4th ed. 2003 Approx. 385 p. 57 illus. Hardcover
0-387-95578-X
This book is an introductory textbook on probability theory and
its applications. Basic concepts such as probability measure,
random variable, distribution, and expectation are fully treated
without technical complications. Both the discrete and continuous
cases are covered, but only the elements of calculus are used in
the latter case.
The emphasis is on essential probabilistic reasoning, amply
motivated, explained and illustrated with a large number of
carefully selected samples. Special topics include: combinatorial
problems, urn schemes, Poisson processes, random walks, and
Markov chains. Problems and solutions are provided at the end of
each chapter. Its elementary nature and conciseness make this a
useful text not only for mathematics majors, but also for
students in engineering and the physical, biological, and social
sciences.
This edition adds two chapters covering introductory material on
mathematical finance as well as expansions on stable laws and
martingales. Foundational elements of modern portfolio and option
pricing theories are presented in a detailed and rigorous manner.
This approach distinguishes this text from others, which are
either too advanced mathematically or cover significantly more
finance topics at the expense of mathematical rigor.
Keywords: Probability, Stochastischer Prozess,
Wahrscheinlichkeitsrechnung
Contents: Set.- Probability.- Counting.- Random Variables.-
Conditioning and Independence.- Mean, Variance and Transforms.-
Poisson and Normal Distributions.- From Random Walks to Markov
Chains.- Mean-Variance Pricing Model.- Option Pricing Theory.
Series: Undergraduate Texts in Mathematics.
2003 Approx. 240 p. Hardcover
0-387-95572-0
In 1984, N. Karmarkar published a seminal paper on algorithmic
linear programming. During the subsequent decade, it stimulated a
huge outpouring of new algorithmic results by researchers world-wide
in many areas of mathematical programming and numerical
computation. This book gives an overview of the resulting,
dramatic reorganization that has occurred in one of these areas:
algorithmic differentiable optimization and equation-solving, or,
more simply, algorithmic differentiable programming. The book is
aimed at readers familiar with advanced calculus, numerical
analysis, in particular numerical linear algebra, the theory and
algorithms of linear and nonlinear programming, and the
fundamentals of computer science, in particular, computer
programming and the basic models of computation and complexity
theory.
Contents: The Karmarkar Revolution.- The Newton-Cauchy Method.-
Euler-Newton and Lagrange-NC Methods.- A Misleading Paradigm.- CG
and the Line Search.- Gilding the Nelder-Mead Lily.- Historic
Parallels.- LP from the Newton-Cauchy Perspective.- Diagonal
Metrics and the QC Method.- LP from the Euler-Newton Perspective.-
Log-Barrier Transformations.- Karmarkar Potentials and Algorithms.-
Algorithmic Principles.- Multialgorithms: A New Paradigm.- An
Emerging Discipline.- Bibliography.- Index.
Series: CMS Books in Mathematics. Volume. 13
This is the fourth conference on "Supersymmetry and
Perturbation Theory" (SPT 2002). The proceedings present
original results and state-of-the-art reviews on topics related
to symmetry, integrability and perturbation theory, etc.
Contents:
An Outline of the Geometrical Theory of the Separation of
Variables in the Hamilton?Jacobi and Schrodinger Equations (S
Benenti)
Partial Symmetries and Symmetric Sets of Solutions to PDE's (G
Cicogna)
On the Algebro-Geometric Solution of 3 x 3 Matrix Riemann?Hilbert
Problem (V Enolski & T Grava)
Bifurcations in Flow-Induced Vibration (S Fatimah & F
Verhulst)
Steklov?Lyapunov Type Systems (Yu N Fedorov)
Renormalization Group and Summation of Divergent Series for
Hyperbolic Invariant Tori (G Gentile)
On the Linearization of Holomorphic Vector Fields in the Siegel
Domain with Linear Parts Having Nontrivial Jordan Blocks (T
Gramchev)
Smooth Normalization of a Vector Field Near an Invariant Manifold
(A Kopanskii)
Inverse Problems for SL(2) Lattices (V B Kuznetsov)
Some Remarks about the Geometry of Hamiltonian Conservation Laws
(J-P Ortega)
Janet's Algorithm (W Plesken)
Some Integrable Billiards (E Previato)
Symmetries of Relative Equilibria for Simple Mechanical Systems (M
Rodriguez-Olmos & M E Sousa Dias)
A Spectral Sequences Approach to Normal Forms (J A Sanders)
Rational Parametrization of Strata in Orbit Spaces of Compact
Linear Groups (G Sartori & G Valente)
Effective Hamiltonians and Perturbation Theory for Quantum Bound
States of Nuclear Motion in Molecules (V G Tyuterev)
Generalized Hasimoto Transformation and Vector Sine-Gordon
Equation (J P Wang)
and other papers
Readership: Researchers and graduate students in mathematical and
theoretical physics, and nonlinear science.
