Mathematik
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Jeanblanc, Monique; Yor, Marc; Chesney, Marc
Mathematical Methods for Financial Markets
Mathematical finance has grown into a huge area of research which requires a
large number of sophisticated mathematical tools. This book simultaneously
introduces the financial methodology and the relevant mathematical tools in a
style that is mathematically rigorous and yet accessible to practitioners and
mathematicians alike. It interlaces financial concepts such as arbitrage
opportunities, admissible strategies, contingent claims, option pricing and
default risk with the mathematical theory of Brownian motion, diffusion
processes, and Lévy processes. The first half of the book is devoted to
continuous path processes whereas the second half deals with discontinuous
processes.
The extensive bibliography comprises a wealth of important references and the
author index enables readers quickly to locate where the reference is cited
within the book, making this volume an invaluable tool both for students and for
those at the forefront of research and practice.
(Series: Springer Finance)
2009, XXVI, 732 p. 9 illus., Hardcover
ISBN: 978-1-85233-376-8
Manin, Yu. I.
A Course in Mathematical Logic for Mathematicians
The book starts with an elementary introduction to formal languages appealing
to the intuition of working mathematicians and unencumbered by philosophical
or normative prejudices such as those of constructivism or intuitionism. It
proceeds to the Proof Theory and presents several highlights of Mathematical
Logic of 20th century: Gödel's and Tarski's Theorems, Cohen's Theorem on
the independence of Continuum Hypothesis. Unusual for books on logic is a
section dedicated to quantum logic.
Then the exposition moves to the Computability Theory, based on the notion of
recursive functions and stressing number{theoretic connections. A complete
proof of Davis{Putnam{Robinson{Matiyasevich theorem is given, as well as a
proof of Higman's theorem on recursive groups. Kolmogorov complexity is
treated.
The third Part of the book establishes essential equivalence of proof theory
and computation theory and gives applications such as Gödel's theorem on the
length of proofs. The new Chapter IX, written for the second edition, treats,
among other things, categorical approach to the theory of computation,
quantum computation, and P/NP problem. The new Chapter X, written for the
second edition by Boris Zilber, contains basic results of Model Theory and its
applications to mainstream mathematics. This theory found deep applications
in algebraic and Diophantine geometry.
Yuri Ivanovich Manin is Professor Emeritus at Max-Planck-Institute for
Mathematics in Bonn, Germany, Board of Trustees Professor at the
Northwestern University, Evanston, USA, and Principal Researcher at the
Steklov Institute of Mathematics, Moscow, Russia. Boris Zilber, Professor of
Mathematics at the University of Oxford, has been added to the second
edition.
(Series: Graduate Texts in Mathematics)
2nd ed., 2010, XVIII, 384 p. 12 illus., Hardcover
ISBN: 978-1-4419-0614-4
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Davidson, Kenneth R.; Donsig, Allan P.
Real Analysis and Applications
Theory in Practice
This new approach to real analysis stresses the use of the subject in
applications, showing how the principles and theory of real analysis can be
applied in various settings. Applications cover approximation by polynomials,
discrete dynamical systems, differential equations, Fourier series and physics,
Fourier series and approximation, wavelets, and convexity and optimization.
Each chapter has many useful exercises.
The treatment of the basic theory covers the real numbers, functions, and
calculus, while emphasizing the role of normed vector spaces, and particularly
of Rn. The applied chapters are mostly independent, giving the reader a choice
of topics. This book is appropriate for students with a prior knowledge of both
calculus and linear algebra who want a careful development of both analysis
and its use in applications.
Review of the previous version of this book, Real Analysis with Real
Applications: "A well balanced book! The first solid analysis course, with
proofs, is central in the offerings of any math.-dept.; ---and yet, the new books
that hit the market don't always hit the mark: the balance between theory and
applications, ---between technical proofs and intuitive ideas, ---between
classical and modern subjects, and between real life exercises vs. the ones
that drill a new concept. The Davidson-Donsig book is outstanding, and it does
hit the mark."
Palle E. T. Jorgenson, Review from Amazon.com
Kenneth R. Davidson is University Professor of Mathematics at the University
of Waterloo. Allan P. Donsig is Associate Professor of Mathematics at the
University of Nebraska-Lincoln.
Oct-09
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Oct-09
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(Series: Undergraduate Texts in Mathematics)
2010, XII, 516 p. 80 illus., Hardcover
ISBN: 978-0-387-98097-3
Kapovich, Michael
Hyperbolic Manifolds and Discrete Groups
This classic book is at the crossroads of several branches of mathematics:
hyperbolic geometry, discrete groups, 3-dimensional topology, geometric
group theory, and complex analysis. The main focus throughout the text is on
Thurston’s hyperbolization theorem, one of the central results of 3-dimensional
topology that has completely changed the landscape of the field. The book
contains a number of open problems and conjectures related to the
hyperbolization theorem as well as rich discussions on related topics including
geometric structures on 3-manifolds, higher dimensional negatively curved
manifolds, and hyperbolic groups.
