Series: CMS Books in Mathematics
2006, XVI, 255 p. 8 illus., Hardcover
ISBN: 0-387-24300-3
About this textbook
Convex functions play an important role in almost all branches of
mathematics as well as other areas of science and engineering.
This book is a thorough introduction to contemporary convex
function theory addressed to all people whose research or
teaching interests intersect with the field of convexity. It
covers a large variety of subjects, from the one real variable
case (with all its mathematical gems) to some of the most
advanced topics such as Choquet's theory, the Prekopa-Leindler
type inequalities and their ramifications, as well as the
variational approach of partial differential equations and convex
programming. Many results are new and the whole book reflects the
authors’ own experience, both in teaching and research. The
book can serve as a reference and source of inspiration to
researchers in several branches of mathematics and engineering
and it can also be used for graduate courses.
Table of contents
Series: Stochastic Modelling and Applied Probability, Vol. 25
2nd ed., 2006, XVII, 429 p., Hardcover
ISBN: 0-387-26045-5
About this book
This book is intended as an introduction to optimal stochastic
control for continuous time Markov processes and to the theory of
viscosity solutions. The authors approach stochastic control
problems by the method of dynamic programming. The text provides
an introduction to dynamic programming for deterministic optimal
control problems, as well as to the corresponding theory of
viscosity solutions. A new Chapter X gives an introduction to the
role of stochastic optimal control in portfolio optimization and
in pricing derivatives in incomplete markets. Chapter VI of the
First Edition has been completely rewritten, to emphasize the
relationships between logarithmic transformations and risk
sensitivity. A new Chapter XI gives a concise introduction to two-controller,
zero-sum differential games. Also covered are controlled Markov
diffusions and viscosity solutions of Hamilton-Jacobi-Bellman
equations. The authors have tried, through illustrative examples
and selective material, to connect stochastic control theory with
other mathematical areas (e.g. large deviations theory) and with
applications to engineering, physics, management, and finance. In
this Second Edition, new material on applications to mathematical
finance has been added. Concise introductions to risk-sensitive
control theory, nonlinear H-infinity control and differential
games are also included.
Table of contents
Preface.- Preface to Second Edition.- Notation.- Deterministic
Optimal Control.- Viscosity Solutions.- Optimal Control of Markov
Processes:Classical Solutions.- Controlled Markov Diffusions in
IRn.- Viscosity Solutions: Scond-Order Case.- Logarithmic
Transformations and Risk Sensitivity.- Singular Perturbations.-
Singular Stochastic Control.- Finite Difference Numerical
Approximations.- Applications to Finance.- Differential Games.-
Duality Relationships.- Dynkin ’s Formula for Random Evolutions
with Markov Chain Parameters.- Extension of Lipschitz Continuous
Functions; Smoothing.
2006, X, 264 p. 262 illus., Softcover
ISBN: 0-8176-3517-3
About this textbook
Questions of maxima and minima have great practical significance,
with applications to physics, engineering, and economics; they
have also given rise to theoretical advances, notably in calculus
and optimization. Indeed, while most texts view the study of
extrema within the context of calculus, this carefully
constructed problem book takes a uniquely intuitive approach to
the subject: it presents hundreds of extreme value problems,
examples, and solutions primarily through Euclidean geometry.
Written by a team of established mathematicians and professors,
this work draws on the authors’ experience in the classroom and
as Olympiad coaches. By exposing readers to a wealth of creative
problem-solving approaches, the text communicates not only
geometry but also algebra, calculus, and topology. Ideal for use
at the junior and senior undergraduate level, as well as in
enrichment programs and Olympiad training for advanced high
school students, this book’s breadth and depth will appeal to a
wide audience, from secondary school teachers and pupils to
graduate students, professional mathematicians, and puzzle
enthusiasts.
