Luke Hodgkin

A History of Mathematics
From Mesopotamia to Modernity

Hardback (laminated boards)
0-19-852937-6
Publication date: 2 June 2005
296 pages, numerous figures & halftones, 246mm x 189mm

Description

Excellent addition to existing literature
Contains exercises (with solutions) to stretch the more advanced reader
Broad global coverage of mathematical development through time
Class-tested, ideal teaching material
Suitable for students of mathematics, philosophy and history
With extensive bibliography and cross-references to key texts
More than 100 illustrations and figures

A History of Mathematics: From Mesopotamia to Modernity covers the evolution of mathematics through time and across the major Eastern and Western civilizations. It begins in Babylon, then describes the trials and tribulations of the Greek mathematicians. The important, and often neglected, influence of both Chinese and Islamic mathematics is covered in detail, placing the description of early Western mathematics in a global context. The book concludes with modern mathematics, covering recent developments such as the advent of the computer, chaos theory, topology, mathematical physics, and the solution of Fermat's Last Theorem.

Containing more than 100 illustrations and figures, this text, aimed at advanced undergraduates and postgraduates, addresses the methods and challenges associated with studying the history of mathematics. The reader is introduced to the leading figures in the history of mathematics (including Archimedes, Ptolemy, Qin Jiushao, al-Kashi, al-Khwarizmi, Galileo, Newton, Leibniz, Helmholtz, Hilbert, Alan Turing, and Andrew Wiles) and their fields. An extensive bibliography with cross-references to key texts will provide invaluable resource to students and exercises (with solutions) will stretch the more advanced reader.

Readership: Students of mathematics, philosophy and history taking a course in the history of science or mathematics.

Contents

Introduction
1 Babylonian mathematics
2 Greeks and 'Origins'
3 Greeks, practical and theoretical
4 Chinese mathematics
5 Islam, neglect and discovery
6 Understanding the 'Scientific Revolution'
7 The Calculus
8 Geometries and Space
9 Modernity and its Anxieties
10 A Chaotic End?
Bibliography
Index

Edited by: G. L. Litvinov, Independent University of Moscow, Russia,
and V. P. Maslov, Moscow Institute of Electrical Engineering, Russia

Idempotent Mathematics and Mathematical Physics

Description

Idempotent mathematics is a rapidly developing new branch of the mathematical sciences that is closely related to mathematical physics. The existing literature on the subject is vast and includes numerous books and journal papers.

A workshop was organized at the Erwin Schrodinger Institute for Mathematical Physics (Vienna) to give a snapshot of modern idempotent mathematics. This volume contains articles stemming from that event. Also included is an introductory paper by G. Litvinov and additional invited contributions.

The resulting volume presents a comprehensive overview of the state of the art. It is suitable for graduate students and researchers interested in idempotent mathematics and tropical mathematics.

Contents

G. L. Litvinov -- The Maslov's dequantization, idempotent and tropical mathematics: A very brief introduction
M. Akian, S. Gaubert, and V. Kolokoltsov -- Set coverings and invertibility of functional Galois connections
M. Akian, S. Gaubert, and C. Walsh -- Discrete max-plus spectral theory
A. Baklouti -- Dequantization of coadjoint orbits: Moment sets and characteristic varieties
P. Butkovic -- On the combinatorial aspects of max-algebra
G. Cohen, S. Gaubert, J.-P. Quadrat, and I. Singer -- Max-plus convex sets and functions
A. Di Nola and B. Gerla -- Algebras of Lukasiewicz's logic and their semiring reducts
W. H. Fleming and W. M. McEneaney -- Max-plus approaches to continuous space control and dynamic programming
K. Khanin, D. Khmelev, and A. Sobolevskii -- A blow-up phenomenon in the Hamilton-Jacobi equation in an unbounded domain
G. L. Litvinov and G. B. Shpiz -- The dequantization transform and generalized Newton polytopes
P. Loreti and M. Pedicini -- An object-oriented approach to idempotent analysis: Integral equations as optimal control problems
P. Lotito, J.-P. Quadrat, and E. Mancinelli -- Traffic assignment & Gibbs-Maslov semirings
D. McCaffrey -- Viscosity solutions on Lagrangian manifolds and connections with tunnelling operators
E. Pap -- Applications of the generated pseudo-analysis to nonlinear partial differential equations
E. Pap -- A generalization of the utility theory using a hybrid idempotent-probabilistic measure
M. Passare and A. Tsikh -- Amoebas: Their spines and their contours
J. Richter-Gebert, B. Sturmfels, and T. Theobald -- First steps in tropical geometry
I. V. Roublev -- On minimax and idempotent generalized weak solutions to the Hamilton-Jacobi equation
E. Wagneur -- Dequantisation: Semi-direct sums of idempotent semimodules
J. van der Woude and G. J. Olsder -- On (min,max,+)-inequalities
K. Zimmermann -- Solution of some max-separable optimization problems with inequality constraints

Details:

Series: Contemporary Mathematics, Volume: 377
Publication Year: 2005
ISBN: 0-8218-3538-6
Paging: 370 pp.
Binding: Softcover

by Herbert Busemann

The Geometry of Geodesics

ISBN: 0-486-44237-3

A comprehensive approach to qualitative problems in intrinsic differential geometry, this text for upper-level undergraduates and graduate students emphasizes cases in which geodesics possess only local uniqueness properties--and consequently, the relations to the foundations of geometry are decidedly less relevant, and Finsler spaces become the principal subject. The book opens with an explanation of the basic concepts and proceeds to discussions of Desarguesian spaces, perpendiculars and parallels, and covering spaces. Concluding chapters examine the influence of the sign of the curvature on geodesics and homogenous spaces. 1955 ed. 66 figures.