Featuring beautiful illustrations, a rich set of examples, numerous exercises,
and an extensive bibliography and index, Hyperbolic Manifolds and Discrete
Groups continues to serve as an ideal graduate text and comprehensive
reference.
The book is very clearly written and fairly self-contained. It will be useful to
researchers and advanced graduate students in the field and can serve as an
ideal guide to Thurston's work and its recent developments. Mathematical
Reviews.
Beyond the hyperbolization theorem, this is an important book which had to be
written; some parts are still technical and will certainly be streamlined and
shortened in the next years, but together with Otal's work a complete published
proof of the hyperbolization theorem is finally available. Apart from the proof
itself, the book contains a lot of material which will be useful for various other
directions of research. Zentralbatt MATH.
This book can act as source material for a postgraduate course and as a
reference text on the topic as the references are full and extensive. ... The text
is self-contained and very well illustrated. ASLIB Book Guide.
(Series: Modern Birkhäuser Classics)
1st ed. 2001. 2nd. printing, 2010, XXVIII, 468 p. 78 illus., Softcover
ISBN: 978-0-8176-4912-8
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Kosmann-Schwarzbach, Yvette
Groups and Symmetries
From Finite Groups to Lie Groups
The theory of group representations is a fundamental subject at the
intersection of algebra, geometry and analysis, with innumerable applications
in other domains of pure mathematics and in the physical sciences: chemistry,
molecular biology and physics, in particular crystallography, classical and
quantum mechanics and quantum field theory.
This book is an introduction to both the theory of group representations and its
applications in quantum mechanics. Unlike many other texts, it deals with finite
groups, compact groups, linear Lie groups and their Lie algebras, concisely
presented in one volume. With only linear algebra and calculus as
prerequisites, it is accessible to advanced undergraduates in mathematics and
physics, and will still be of interest to beginning graduate students. Exercises
for each chapter and a collection of problems with complete solutions make
this an ideal text for the classroom or for independent study.
Oct-09
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(Series: Universitext)
2010, XVI, 196 p. 44 illus., Softcover
ISBN: 978-0-387-78865-4
Kilian, Axel
Programmieren mit Wolfram Mathematica®
Dieses von einem erfahrenen Praktiker geschriebene Buch wendet sich an alle
Benutzer von Mathematica®. Der Neuling macht schnell die ersten Schritte
und lernt vor allem zunächst, die eingebaute Hilfe und Dokumentation effizient
zu nutzen. Dem Fortgeschrittenen helfen die prototypischen Beispiele und vor
allem auch eine umfangreiche Sammlung elementarer Tricks und Kniffe. Der
Experte findet hier nicht einfach nur Rezepte, sondern vor allem Konzepte und
Techniken zur Behandlung komplexerer Aufgabenstellungen.
Anhand der vielen Programmierbeispiele unterschiedlichen
Schwierigkeitsgrades, lernt der Leser ganz nebenbei Lösungen konkreter
Probleme kennen. Jedes der Programmierbeispiele beginnt mit einer
Beschreibung der Aufgabenstellung, gefolgt von der Analyse, der Diskussion
verschiedener Lösungsansätze und schließlich einer Implementierung im
Sinne der beschriebenen Programmiergrundsätze. Die ebenfalls behandelten
grafischen Benutzeroberflächen bilden einen weiteren Schwerpunkt dieses
Buches.
Das Buch bezieht sich auf die aktuelle Version 7 sowie die Version 6.
(Series: eXamen.press)
2010, VIII, 264 S., Softcover
ISBN: 978-3-642-04671-1
Treschev, Dmitry; Zubelevich, Oleg
Introduction to the Perturbation Theory of Hamiltonian Systems
This book presents the basic methods of regular perturbation theory of
Hamiltonian systems, including KAM-theory, splitting of asymptotic manifolds,
the separatrix map, averaging, anti-integrable limit, etc. in a readable way.
Despite its small size, it discusses all main aspects of the basic modern theory
of perturbed Hamiltonian systems and most results are given with complete
proofs. It will be of interest to researchers and graduate students of the KAM
community and to scientists working in mechanics.
(Series: Springer Monographs in Mathematics)
2010, X, 211 p., Hardcover
ISBN: 978-3-642-03027-7
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Yin, G. George; Zhu, Chao
Hybrid Switching Diffusions
Properties and Applications
This book focuses on switching diffusion processes involving both continuous
dynamics and discrete events.
The first part, including three chapters, presents basic properties such as
Feller and strong Feller, recurrence, and ergodicity. With a brief review of
existence and uniqueness of solutions of switching diffusions, basic properties
such as recurrence, Feller properties etc. are dealt with.
The second part of the book is devoted to numerical solutions of switching
diffusions.
Containing three chapters, the third part focuses on stability. Chapter seven
and chapter eight proceed with the stability analysis. The approach is based on
Liapunov function methods.
