Due 2018-06-24
1st ed. 2018, XXIII, 565 p.
36 illus., 30 illus. in color.
Softcover
ISBN 978-3-319-90274-6
Series : Universitext
Written by an expert in the subject
Covers discretization schemes of stochastic differential equations
Includes over 150 exercises
Contains an extensive bibliography
This textbook provides a self-contained introduction to numerical methods in probability with a
focus on applications to finance. Topics covered include the Monte Carlo simulation (including
simulation of random variables, variance reduction, quasi-Monte Carlo simulation, and more
recent developments such as the multilevel paradigm), stochastic optimization and
approximation, discretization schemes of stochastic differential equations, as well as optimal
quantization methods. The author further presents detailed applications to numerical aspects
of pricing and hedging of financial derivatives, risk measures (such as value-at-risk and
conditional value-at-risk), implicitation of parameters, and calibration. Aimed at graduate
students and advanced undergraduate students, this book contains useful examples and over
150 exercises, making it suitable for self-study.
Due 2018-07-23
1st ed. 2018, X, 240 p. 31 illus. in color.
Softcover
ISBN 978-3-319-91369-8
Series : Lecture Notes in Mathematics
From Symplectic Ruled Surfaces to Planar Contact Manifolds
Provides an up-to-date perspective on certain foundational results in 4-
dimensional symplectic topology
Includes the first exposition aimed at graduate students on the classification
of uniruled symplectic 4-manifolds
Illustrates the connection between McDuff's classic results on rational/ruled
surfaces and more recent developments involving symplectic fillings of
contact 3-manifolds and the Weinstein conjecture
Offers a concise survey of the essential analytical results in the theory of
punctured holomorphic curves
This monograph provides an accessible introduction to the applications of pseudoholomorphic
curves in symplectic and contact geometry, with emphasis on dimensions four and three. The
first half of the book focuses on McDuff's characterization of symplectic rational and ruled
surfaces, one of the classic early applications of holomorphic curve theory. The proof presented
here uses the language of Lefschetz fibrations and pencils, thus it includes some background
on these topics, in addition to a survey of the required analytical results on holomorphic
curves. Emphasizing applications rather than technical results, the analytical survey mostly
refers to other sources for proofs, while aiming to provide precise statements that are widely
applicable, plus some informal discussion of the analytical ideas behind them. The second half
of the book then extends this program in two complementary directions: (1) a gentle
introduction to Gromov-Witten theory and complete proof of the classification of uniruled
symplectic 4-manifolds; and (2) a survey of punctured holomorphic curves and their
applications to questions from 3-dimensional contact topology, such as classifying the
symplectic fillings of planar contact manifolds. This book will be particularly useful to graduate
students and researchers who have basic literacy in symplectic geometry and algebraic
topology, and would like to learn how to apply standard techniques from holomorphic curve
theory without dwelling more than necessary on the analytical details.
Due 2018-08-01
1st ed. 2018, X, 126 p. 26 illus., 19 illus. in color.
Softcover
ISBN 978-3-0348-0982-5
Series : Compact Textbooks in Mathematics
Lecture-tested introduction to topology, differential topology, and differential
geometry
Contributes to a wide range of topics on a few pages
About 70 exercises motivate the application of the learned field
Contains valuable hints for further reading
This book provides an introduction to topology, differential topology, and differential geometry.
It is based on manuscripts refined through use in a variety of lecture courses. The first chapter
covers elementary results and concepts from point-set topology. An exception is the Jordan
Curve Theorem, which is proved for polygonal paths and is intended to give students a first
glimpse into the nature of deeper topological problems. The second chapter of the book
introduces manifolds and Lie groups, and examines a wide assortment of examples. Further
discussion explores tangent bundles, vector bundles, differentials, vector fields, and Lie brackets
of vector fields. This discussion is deepened and expanded in the third chapter, which
introduces the de Rham cohomology and the oriented integral and gives proofs of the Brouwer
Fixed-Point Theorem, the Jordan-Brouwer Separation Theorem, and Stokes's integral formula.
The fourth and final chapter is devoted to the fundamentals of differential geometry and traces
the development of ideas from curves to submanifolds of Euclidean spaces. Along the way, the
book discusses connections and curvature--the central concepts of differential geometry. The
discussion culminates with the Gaus equations and the version of Gaus's theorema egregium
for submanifolds of arbitrary dimension and codimension. This book is primarily aimed at
advanced undergraduates in mathematics and physics and is intended as the template for a
one- or two-semester bachelor's course.
Due 2018-08-07
1st ed. 2018, IX, 273 p.
Hardcover
ISBN 978-3-319-91679-8
Series : Developments in Mathematics
A Survey of Classic and New Results with Open Problems
Presents many useful results and new notions that cannot be found in
existing books and are difficult (or impossible) to find in journal articles
Gives special attention to new lines of research
Appropriate level for postgraduate students or researchers in general (or settheoretic)
topology
Written in a style that is easy to read for both students and experienced
researchers in this area
Focuses on topological groups and their generalizations, a subject in which
there has been a lot of activity the last decades
This book, intended for postgraduate students and researchers, presents many results of
historical importance on pseudocompact spaces. In 1948, E. Hewitt introduced the concept of
pseudocompactness which generalizes a property of compact subsets of the real line. A
topological space is pseudocompact if the range of any real-valued, continuous function
defined on the space is a bounded subset of the real line. Pseudocompact spaces constitute a
natural and fundamental class of objects in General Topology and research into their
properties has important repercussions in diverse branches of Mathematics, such as Functional
Analysis, Dynamical Systems, Set Theory and Topological-Algebraic structures. The collection of
authors of this volume include pioneers in their fields who have written a comprehensive
explanation on this subject. In addition, the text examines new lines of research that have been
at the forefront of mathematics. There is, as yet, no text that systematically compiles and
develops the extensive theory of pseudocompact spaces, making this book an essential asset
for anyone in the field of topology.
Due 2018-09-27
2nd ed. 2018, Approx. 220 p.
Hardcover
ISBN 978-4-431-56836-0
Presents a unique combination of birational geometry, traditional local
aspects of singularities, and new developments in research on singularities
Shows concise introductions of tools for study of singularities such as
homological algebra, spectral sequence, toric varieties, and Hodge theory,
which are also useful for study of other subjects in algebra and algebraic
geometry
Describes briefly the recent dramatic developments of the three directions in
research on singularities
This book is an introduction to singularities for graduate students and researchers. Algebraic
geometry is said to have originated in the seventeenth century with the famous work Discours
de la methode pour bien conduire sa raison, et chercher la verite dans les sciences by
Descartes. In that book he introduced coordinates to the study of geometry. After its
publication, research on algebraic varieties developed steadily. Many beautiful results emerged
in mathematiciansf works. First, mostly non-singular varieties were studied. In the past three
decades, however, it has become clear that singularities are necessary for us to have a good
description of the framework of varieties. For example, it is impossible to formulate minimal
model theory for higher-dimensional cases without singularities. A remarkable fact is that the
study of singularities is developing and people are beginning to see that singularities are
interesting and can be handled by human beings. This book is a handy introduction to
singularities for anyone interested in singularities. The focus is on an isolated singularity in an
algebraic variety. After preparation of varieties, sheaves, and homological algebra, some known
results about 2-dimensional isolated singularities are introduced. Then a classification of higherdimensional
isolated singularities is shown according to plurigenera and the behavior of
singularities under a deformation is studied. In the second edition, brief descriptions about
recent remarkable developments of the researches are added as the last chapter.