Table of contents
Preface.- Methods for Finding Geometric Extrema.- Selected Types
of Geometric Extremum Problems.- Miscellaneous.- Hints and
Solutions to the Exercises.- Notation.- Glossary of Terms.-
Bibliography.
2006, XII, 260 p. 31 illus., Hardcover
ISBN: 0-387-20220-X
About this book
The square root of 2 is a fascinating number ? if a little less
famous than such mathematical stars as pi, the number e, the
golden ratio, or the square root of ?1. (Each of these has been
honored by at least one recent book.) Here, in an imaginary
dialogue between teacher and student, readers will learn why v2
is an important number in its own right, and how, in puzzling out
its special qualities, mathematicians gained insights into the
illusive nature of irrational numbers. Using no more than basic
high school algebra and geometry, David Flannery manages to
convey not just why v2 is fascinating and significant, but how
the whole enterprise of mathematical thinking can be played out
in a dialogue that is imaginative, intriguing, and engaging.
Original and informative, The Square Root of 2 is a one-of-a-kind
introduction to the pleasure and playful beauty of mathematical
thinking.
Table of contents
2006, XIX, 219 p. 12 illus., Softcover
ISBN: 0-8176-4353-2
About this book
The problem of approximating a given quantity is one of the
oldest challenges faced by mathematicians. Its increasing
importance in contemporary mathematics has created an entirely
new area known as Approximation Theory. The modern theory was
initially developed along two divergent schools of thought: the
Eastern or Russian group, employing almost exclusively algebraic
methods, was headed by Chebyshev together with his coterie at the
Saint Petersburg Mathematical School, while the Western
mathematicians, adopting a more analytical approach, included
Weierstrass, Hilbert, Klein, and others.
Table of contents
Dedication
Foreword
Preface
Introduction
Forerunners
1.1 Euler’s Analysis of Delisle’s Map
1.2 Laplace’s Approximation of Earth’s Surface
Pafnuti Lvovich Chebyshev
2.1 Chebyshev’s Curriculum Vitae
2.2 Stimuli for the Development of a Theory
2.3 First Theoretical Approaches
2.4 First Theoretical Compositions
2.5 Theory of Orthogonal Polynomials
2.6 Other Contributions of P. L. Chebyshev
2.7 Chebyshev - Euler of the 18th Century?
The Saint Petersburg Mathematical School
3.1 Aleksandr Nikolaevich Korkin
3.2 Egor Ivanovich Zolotarev
3.3 Andrey and Vladimir Andreevich Markov
3.4 Julian Karol Sochocki
3.5 Konstantin Aleksandrovich Posse
3.6 A. A. Markov’s Lectures
3.7 Resume
Development Outside Russia
4.1 The Mediator: Felix Klein
4.2 Blichfeldt’s Note
4.3 Kirchberger’s Thesis
4.4 Other Non-Quantitative Contributions
4.5 On Convergence and Series Expansions
4.6 Fejer and Runge
4.7 Quantitative Approximation Theory
4.8 Jackson’s Thesis
4.9 A Note About Gottingen’s Role
Constructive Function Theory: Kharkiv
5.1 Antony-Bonifatsi Pavlovich Psheborski
5.2 A Short Biography of Sergey Natanovich Bernstein
5.3 First Contributions to Approximation Theory
5.4 Constructive Function Theory as the Development of Chebyshev’s
Ideas
Biographies...
A.1 Matvey Aleksandrovich Tikhomandritski
A.2 Nikolaj Yakovlevich Sonin
A.3 Aleksandr Vasilevich Vasilev
A.4 Ivan Lvovich Ptashitski
A.5 Dmitry Fedorovich Selivanov
A.6 Aleksandr Mikhaylovich Lyapunov
A.7 Ivan Ivanovich Ivanov
A.8 Dmitry Alksandrovich Grave
A.9 Georgi Feodosievich Voronoy
Explanations
B.1 Russian Academic Degrees
References
Index
List of Figures
List of Tables