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For convenient references, an appendix including a number of mathematical
preliminaries are placed at the end of the book. Topics discussed here
including Markov chains, martingales, Gaussian processes, diffusions, jump
diffusions, and weak convergence methods. Although detailed developments
are often omitted, appropriate references are provided for the reader for further
reading.
(Series: Stochastic Modelling and Applied Probability)
2010, XVIII, 398 p., Hardcover
ISBN: 978-1-4419-1104-9
Engel, Joachim
Anwendungsorientierte Mathematik: Von Daten zur Funktion.
Eine Einführung in die mathematische Modellbildung für
Lehramtsstudierende
Gegenstand des vorliegenden Lehrbuches ist der Prozess des Anwendens
von Mathematik. Im Mittelpunkt stehen dabei der Funktionsbegriff sowie
mathematische Methoden zur Modellierung funktionaler Abhängigkeiten
zwischen zwei Größen.
Das Buch zeichnet sich durch folgende besonderen Merkmale aus: Reale
Daten als Grundlage für viele Modellierungen als eine wichtige Voraussetzung
für einen authentischen und glaubwürdigen Unterricht an Hochschule und
Schule - Einsatz von Technologie als Werkzeug zum Problemlösen und zur
Illustrierung von Konzepten und Zusammenhängen - Vernetzung
verschiedener Inhalte der Mathematik wie Elementare Funktionenlehre,
Analysis, Stochastik, Lineare Algebra; Numerik.
Detaillierte Ableitungen von Ergebnissen sowie Übungen und Fragen am Ende
der einzelnen Kapitel mit teilweise ausgearbeiteten Lösungen und mit
Lösungshinweisen helfen bei der Vertiefung des Stoffes.
(Series: Mathematik für das Lehramt)
2010, XIV, 468 S., Softcover
ISBN: 978-3-540-89086-7
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Freitag, Eberhard
Funktionentheorie 2
Riemann´sche Flächen, Mehrere komplexe Variable, Abel´sche
Funktionen, Höhere Modulformen
Das Buch bietet eine vollständige Darstellung der Funktionentheorie,
beginnend mit der Theorie der Riemann`schen Flächen einschließlich
Uniformisierungstheorie sowie einer ausführlichen Darstellung der Theorie der
kompakten Riemann`schen Flächen, Riemann-Roch`schem Satz, Abel`schem
Theorem und Jacobi`schem Umkehrtheorem. Hierdurch motiviert wird eine
kurze Einführung in die Funktionentheorie mehrerer Veränderlicher gegeben
und dann die Theorie der Abel`schen Funktionen bis hin zum Thetasatz
entwickelt. Daran anschließend und hierdurch motiviert wird eine Einführung in
die Theorie der höheren Modulfunktionen gegeben.
Oct-09
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Oct-09
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(Series: Springer-Lehrbuch)
2009, XI, 523 S. 80 Abb., Softcover
ISBN: 978-3-540-87896-4
Modler, Florian; Kreh, Martin
Tutorium Analysis 1 und Lineare Algebra 1
Mathematik von Studenten für Studenten erklärt und kommentiert
Dieses Buch soll Ihnen als Mathematik-Erstsemester den Einstieg und
Umstieg von der Schulmathematik in die Hochschulmathematik erleichtern und
Ihnen somit helfen, viele der üblichen Erstsemester-Fehler zu vermeiden.
Das Buch ist anders als alle anderen, denn es wurde von Studenten
geschrieben, die Erfahrung als Tutor, Übungsleiter und Korrektoren haben.
Dadurch wissen die Autoren zum einen, welche Themen schwer verständlich
sind und besonders ausführlich behandelt werden müssen, und zum anderen
kennen sie häufige Fehler und können auf diese hinweisen. In dem Buch gibt
es einen mathematischen Teil, den der Student für Prüfungen beherrschen
muss. Bei Fragen oder Problemen kann er dann in dem Kommentarteil
nachschauen und dort ausführliche Erklärungen, Hilfen und Beispiele der
Autoren finden.
2010, XI, 363 S. 45 Abb., Softcover
ISBN: 978-3-8274-2345-0
Chavent, Guy
Nonlinear Least Squares for Inverse Problems
Theoretical Foundations and Step-by-Step Guide for Applications
This book provides an introduction into the least squares resolution of
nonlinear inverse problems. The first goal is to develop a geometrical theory to
analyze nonlinear least square (NLS) problems with respect to their quadratic
wellposedness, i.e. both wellposedness and optimizability. Using the results,
the applicability of various regularization techniques can be checked. The
second objective of the book is to present frequent practical issues when
solving NLS problems. Application oriented readers will find a detailed analysis
of problems on the reduction to finite dimensions, the algebraic determination
of derivatives (sensitivity functions versus adjoint method), the determination of
the number of retrievable parameters, the choice of parametrization
(multiscale, adaptive) and the optimization step, and the general organization
of the inversion code. Special attention is paid to parasitic local minima, which
can stop the optimizer far from the global minimum: multiscale parametrization
is shown to be an efficient remedy in many cases, and a new condition is given
to check both wellposedness and the absence of parasitic local minima.