Table of Contents for The Geometry of Geodesics Preface

I. The Basic Concepts
II. Desarguesian Spaces
III. Perpendiculars and Parallels
IV. Covering Spaces
V. The Influence of the Sign of the Curvature on the Geodesics
VI. Homogenous Spaces
Appendix
Notes to the Text
Index

Saber Elaydi Trinity University, San Antonio, Texas, USA /Gerasimos Ladas University of Rhode Island, Kingston, Rhode Island, USA Bernd Aulbach University of Augsburg, Germany /Ondrej Dosly Masaryk University, Czech Republic

Proceedings of the Eighth International Conference on Difference Equations and Applications

ISBN: 1-58488-536-X
Publication Date: 4/29/2005
Number of Pages: 304

The Eighth International Conference on Difference Equations and Applications was held at Masaryk University in Brno, Czech Republic. This volume comprises refereed papers presented at this conference. These papers cover all important themes, conjectures, and open problems in the fields of discrete dynamical systems and ordinary and partial difference equations, classical and contemporary, theoretical and applied.

Table of Contents

On Some Simple Floquet Theory on Time Scales. On a Condition for Transitivity of Lorenz Maps. Iterated Multifunction Systems. Invariant Manifolds as Pullback Attractors of Nonautonomous Difference Equations. Determination of Initial Data Generating Solutions of Bernoulli's Type Difference Equations with Prescribed Asymptotic Behaviour. Solutions bounded on the Whole Line for Perturbed Difference Systems. On Rational Third Order Difference Equations. Decaying Solutions for Difference Equations with Deviating Argument. On a Differential and Difference Equation with a Constant Delay. Some Discrete Nonlinear Inequalities and Applications To Boundary Value Problems. The Asymptotic Stability of x(n + k) + ax(n) + bx(n _ l ) = 0. On Nonoscillatory Solutions of Third Order Difference Equations. Global Stability of Periodic Orbits of Nonautonomous Difference Equations in Population Biology and the Cushing-Henson Conjectures. Symplectic Factorizations and the Definition of a Focal Point. Second Smaller Zero of Kneading Determinant for Iterated Maps. Bifurcation of Almost Periodic Solutions in a Difference Equation. The Harmonic Oscillator { An Extension Via Measure Chains. Solution of Dirichlet Problems with Discrete Double-Layer Potentials. Moments of Solutions of Linear Difference Equations. Time Variant Consensus Formation in Higher Dimensions. On Asymptotic Properties of Solutions of the Difference Equation Dx(t) = -ax(t) + bx(g (t)). Oscillation Theorems for a Class of Fourth Order Nonlinear Difference Equations . 193. Iterates of the Tangent Map -- the Bifurcation Scheme. Difference Equations for Photon-Number Distribution in the Stationary Regime of a Random Laser. Delay Equations on Measure Chains: Basics and Linearized Stability. On the System of two Difference Equations xn+1 = p+yn-k / yn, yn+1 = q+xn-k / xn. Asymptotic Behavior of Solutions of Certain Second Order Nonlinear Difference Equations. Asymptotic Behavior of the Solutions of the Fuzzy Difference Equation . On the Gauss Hypergeometric Series with Roots Outside the Unit Disk. Symbolic Dynamics Generated by an Idealized Time-delayed Chua's Circuit.

SANZ-SOLE,M.

Malliavin Calculus with Applications to Stochastic Partial Differential Equations

ISBN: 0-8493-4030-6
Publication Date: 6/30/2005
Number of Pages: 150

Presents applications of Malliavin calculus to the analysis of probability laws of solutions of stochastic partial differential equations
Introduces this type of calculus based on Gaussian space
Includes finite-dimensional and infinite-dimensional settings
Addresses applications based on recent research

Presented in a comprehensive way, A Course on Malliavin Calculus with Applications to Stochastic Partial Differential Equations describes applications of Malliavin calculus to the analysis of probability laws of solutions of stochastic partial differential equations, driven by Gaussian noises that are white in time and colored in space. The text begins with an introduction to this type of calculus based on a general Gaussian space, from finite-dimensional to infinite-dimensional settings. The book later presents applications to stochastic partial differential equations based on current research, supplemented by comments concerning the origin of the work developed within and its references.

Table of Contents

Introduction. Integration by Parts and Absolute Continuity of Probability Laws. Finite Dimensional Malliavin Calculus. The Basic Operators of Malliavin Calculus. Representation of Wiener Functionals. Criteria for Absolute Continuity and Smoothness of Probability Laws. Stochastic Partial Differential Equations driven by Spatially Homogenous Gaussian Noise. Malliavin Regularity of Solutions of SPDEs. Analysis of the Malliavin Matrix of Solutions of SPDEs. Definition of Spaces Used Throughout the Course