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This book gives an introduction to the basic theory of stochastic calculus and its applications. Examples are given throughout the text, in order to motivate and illustrate the theory and show its importance for many applications in e.g. economics, biology and physics. The basic idea of the presentation is to start from some basic results (without proofs) of the easier cases and develop the theory from there, and to concentrate on the proofs of the easier case (which nevertheless are often sufficiently general for many purposes) in order to be able to reach quickly the parts of the theory which is most important for the applications. For the 6th edition the author has added further exercises and, for the first time, solutions to many of the exercises are provided.

This revised and enlarged sixth edition of Proofs from THE BOOK features an entirely new chapter on Van der Waerden’s permanent conjecture, as well as additional, highly original and delightful proofs in other chapters.From the citation on the occasion of the 2018 "Steele Prize for Mathematical Exposition"“… It is almost impossible to write a mathematics book that can be read and enjoyed by people of all levels and backgrounds, yet Aigner and Ziegler accomplish this feat of exposition with virtuoso style. […] This book does an invaluable service to mathematics, by illustrating for non-mathematicians what it is that mathematicians mean when they speak about beauty.”From the Reviews"... Inside PFTB (Proofs from The 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. ... 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. ... "Notices of the AMS, August 1999"... This book is a pleasure to hold and to look at: ample margins, nice photos, instructive pictures and beautiful drawings ... It is a pleasure to read as well: the style is clear and entertaining, the level is close to elementary, the necessary background is given separately and the proofs are brilliant. ..."LMS Newsletter, January 1999"Martin Aigner and Günter Ziegler succeeded admirably in putting together a broad collection of theorems and their proofs that would undoubtedly be in the Book of Erdös. The theorems are so fundamental, their proofs so elegant and the remaining open questions so intriguing that every mathematician, regardless of speciality, can benefit from reading this book. ..." SIGACT News, December 2011

Seafloor surveying with acoustic remote sensing has become a powerful tool for researchers and professionals seeking knowledge about the structure and behavior of the seafloor. In particular, sidescan sonar is proving to be the preeminent technique, but its data is often difficult to interpret due to the physics of acoustic remote sensing, and to the varied geological processes at play. This handbook not only presents all the fundamentals but also explains how to interpret sidescan sonar imagery and bathymetry. It fully explores the most recent advances, both in the technology and in the knowledge of marine structures, and provides deep insights for interpretation and decision-making. Broadly expanded and updated from the previous 1997 “Handbook of Seafloor Sonar Imagery”, this handbook is indispensable to oceanographers, resource exploiters, telecommunications engineers, and marine researchers of all kinds.

Percolation theory is the study of an idealized random medium in two or more dimensions. The mathematical theory is mature, and continues to give rise to problems of special beauty and difficulty. Percolation is pivotal for studying more complex physical systems exhibiting phase transitions. The emphasis of this book is upon core mathematical material and the presentation of the shortest and most accessible proofs. The book is intended for graduate students and researchers in probability and mathematical physics. Almost no specialist knowledge is assumed. Much new material appears in this second edition, including: dynamic and static renormalization, strict inequalities between critical points, a sketch of the lace expansion, and several essays on related fields and applications.

15 years after the ?rst printing of Algebraic Function Fields and Codes,the mathematics editors of Springer Verlag encouraged me to revise and extend the book. Besides numerous minor corrections and amendments, the second edition di?ers from the ?rst one in two respects. