variation of Constant Formula for Delay Differential
Equations; M.L. Hbid, K. Ezzinbi. 5. Introduction to Hopf
Bifurcation Theory for Delay Differential Equations; M.L. Hbid. 6.
An Algorithmic Scheme for Approximating Center Manifolds and
Normal Forms for Functional Differential Equations; M. Ait Babram.
7. Normal Forms and Bifurcations for Delay Differential
Equations; T. Faria.-
Part III Functional Differential Equations in Infinite
Dimensional Spaces.
8. A Theory of Linear Delay Differential Equations in Infinite
Dimensional Spaces; O. Arino, E. Sanchez. 9. The Basic Theory of
Abstract Semilinear Functional Differential Equations with Non-Dense
Domain; K. Ezzinbi, M. Adimy.-
Part IV More on Delay Differential Equations and Applications.
10. Dynamics of Delay Differential Equations; H.O. Walther. 11.
Delay Differential Equations in Single Species Dynamics; Sh. Ruan.
12. Well-Posedness, Regularity and Asymptotic Behaviour of
Retarded Differential Equations by Extrapolation Theory; L.
Maniar.-
References. Index.
Series: K-Monographs in Mathematics, Vol. 8
2005, Approx. 295 p., Hardcover
ISBN: 1-4020-3511-X
About this book
The seminal `MIT notes' of Dennis Sullivan were issued in June
1970 and were widely circulated at the time, but only privately.
The notes had a major influence on the development of both
algebraic and geometric topology, pioneering the localization and
completion of spaces in homotopy theory, including P-local,
profinite and rational homotopy theory, the Galois action on
smooth manifold structures in profinite homotopy theory, and the
K-theory orientation of PL manifolds and bundles. This is the
first time that this major work has actually been published, and
made available to anyone interested in topology.
Table of contents
Algebraic Constructions.- Homotopy Theoretical Localization.-
Completions in Homotopy Theory.- Spherical Fibrations.- Algebraic
Geometry.- The Galois Group in Geometric Topology.- References.
Galois Symmetry in Manifold Theory At the Primes (Reprint from
Proc. 1970 Nice ICM).- Postscript (2004).
Series: Mathematics and Its Applications, Vol. 580
2005, Approx. 300 p., Hardcover
ISBN: 1-4020-3719-8
About this book
The book is self-contained. It starts with the basic material on
distributions and foliations. Then it proceeds to gradually
introduce and build the tools needed for studying the geometry of
foliated manifolds. The main theme of the book is to investigate
the interrelations between foliations of a manifold on one hand ,
and the many geometric structures that the manifold may admit on
the other hand. Among these structures we mention: affine ,
Riemannian, semi-Riemannian , Finsler , symplectic, complex and
contact structures. Using these structures , the book presents
interesting classes of foliations whose geometry is very rich and
promising. These include the classes of : Riemannian , totally
geodesic, totally umbilical, minimal , parallel non-degenerate ,
parallel totally - null, parallel partially - null, symmetric ,
transversally symmetric , Lagrange , totally real and Legendre
foliations. Some of these classes appear for the first time in
the literature in a book form. Finally, the vertical foliation of
a vector bundle is used to develop a gauge theory on the total
space of a vector bundle.
The book will be of interest to graduate students who want to be
introduced to the geometry of foliations , to researchers working
on foliations and geometric structures , and to physicists
interested in gauge theories .
Table of contents
1. Geometry of Distributions on a Manifold, 2. Structural and
Transveral Geometry of Foliations, 3. Foliations on Semi-Riemannian
Manifolds, 4. Parallel Foliations, 5. Foliations Induced by
Geometric Structures, 6. A Gauge Theory on a Vector Bundle, Basic
Notations and Terminology, References, Index