For readers that are interested in projection on non-convex sets, Part II of this
book presents the geometric theory of quasi-convex and strictly quasi-convex
(s.q.c.) sets. S.q.c. sets can be recognized by their finite curvature and limited
deflection and possess a neighborhood where the projection is well-behaved.
Throughout the book, each chapter starts with an overview of the presented
concepts and results.
(Series: Scientific Computation)
2010, XIV, 360 p., Hardcover
ISBN: 978-90-481-2784-9
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Deiser, Oliver
Einführung in die Mengenlehre
Die Mengenlehre Georg Cantors und ihre Axiomatisierung durch Ernst
Zermelo
Das Buch, das nun in dritter, korrigierter Auflage vorliegt, behandelt die BasisResultate der Mengenlehre aus der Zeit Cantors und Zermelos, was etwa den
Zeitraum von 1870 - 1930 abdeckt. Die Ideen dieser Zeit bilden das Herz der
Disziplin und haben das heutige Bild der Mathematik entscheidend mit
geprägt.
Ziel ist, die zentralen Konzepte und Probleme der Mengenlehre Mächtigkeiten, Kardinalzahlen, Kontinuumsproblem, Wohlordnungen,
transfinite Zahlen und transfinite Rekursion, mengentheoretische
Untersuchungen von R - in ihrem Wesen begreifbar zu machen. Eine
Axiomatik wird in Übereinstimmung mit der historischen Entwicklung erst dann
eingeführt, wenn die Theorie bereits weit gediehen ist und nach einem stabilen
Fundament verlangt. Schließlich wird die Axiomatik in einen formalen Rahmen
eingebettet, was Resultate über die Grenzen des Gebäudes ermöglicht (wie
z.B. die Unabhängigkeit der Kontinuumshypothese). Das Buch wendet sich an
Studierende und Dozenten der Mathematik.
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(Series: Springer-Lehrbuch)
3., korr. Aufl., 2010, V, 551 S. 64 Abb., Softcover
ISBN: 978-3-642-01444-4
Ritoré, Manuel; Sinestrari, Carlo
Mean Curvature Flow and Isoperimetric Inequalities
Geometric flows have many applications in physics and geometry. The mean
curvature flow occurs in the description of the interface evolution in certain
physical models. This is related to the property that such a flow is the gradient
flow of the area functional and therefore appears naturally in problems where a
surface energy is minimized. The mean curvature flow also has many
geometric applications, in analogy with the Ricci flow of metrics on abstract
riemannian manifolds. One can use this flow as a tool to obtain classification
results for surfaces satisfying certain curvature conditions, as well as to
construct minimal surfaces. Geometric flows, obtained from solutions of
geometric parabolic equations, can be considered as an alternative tool to
prove isoperimetric inequalities. On the other hand, isoperimetric inequalities
can help in treating several aspects of convergence of these flows.
Isoperimetric inequalities have many applications in other fields of geometry,
like hyperbolic manifolds.
(Series: Advanced Courses in Mathematics - CRM Barcelona)
2010, 124 p., Softcover
ISBN: 978-3-0346-0212-9
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Ruzhansky, Michael; Turunen, Ville
Pseudo-Differential Operators and Symmetries
Background Analysis and Advanced Topics
This monograph develops a global quantization theory of pseudo-differential
operators on compact Lie groups.
Traditionally, the theory of pseudo-differential operators was introduced in the
Euclidean setting with the aim of tackling a number of important problems in
analysis and in the theory of partial differential equations. This also yields a
local theory of pseudo-differential operators on manifolds. The present book
takes a different approach by using global symmetries of the space which are
often available. First, a particular attention is paid to the theory of periodic
operators, which are realized in the form of pseudo-differential and Fourier
integral operators on the torus. Then, the cases of the unitary group SU(2) and
the 3-sphere are analyzed in extensive detail. Finally, the monograph also
develops elements of the theory of pseudo-differential operators on general
compact Lie groups and homogeneous spaces.
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The exposition of the book is self-contained and provides the reader with the
background material surrounding the theory and needed for working with
pseudo-differential operators in different settings. The background section of
the book may be used for independent learning of different aspects of analysis
and is complemented by numerous examples and exercises.
