Expected publication date is September 29, 2005
Description
This book contains articles on analysis, theory of functions,
partial differential equations, representation theory, and other
areas of mathematics. It also includes two historical papers: an
article about Professor G. I. Natanson and a note about the role
of L. V. Kantorovich in developing computational mathematics in
the Soviet Union.
The book is suitable for graduate students and researchers
interested in analysis and differential equations. It has many
articles of interest for a broad mathematical audience.
Contents
S. A. Avdonin and M. I. Belishev -- Dynamical inverse problem for
the Schrodinger equation (BC-method)
G. A. Leonov and M. S. Poltinnikova -- On the Lyapunov dimension
of the attractor of the Chirikov dissipative mapping
A. I. Nazarov -- On solutions to the Dirichlet problem for an
equation with $p$-Laplacian in a spherical layer
S. A. Nazarov and A. S. Slutskii -- Asymptotic analysis of an
arbitrary spatial system of thin rods
N. I. Nessonov -- Kubo-Martin-Schwinger states on the group $GL(\infty)$
and admissible representations of $GL(\infty)^X$
S. Yu. Pilyugin -- $C^1$-version of Arnold's conjecture about
limit sets of domains
B. A. Samokish -- $H_2$-optimal quadrature formula with Chebyshev
weight of the second kind: Estimate for the remainder term
O. V. Sarafanov -- Calculus of pseudodifferential boundary value
problems on manifolds with smooth edges
O. L. Vinogradov, V. V. Zhuk, V. L. Fainshmidt, and V. P. Khavin
-- Garal$^\prime$d Isidorovich Natanson
I. K. Daugavet, V. M. Ryabov, and B. A. Samokish -- Leonid
Vital$^\prime$evich Kantorovich and computational mathematics
Details:
Series: American Mathematical Society Translations--Series 2,
Volume: 214
Publication Year: 2005
ISBN: 0-8218-3861-X
Paging: approximately 264 pp.
Binding: Hardcover
Expected publication date is September 24, 2005
From a review of the original edition:
"A very readable book which should serve as an excellent
source from which a student could learn the subject ... a
convenient reference for the specialist for theorems which must
by now be regarded as basic to the subject."
-- Mathematical Reviews
Description
Having been out of print for over 10 years, the AMS is delighted
to bring this classic volume back to the mathematical community.
With this fine exposition, the author gives a cohesive account of
the theory of probability measures on complete metric spaces (which
he views as an alternative approach to the general theory of
stochastic processes). After a general description of the basics
of topology on the set of measures, he discusses regularity,
tightness, and perfectness of measures, properties of sampling
distributions, and metrizability and compactness theorems. Next,
he describes arithmetic properties of probability measures on
metric groups and locally compact abelian groups. Covered in
detail are notions such as decomposability, infinite
divisibility, idempotence, and their relevance to limit theorems
for "sums" of infinitesimal random variables. The book
concludes with numerous results related to limit theorems for
probability measures on Hilbert spaces and on the spaces $C[0,1]$.
The Mathematical Reviews comments about the original edition of
this book are as true today as they were in 1967. It remains a
compelling work and a priceless resource for learning about the
theory of probability measures.
The volume is suitable for graduate students and researchers
interested in probability and stochastic processes and would make
an ideal supplementary reading or independent study text.
Contents
The Borel subsets of a metric space
Probability measures in a metric space
Probability measures in a metric group
Probability measures in locally compact abelian groups
The Kolmogorov consistency theorem and conditional probability
Probability measures in a Hilbert space
Probability measures on $C[0,1]$ and $D[0,1]$
Bibliographical notes
Bibliography
List of symbols
Author index
Subject index
Details:
Series: AMS Chelsea Publishing
Publication Year: 1967
Reprint/Revision History: first AMS printing 2005
ISBN: 0-8218-3889-X
Paging: 276 pp.