308pp Pub. date: Jan 2003
ISBN 981-238-241-0
This volume consists of 18 research papers reflecting the
impressive progress made in the field. It includes new results on
quantum stochastic integration, the stochastic limit, quantum
teleportation and other areas.
Contents:
Markov Property ? Recent Developments on the Quantum Markov
Property (L Accardi & F Fidaleo)
Stationary Quantum Stochastic Processes from the Cohomological
Point-of-View (G G Amosov)
The Feller Property of a Class of Quantum Markov Semigroups II (R
Carbone & F Fagnola)
Recognition and Teleportation (K-H Fichtner et al.)
Prediction Errors and Completely Positive Maps (R Gohm)
Multiplicative Properties of Double Stochastic Product Integrals
(R L Hudson)
Isometric Cocycles Related to Beam Splittings (V Liebscher)
Multiplicativity via a Hat Trick (J M Lindsay & S J Wills)
Dilation Theory and Continuous Tensor Product Systems of Hilbert
Modules (M Skeide)
Quasi-Free Fermion Planar Quantum Stochastic Integrals (W J
Spring & I F Wilde)
and other papers
Readership: Researchers in probability and statistics, quantum
physics and mathematical physics.
260pp (approx.) Pub. date: Scheduled Spring 2003
ISBN 981-238-288-7
About the Author
Martin Krieger has taught at the University of California (Berkeley),
the University of Minnesota (Twin Cities), MIT, and the
University of Michigan (Ann Arbor). He has been a fellow at the
Center for Advanced Study in the Behavioral Sciences and at the
National Humanities Center. He is professor of planning at the
University of Southern California. Professor Krieger was trained
as physicist.
Professor Krieger's earlier books include Marginalism and
Discontinuity, Tools for the Crafts of Knowledge and Decision (1989),
Doing Physics, How Physicists Take Hold of the World (1992), and
Constitutions of Matter, Mathematically Modeling the Most
Everyday of Physical Phenomena (1996).
This book discusses some ways of doing mathematical work and the
subject matter that is being worked upon and created. It argues
that the conventions we adopt, the subject areas we delimit, what
we can prove and calculate about the physical world, and the
analogies that work for mathematicians ? all depend on
mathematics, what will work out and what won't. And the
mathematics, as it is done, is shaped and supported, or not, by
convention, subject matter, calculation, and analogy. The cases
studied include the central limit theorem of statistics, the
sound of the shape of a drum, the connection between algebra and
topology, the stability of matter, the Ising model, and the
Langlands Program in number theory and representation theory.
Contents:
Convention: How Means and Variances are Entrenched as Statistics
Subject: The Fields of Topology
Appendix: The Two-Dimensional Ising Model of a Ferromagnet
Calculation: Strategy, Structure, and Tactics in Applying
Classical Analysis
Analogy: A Syzygy Between a Research Program in Mathematics and a
Research Program in Physics, Each of Which is Itself an Analogy
Mathematics in Concreto
Readership: Mathematicians, physicists, philosophers and
historians of science.
472pp (approx.) Pub. date: Scheduled Spring 2003
ISBN 981-238-200-3
ISBN 981-238-206-2(pbk)