(Series: Pseudo-Differential Operators)
2010, 724 p., Softcover
ISBN: 978-3-7643-8513-2
Benedetto, John J.; Czaja, Wojciech
Integration and Modern Analysis
This textbook and treatise begins with classical real variables, systematically
develops the Lebesgue theory abstractly and for Euclidean space, and
analyzes the structure of measures. The authors' vision of modern real
analysis is based in a fascinating historical commentary interwoven into an
exposition that includes perspectives with other fields. Comprehensive
treatments include: the role of absolute continuity in differentiation and
integration; the evolution of the Riesz representation theorem to Radon
measures and distribution theory; weak convergence of measures and the
Dieudonné–Grothendieck theorem; and the deepest results in modern
differentiation theory. Fundamental topics include: fractals and self-similarity;
rearrangements and maximal functions; and the relation between surface and
Hausdorff measures. There are hundreds of exercises ranging from routine to
challenging.
The self-contained presentation, including extensive appendices on functional
and Fourier analysis, make this book ideal for the classroom, self-study, or
professional reference.
(Series: Birkhäuser Advanced Texts / Basler Lehrbücher)
2009, XVII, 571 p. 24 illus., Hardcover
ISBN: 978-0-8176-4306-5
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Stalker, John
Complex Analysis
Fundamentals of the Classical Theory of Functions
This clear, concise introduction to the classical theory of one complex variable
is based on the premise that "anything worth doing is worth doing with
interesting examples." The content is driven by techniques and examples
rather than definitions and theorems. This self-contained monograph is an
excellent resource for a self-study guide and should appeal to a broad
audience. The only prerequisite is a standard calculus course.
"The first chapter deals with a beautiful presentation of special functions. . . .
The third chapter covers elliptic and modular functions. . . in much more detail,
and from a different point of view, than one can find in standard introductory
books. . . . For [the] subjects that are omitted, the author has suggested some
excellent references for the reader who wants to go through these topics. The
book is read easily and with great interest. It can be recommended to both
students as a textbook and to mathematicians and physicists as a useful
reference."(Mathematical Reviews)
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"Mainly original papers are cited to support the historical remarks. The book is
well readable." (Zentralblatt für Mathematik)
"This is an unusual textbook, incorporating material showing how classical
function theory can be used. . . . The general scheme is to show the reader
how things were developed without following the traditional approach of most
books on functional theory. . . . This book can be recommended to those who
like to see applications of the theory taught in classical courses." (EMS)
(Series: Modern Birkhäuser Classics)
1st ed. 1998. 2nd printing, 2010, XIV, 228 p. 5 illus., Softcover
ISBN: 978-0-8176-4918-0
Scriba, C. J.; Schreiber, P.
5000 Jahre Geometrie
Geschichte, Kulturen, Menschen
Schon lange bevor die Schrift entwickelt wurde, hat der Mensch geometrische
Strukturen wahrgenommen und systematisch verwendet. So entstehen beim
Weben und Flechten einfache zweidimensionale Muster und ohne
dreidimensionale Körper wie Quader, Würfel oder Pyramide ist keine
Bautätigkeit denkbar. Das vorliegende Buch gibt einen faszinierenden
Überblick über die geometrischen Vorstellungen und Erkenntnisse der
Menschen von der Urgesellschaft bis hin zu den komplexen mathematischen
wie auch künstlerischen Ideen des 20. Jahrhunderts. Neben vielen
Abbildungen wird jede Epoche mit einer Tabelle zeit- und kulturgeschichtlicher
Daten eingeleitet und mit einer tabellarischen Darstellung der wesentlichen
Inhalte der Geometrie dieser Zeit abgeschlossen. Aufgaben am Ende jeden
Kapitels laden den Leser ein, sich an den Problemen der alten Meister selber
zu versuchen. Ein Buch für alle, die der Lebendigkeit und Entwicklung der
Geometrie als erste "Anwendungswissenschaft" nachspüren wollen.
Für die 3. Auflage wurden neuste Forschungsergebnisse über steinzeitliche
Kreisgrabenanlagen und die Himmelsscheibe von Nebra aus der Bronzezeit
aufgenommen. Zahlreiche Abbildungen, viele davon jetzt in Farbe, erhöhen
den Lesegenuss des Buches.
(Series: Vom Zählstein zum Computer)
3. Aufl., 2010, XIII, 631 S. 233 Abb., 62 in Farbe., Hardcover
ISBN: 978-3-642-02361-3
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Aigner, Martin; Ziegler, Günter M.
Das BUCH der Beweise
Diese deutlich erweiterte dritte Auflage enthält fünf neue Kapitel, in denen es
um Klassiker geht wie den "Fundamentalsatz der Algebra", um
kombinatorisch-geometrische Zerlegungsprobleme, aber auch um Beweise
aus letzter Zeit, etwa für die "Kneser-Vermutung" in der Graphentheorie. Die
Neuausgabe wartet auch mit weiteren Verbesserungen und Überraschungen
auf - darunter ein neuer Beweis für "Hilberts drittes Problem".