Binding: Hardcover
Expected publication date is October 27, 2005
Description
Mathematical billiards describe the motion of a mass point in a
domain with elastic reflections off the boundary or,
equivalently, the behavior of rays of light in a domain with
ideally reflecting boundary. From the point of view of
differential geometry, the billiard flow is the geodesic flow on
a manifold with boundary. This book is devoted to billiards in
their relation with differential geometry, classical mechanics,
and geometrical optics.
Topics covered include variational principles of billiard motion,
symplectic geometry of rays of light and integral geometry,
existence and nonexistence of caustics, optical properties of
conics and quadrics and completely integrable billiards, periodic
billiard trajectories, polygonal billiards, mechanisms of chaos
in billiard dynamics, and the lesser-known subject of dual (or
outer) billiards.
The book is based on an advanced undergraduate topics course.
Minimum prerequisites are the standard material covered in the
first two years of college mathematics (the entire calculus
sequence, linear algebra). However, readers should show some
mathematical maturity and rely on their mathematical common sense.
A unique feature of the book is the coverage of many diverse
topics related to billiards, for example, evolutes and involutes
of plane curves, the four-vertex theorem, a mathematical theory
of rainbows, distribution of first digits in various sequences,
Morse theory, the Poincare recurrence theorem, Hilbert's fourth
problem, Poncelet porism, and many others. There are
approximately 100 illustrations.
The book is suitable for advanced undergraduates, graduate
students, and researchers interested in ergodic theory and
geometry.
This volume has been copublished with the Mathematics Advanced
Study Semesters program at Penn State.
Contents
Motivation: Mechanics and optics
Billiard in the circle and the square
Billiard ball map and integral geometry
Billiards inside conics and quadrics
Existence and non-existence of caustics
Periodic trajectories
Billiards in polygons
Chaotic billiards
Dual billiards
Bibliography
Index
Details:
Series: Student Mathematical Library, Volume: 30
Publication Year: 2005
ISBN: 0-8218-3919-5
Paging: 176 pp.
Binding: Softcover
Expected publication date is October 27, 2005
Description
The Workshop on Group Theory and Numerical Analysis brought
together scientists working in several different but related
areas. The unifying theme was the application of group theory and
geometrical methods to the solution of differential and
difference equations. The emphasis was on the combination of
analytical and numerical methods and also the use of symbolic
computation. This meeting was organized under the auspices of the
Centre de Recherches Mathematiques, Universite de Montreal (Canada).
This volume has the character of a monograph and should represent
a useful reference book for scientists working in this highly
topical field.
Contents
A. Atoyan and J. Patera -- Continuous extension of the discrete
cosine transform, and its applications to data processing
D. Baldwin, W. Hereman, and J. Sayers -- Symbolic algorithms for
the Painleve test, special solutions, and recursion operators for
nonlinear PDEs
C. M. Bender -- Continuum limit of lattice approximation schemes
H. Berland and B. Owren -- Algebraic structures on ordered rooted
trees and their significance to Lie group integrators
A. M. Bloch and A. Iserles -- Aspects of generalized double-bracket
flows
E. Celledoni -- Eulerian and semi-Lagrangian schemes based on
commutator-free exponential integrators
E. S. Cheb-Terrab -- Second order linear ODEs: Two non-Liouvillian
approaches
P. A. Clarkson -- On rational solutions of the fourth Painleve
equation and its Hamiltonian
C. Cyr-Gagnon -- Comparison of symmetry preserving difference
schemes with standard numerical methods
W. Hereman, J. A. Sanders, J. Sayers, and J. P. Wang -- Symbolic
computation of polynomial conserved densities, generalized
symmetries, and recursion operators for nonlinear differential-difference
equations
A. Iserles -- On the numerical analysis of rapid oscillation
R. Kozlov -- On conservation properties of semidiscrete canonical
Hamiltonian equations
D. Levi and M. A. Rodriguez -- Discrete Lie symmetries for
difference equations
D. Lewis -- Trivializations, factorizations, and geometric
integration for pseudo-rigid bodies
E. L. Mansfield and G. R. W. Quispel -- Towards a variational
complex for the finite element method
J. Middleton and J. A. Tuszynski -- Models of resonantly driven
motion of motor proteins in 2D potentials
J. Bonasia, F. Lemaire, G. Reid, R. Scott, and L. Zhi --
Determination of approximate symmetries of differential equations
K. B. Wolf -- Discrete and finite fractional Fourier transform
W. J. Zakrzewski -- Some nanotube-like systems and their discrete
equations
A. Zhedanov -- Explicit multipoint rational interpolation Pade
table for exponential and power functions
Details:
Series: CRM Proceedings & Lecture Notes,Volume: 39
Publication Year: 2005
ISBN: 0-8218-3565-3
Paging: approximately 320 pp.
