Series: Sources and Studies in the History of Mathematics and Physical Sciences
1st ed. 2016, XVIII, 305 p. 75 illus., 1 illus. in
color.
Hardcover
ISBN 978-3-319-47990-3
* Provides the first critical edition with translation and commentary of
Ibn al-Haytham's On the Shape of the Eclipse
* Contains Arabic text, translation, and glossary
* Gives and overview of all studies of Ibn al-Haytham's work
This book provides the first critical edition of Ibn al-Haythamfs On the Shape of the
Eclipse with English translation and commentary, which records the first scientific analysis
of the camera obscura. On the Shape of the Eclipse includes pioneering research on the
conditions of formation of the image, in a time deemed to be committed to aniconism. It
also provides an early attempt to merge the two branches of Ancient optics?the theory
of light and theory of vision.
What perhaps most strongly characterizes this treatise is the close interaction of a
geometric analysis of light and experimental reasoning. Ibn al-Haytham conducted his
experiments in a systematic way by varying all that could be changed: the shape and size
of the aperture, the focal length of the camera obscura, the distance and shape of the
celestial bodies. This way, he achieved a thorough understanding. This work represents a
decisive step in both the history of optics and the application of the experimental method
that was just as efficient in medieval Islam as today.
Series: CMS Books in Mathematics
2016, XIX, 617 p. 18 illus.
Hardcover
ISBN 978-3-319-48310-8
* Tight interplay among the key notions of convexity, monotonicity, and nonexpansiveness
* Accessible to a broad audience
* Coverage of many applications of interest to practitioners in infinitedimensional spaces
* More than 400 exercises are distributed throughout the book
This reference text, now in its second edition, offers a modern unifying presentation
of three basic areas of nonlinear analysis: convex analysis, monotone operator theory,
and the fixed point theory of nonexpansive operators. Taking a unique comprehensive
approach, the theory is developed from the ground up, with the rich connections and
interactions between the areas as the central focus, and it is illustrated by a large number
of examples. The Hilbert space setting of the material offers a wide range of applications
while avoiding the technical difficulties of general Banach spaces. The authors have
also drawn upon recent advances and modern tools to simplify the proofs of key results
making the book more accessible to a broader range of scholars and users. Combining
a strong emphasis on applications with exceptionally lucid writing and an abundance
of exercises, this text is of great value to a large audience including pure and applied
mathematicians as well as researchers in engineering, data science, machine learning,
physics, decision sciences, economics, and inverse problems. The second edition of
Convex Analysis and Monotone Operator Theory in Hilbert Spaces greatly expands on the
first edition, containing over 140 pages of new material, over 270 new results, and more
than 100 new exercises. It features a new chapter on proximity operators including two
sections on proximity operators of matrix functions, in addition to several new sections
distributed throughout the original chapters. Many existing results have been improved,
and the list of references has been updated.
Heinz H. Bauschke is a Full Professor of Mathematics at the Kelowna campus of the
University of British Columbia, Canada.
Patrick L. Combettes, IEEE Fellow, was on the faculty of the City University of New York and
of Universite Pierre et Marie Curie Paris 6 before joining North Carolina State University
as a Distinguished Professor of Mathematics in 2016.
Series: Universitext
2016, XII, 266 p.
Softcover
ISBN 978-3-319-47972-9
* Quicker paced introduction to the basics allows for a more in-depth
treatment of such topics as convergence theory and Brownian motion
* Self-contained and suitable for students with varying levels of background in analysis and measure theory
* Includes a complete overview of basic measure theory and analysis (with proofs), and an extensive bibliography for further reading in the area
* Written in a lively and engaging style
* Second edition has additional exercises and expanded basic theory, and a new chapter on general Markov dependent sequences
This text develops the necessary background in probability theory underlying diverse
treatments of stochastic processes and their wide-ranging applications. In this second
edition, the text has been reorganized for didactic purposes, new exercises have been
added and basic theory has been expanded. General Markov dependent sequences
and their convergence to equilibrium is the subject of an entirely new chapter. The
introduction of conditional expectation and conditional probability very early in the
text maintains the pedagogic innovation of the first edition; conditional expectation is
illustrated in detail in the context of an expanded treatment of martingales, the Markov
property, and the strong Markov property. Weak convergence of probabilities on metric
spaces and Brownian motion are two topics to highlight. A selection of large deviation
and/or concentration inequalities ranging from those of Chebyshev, Cramer?Chernoff,
Bahadur?Rao, to Hoeffding have been added, with illustrative comparisons of their use in
practice. This also includes a treatment of the Berry?Esseen error estimate in the central
limit theorem.
The authors assume mathematical maturity at a graduate level; otherwise the book is
suitable for students with varying levels of background in analysis and measure theory.
For the reader who needs refreshers, theorems from analysis and measure theory used in
the main text are provided in comprehensive appendices, along with their proofs, for ease
of reference.
Rabi Bhattacharya is Professor of Mathematics at the University of Arizona. Edward
Waymire is Professor of Mathematics at Oregon State University. Both authors have coauthored
numerous books, including a series of four upcoming graduate textbooks in
stochastic processes with applications.
Series: Universitext
1st ed. 2016, XIV, 283 p. 68 illus., 61 illus. in
Hardcover
ISBN 978-3-319-48934-6
* Perfect book for a One-semester PDE course
* Includes a thorough discussion of modeling process for each equation
* Covers indepth three types of linear PDES: elliptic, parabolic, and hyperbolic
This modern take on partial differential equations does not require knowledge beyond
vector calculus and linear algebra. The author focuses on the most important classical
partial differential equations, including conservation equations and their characteristics,
the wave equation, the heat equation, function spaces, and Fourier series, drawing on
tools from analysis only as they arise.Within each section the author creates a narrative
that answers the five questions:
(1) What is the scientific problem we are trying to understand?
(2) How do we model that with PDE?
(3) What techniques can we use to analyze the PDE?
(4) How do those techniques apply to this equation?
(5) What information or insight did we obtain by developing and analyzing the PDE?
The text stresses the interplay between modeling and mathematical analysis, providing a
thorough source of problems and an inspiration for the development of methods.
Series: Universitext
1st ed. 2016, X, 525 p. 21 illus.
Softcover
ISBN 978-3-319-48813-4
* Provides a self-contained and easy-to-read introduction to dynamic programming
* Provides a comprehensive treatment of discrete-time multistage optimization
* Presents the theory of Markov decision processes without advanced measure theory
* Includes various examples and exercises (without solutions)
This book explores discrete-time dynamic optimization and provides a detailed
introduction to both deterministic and stochastic models. Covering problems with finite
and infinite horizon, as well as Markov renewal programs, Bayesian control models and
partially observable processes, the book focuses on the precise modelling of applications
in a variety of areas, including operations research, computer science, mathematics,
statistics, engineering, economics and finance.
Dynamic Optimization is a carefully presented textbook which starts with discrete-time
deterministic dynamic optimization problems, providing readers with the tools for
sequential decision-making, before proceeding to the more complicated stochastic
models. The authors present complete and simple proofs and illustrate the main results
with numerous examples and exercises (without solutions). With relevant material
covered in four appendices, this book is completely self-contained.