Aus den Rezensionen: "Ein prächtiges, äußerst sorgfältig und liebevoll
gestaltetes Buch! Erdös hatte die Idee DES BUCHES, in dem Gott die
perfekten Beweise mathematischer Sätze eingeschrieben hat. ... Das Buch
von Aigner und Ziegler ist gelungen ..." Mathematische Semesterberichte 1999
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"... Der Beweis selbst, seine Ästhetik, seine Pointe geht ins Geschichtsbuch
der Königin der Wissenschaften ein. Ihre Anmut offenbart sich in dem
gelungenen und geschickt illustrierten Buch über das BUCH. ...." Die Zeit,
13.August 1998
"......ein Feuerwerk mathematischer Geistesblitze. ..." Die Weltwoche 16/02
3. Aufl., 2010, VIII, 312 S. 250 Abb., 6 in Farbe., Hardcover
ISBN: 978-3-642-02258-6
Aigner, Martin; Ziegler, Günter M.
Proofs from THE BOOK
This revised and enlarged fourth edition features five new chapters, which treat
classical results such as the "Fundamental Theorem of Algebra", problems
about tilings, but also quite recent proofs, for example of the Kneser conjecture
in graph theory. The new edition also presents further improvements and
surprises, among them a new proof for "Hilbert's Third Problem".
From the Reviews:
"... Inside [this book] is indeed a glimpse of mathematical heaven, where clever
insights and beautiful ideas combine in astonishing and glorious ways. There is
vast wealth within its pages, one gem after another. ..., but many [proofs] are
new and brilliant proofs of classical results. ...Aigner and Ziegler... write: "... all
we offer is the examples that we have selected, hoping that our readers will
share our enthusiasm about brilliant ideas, clever insights and wonderful
observations." I do. ... " AMS Notices 1999
"... the level is close to elementary ... the proofs are brilliant. ..." LMS
Newsletter 1999
4th ed., 2010, VIII, 274 p. 250 illus., 6 in color., Hardcover
ISBN: 978-3-642-00855-9
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Luptácik, Mikulás
Mathematical Optimization and Economic Analysis
"Mathematical Optimization and Economic Analysis" is a self-contained
introduction to various optimization techniques used in economic modeling and
analysis such as geometric, linear, and convex programming and data
envelopment analysis. Through a systematic approach, this book
demonstrates the usefulness of these mathematical tools in quantitative and
qualitative economic analysis.
The book presents specific examples to demonstrate each technique’s
advantages and applicability as well as numerous applications of these
techniques to industrial economics, regulatory economics, trade policy,
economic sustainability, production planning, and environmental policy.
Key Features include:
- A detailed presentation of both single-objective and multiobjective
optimization;
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- An in-depth exposition of various applied optimization problems;
- Implementation of optimization tools to improve the accuracy of various
economic models;
- Extensive resources suggested for further reading.
This book is intended for graduate and postgraduate students studying
quantitative economics, as well as economics researchers and applied
mathematicians. Requirements include a basic knowledge of calculus and
linear algebra, and a familiarity with economic modeling.
(Series: Springer Optimization and Its Applications)
2010, XIV, 294 p. 53 illus., Hardcover
ISBN: 978-0-387-89551-2
Prasolov, Victor V.
Polynomials
From the reviews:
"... Despite the appearance [...] in a series titled Algorithms and Computation
of Mathematics, computation occupies only a small part of the monograph. It is
best described as a useful reference for one's personal collection and a text for
a full-year course given to graduate or even senior undergraduate students.
[...] the book under review is worth purchasing for the library and possibly even
for one's own collection. The author's interest in the history and development
of this area is evident, and we have pleasant glimpses of progress over the last
three centuries [...] the reader gains a synopsis of and guide to the literature
..." E.Barbeau, SIAM Review 47:3, 2005.
"This is an exposition of polynomial theory and results, both classical and
modern. [...] the volume is packed with results and proofs that are well
organised thematically [...] What is unusual is to have a text that embraces and
intermingles both analytic and algebraic aspects of the theory…" S.D.Cohen,
Math.Reviews 2005
(Series: Algorithms and Computation in Mathematics)
1st ed. 2004. 2nd printing, 2010, XIII, 301 p. 8 illus., Softcover
ISBN: 978-3-642-03979-9
SPRINGER TITEL IN: MATHEMATIK
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Agarwal, Ravi P.; Ding, Shusen; Nolder, Craig
Inequalities for Differential Forms
Differential forms satisfying the A-harmonic equations have found wide
applications in fields such as general relativity, theory of elasticity,
quasiconformal analysis, differential geometry, and nonlinear differential
equations in domains on manifolds.
This monograph is the first one to systematically present a series of local and
global estimates and inequalities for such differential forms in particular. It
concentrates on the Hardy-Littlewood, Poincaré, Cacciooli, imbedded and
reverse Holder inequalities. Integral estimates for operators, such as homotopy
operator, the Laplace-Beltrami operator, and the gradient operator are also
presented. Additionally, some related topics such as BMO inequalities,
Lipschitz classes, Orlicz spaces and inequalities in Carnot groups are
discussed in the concluding chapter. An abundance of bibliographical
references and historical material supplement the text throughout.