Binding: Softcover
Expected publication date is October 16, 2005
From a review of the previous edition:
"This book contains more than it would seem possible from
the title ... the author demonstrates that he is taking pains to
bring scientific rigor into accord with pedagogical
considerations."
-- translation of Jahrbuch Database review cited in Zbl. Reviews
Description
At the beginning of the twentieth century, college algebra was
taught differently than it is nowadays. There are many topics
that are now part of calculus or analysis classes. Other topics
are covered only in abstract form in a modern algebra class on
field theory. Fine's College Algebra offers the reader a chance
to learn the origins of a variety of topics taught in today's
curriculum, while also learning valuable techniques that, in some
cases, are almost forgotten.
In the early 1900s, methods were often emphasized, rather than
abstract principles. In this book, Fine includes detailed
discussions of techniques of solving quadratic and cubic
equations, as well as some discussion of fourth-order equations.
There are also detailed treatments of partial fractions, the
method of undetermined coefficients, and synthetic division.
Although the book is ostensibly an algebra book, it covers many
topics that are spread around today's curriculum:
Calculus and analysis: infinite series, partial fractions,
undetermined coefficients, properties of continuous functions
Number theory: continued fractions
Probability: basic results in probability
While structured as a textbook, modern mathematicians will find
this book a delight to dip into. There are many gems in here that
have been overlooked by today's emphasis on abstraction and
generality. By revisiting familiar topics, such as continued
fractions or solutions of polynomial equations, modern readers
will enrich their knowledge of fundamental areas of mathematics,
while gaining concrete methods for working with their modern
incarnations. The book is suitable for undergraduates, graduate
students, and researchers interested in algebra.
Contents
Numbers
The natural numbers-couting, addition, and multiplication
Subtraction and the negative
Division and fractions
Irrational numbers
The imaginary and complex numbers
Algebra
Preliminary considerations
The fundamental operations
Simple equations in one unknown letter
Systems of simultaneous simple equations
The division transformation
Factors of rational integral expressions
Highest common factor and lowest common multiple
Rational fractions
Symmetric functions
The binomial theorem
Evolution
Irrational functions. Radicals and fractional exponents
Quadratic equations
Discussion of the quadratic equation. Maxima and minima
Equations of higher degree which can be solved by means of
quadratics
Simultaneous equations which can be solved by means of quadratics
Inequalities
Indeterminate equations of the first degree
Ratio and proportion. Variation
Arithmetical progression
Harmonic progression
Geometrical progression
Method of differences. Arithmetical progressions of higher orders.
Interpolation
Logarithms
Permutations and combinations
The multinomial theorem
Probability
Mathematical induction
Theory of equations
The general cubic and biquadratic equations
Determinants and elimination
Convergence of infinite series
Operations with infinite series
The binomial, exponential, and logarithmic series
Recurring series
Infinite products
Continued fractions
Properties of continuous functions
Answers
Index
Barcode
Details:
Publication Year: 1961
Reprint/Revision History: first AMS printing 2005
ISBN: 0-8218-3863-6
Paging: 631 pp.
Binding: Hardcover