Clifford A. Pickover

A Passion for Mathematics:
Numbers, Puzzles, Madness, Religion, and the Quest for Reality

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


Granville Sewell

Computational Methods of Linear Algebra, 2nd Edition

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

Phemister, Pauline

Leibniz and the Natural World
Activity, Passivity and Corporeal Substances in Leibniz's Philosophy

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.

Arino, O.; Hbid, M.L.; Dads, E. Ait (Eds.)

Delay Differential Equations and Applications
Proceedings of the NATO Advanced Study Institute held in Marrakech, Morocco, 9-21 September 2002

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.

Sullivan, Dennis P.
Ranicki, Andrew (Ed.)

Geometric Topology: Localization, Periodicity and Galois Symmetry
The 1970 MIT notes

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).

Bejancu, Aurelian, Farran, Hani Reda

Foliations and Geometric Structures

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