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This book will serve as an invaluable reference for researchers, instructors and
graduate students in analysis and partial differential equations and could be
used as additional material for specific courses in these fields.
2010, XVI, 388 p., Hardcover
ISBN: 978-0-387-36034-8
Cabrelli, Carlos; Torrea, José Luis
Recent Developments in Real and Harmonic Analysis
In Honor of Carlos Segovia
A collection of invited chapters dedicated to Carlos Segovia, this unified and
self-contained volume examines recent developments in real and harmonic
analysis. The work begins with a chronological description of Segovia’s
mathematical life, highlighting his original ideas and their evolution. Also
included are surveys dealing with Carlos’ favorite topics, and PDE works
written by students and colleagues close to Segovia whose careers were in
some way influenced by him.
Specific topics covered include: Vector-valued singular integral equations;
Harmonic analysis related to Hermite expansions; Gas flow in porous media;
Global well-posedness of the KPI Equation; Monge–Ampère type equations
and applications; Spaces of homogeneous type; Hardy and Lipschitz spaces;
One-sided operators.
Contributors: H. Aimar, A. Bonami, O. Blasco, L.A. Caffarelli, S. Chanillo, J.
Feuto, L. Forzani, C.E. Gutíerrez, E. Harboure, A.L. Karakhanyan, C.E. Kenig,
R.A. Macías, J.J. Manfredi, F.J. Martín-Reyes, P. Ortega, R. Scotto, A. de la
Torre, J.L. Torrea.
(Series: Applied and Numerical Harmonic Analysis)
2010, XXII, 195 p. 13 illus., Hardcover
ISBN: 978-0-8176-4531-1
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Komech, Alexander; Komech, Andrew
Principles of Partial Differential Equations
This concise book covers the classical tools of PDE theory used in today's
science and engineering: characteristics, the wave propagation, the Fourier
method, distributions, Sobolev spaces, fundamental solutions, and Green's
functions. The approach is problem-oriented, giving the reader an opportunity
to master solution techniques. The theoretical part is rigorous and with
important details presented with care. Hints are provided to help the reader
restore the arguments to their full rigor. Many examples from physics are
intended to keep the book intuitive and to illustrate the applied nature of the
subject. The book is useful for a higher-level undergraduate course and for
self-study.
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*sFr 62,00
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*€(A) 43,95
*sFr 64,90
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*€(A) 120,95
*sFr 182,50
(Series: Problem Books in Mathematics)
2010, X, 161 p. 85 illus., Hardcover
ISBN: 978-1-4419-1095-0
Goerss, Paul G.; Jardine, John F.
Simplicial Homotopy Theory
Since the beginning of the modern era of algebraic topology, simplicial
methods have been used systematically and effectively for both computation
and basic theory. With the development of Quillen's concept of a closed model
category and, in particular, a simplicial model category, this collection of
methods has become the primary way to describe non-abelian homological
algebra and to address homotopy-theoretical issues in a variety of fields,
including algebraic K-theory. This book supplies a modern exposition of these
ideas, emphasizing model category theoretical techniques.
Discussed here are the homotopy theory of simplicial sets, and other basic
topics such as simplicial groups, Postnikov towers, and bisimplicial sets. The
more advanced material includes homotopy limits and colimits, localization
with respect to a map and with respect to a homology theory, cosimplicial
spaces, and homotopy coherence. Interspersed throughout are many results
and ideas well-known to experts, but uncollected in the literature.
Intended for second-year graduate students and beyond, this book introduces
many of the basic tools of modern homotopy theory. An extensive background
in topology is not assumed.
(Series: Modern Birkhäuser Classics)
2010, XVI, 510 p., Softcover
ISBN: 978-3-0346-0188-7
Baas, Nils; Friedlander, Eric M.; Jahren, Björn; Østvær, Paul Arne
Algebraic Topology
The Abel Symposium 2007
The 2007 Abel Symposium took place at the University of Oslo in August
2007. The goal of the symposium was to bring together mathematicians
whose research efforts have led to recent advances in algebraic geometry,
algebraic K-theory, algebraic topology, and mathematical physics. A common
theme of this symposium was the development of new perspectives and new
constructions with a categorical flavor. As the lectures at the symposium and
the papers of this volume demonstrate, these perspectives and constructions
have enabled a broadening of vistas, a synergy between once-differentiated
subjects, and solutions to mathematical problems both old and new.
(Series: Abel Symposia)
2009, XIV, 409 p., Hardcover
ISBN: 978-3-642-01199-3
SPRINGER TITEL IN: MATHEMATIK
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Guo, Xianping; Hernández-Lerma, Onésimo
Continuous-Time Markov Decision Processes
Theory and Applications
Continuous-time Markov decision processes (MDPs), also known as controlled
Markov chains, are used for modeling decision-making problems that arise in
operations research (for instance, inventory, manufacturing, and queueing
systems), computer science, communications engineering, control of
populations (such as fisheries and epidemics), and management science,
among many other fields. This volume provides a unified, systematic, selfcontained presentation of recent developments on the theory and applications
of continuous-time MDPs. The MDPs in this volume include most of the cases
that arise in applications, because they allow unbounded transition and
reward/cost rates. Much of the material appears for the first time in book form.
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*sFr 171,00
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(Series: Stochastic Modelling and Applied Probability)
2009, XVII, 231 p., Hardcover
ISBN: 978-3-642-02546-4
Bove, Antonio; Del Santo, Daniele; Murthy, M.K. Venkatesha
Advances in Phase Space Analysis of Partial Differential Equations
In Honor of Ferruccio Colombini's 60th Birthday
This collection of original articles and surveys addresses the recent advances
in linear and nonlinear aspects of the theory of partial differential equations.
The key topics include operators as "sums of squares" of real and complex
vector fields, nonlinear evolution equations, local solvability, and hyperbolic
questions. Contributors: Ambrosio, Berhanu, J.-M. Bony, Chemin, Dencker,
Gallagher, Gerard, Hounie, Jannelli, Kajitani, Lerner, Nishitani, Petkov, Rauch,
Reissig, Spagnolo, Tataru, Treves, Uhlmann, and Zuazua.
(Series: Progress in Nonlinear Differential Equations and Their Applications)
2009, XIV, 302 p. 1 illus., Hardcover
ISBN: 978-0-8176-4860-2
Hurlbert, Glenn H.
Linear Optimization
The Simplex Workbook
This undergraduate textbook is written for a junior/senior level course on linear
optimization. Unlike other texts, the treatment follows the "modified Moore
method" approach in which examples and proof opportunities are worked into
the text in order to encourage students to develop some of the content through
their own experiments and arguments while they are reading the text.
Additionally, the focus is on the mathematics underlying the ideas of optimizing
linear functions under linear constraints and the algorithms used to solve them.
In particular, the author uses the Simplex Algorithm to motivate these
concepts. The text progresses at a gentle and inviting pace. The presentation
is driven by examples and illustrations. Ample exercises are provided at the
end of each chapter for mastering the material.
The instructor's version of the text contains solutions embedded within the text,
rather than in an appendix. It also has extra material and suggestions for the
teacher’s benefit. Junior/senior level undergraduate students will benefit from
the book. Future secondary school mathematics teachers will also find this
book useful.
(Series: Undergraduate Texts in Mathematics)
2010, XVII, 272 p. 40 illus., Hardcover
ISBN: 978-0-387-79147-0
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Klin, Mikhail; Jones, Gareth A.; Jurisic, Aleksandar; Muzychuk, Mikhail;
Ponomarenko, Ilia
Algorithmic Algebraic Combinatorics and Gröbner Bases
This collection of tutorial and research papers introduces readers to diverse
areas of modern pure and applied algebraic combinatorics and finite
geometries with a special emphasis on algorithmic aspects and the use of the
theory of Gröbner bases.
Topics covered include coherent configurations, association schemes,
permutation groups, Latin squares, the Jacobian conjecture, mathematical
chemistry, extremal combinatorics, coding theory, designs, etc. Special
attention is paid to the description of innovative practical algorithms and their
implementation in software packages such as GAP and MAGMA.
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Readers will benefit from the exceptional combination of instructive training
goals with the presentation of significant new scientific results of an
interdisciplinary nature.
2009, XII, 311 p., Hardcover
ISBN: 978-3-642-01959-3
Inselberg, Alfred
Parallel Coordinates
Visual Multidimensional Geometry and Its Applications
This book is about visualization, systematically incorporating the fantastic
human pattern recognition into the problem-solving process, and focusing on
parallel coordinates. The barrier, imposed by our three-dimensional habitation
and perceptual experience, has been breached by this innovative and versatile
methodology. The accurate visualization of multidimensional problems and
multivariate data unlocks insights into the role of dimensionality.
Key features of Parallel Coordinates: (1) An easy-to-read self-contained
chapter on data mining and information visualization is included. (2) Numerous
exercises with solutions, from basic to advanced topics, course projects and
research directions. (3) “Fast Track” markers throughout provide a quick grasp
of essential material. (4) Interactive Learning Module (ILM) CD designed for
classroom demonstration and fun experimentation for mastering key topics and
examples cross-referenced in the text. (5) Extensive bibliography, index, and a
chapter containing a collection of recent results (i.e. visualizing large networks,
complex-valued functions and more).
Parallel Coordinates requires only an elementary knowledge of linear algebra.
It is well-suited for self-study and as a textbook (or companion) for courses on
information visualization, data mining, mathematics, statistics, computer
science, engineering, finance, management, manufacturing, in scientific
disciplines and even the arts.
2009, XXVI, 554 p. 401 illus., 231 in color. With CD-ROM., Hardcover
ISBN: 978-0-387-21507-5
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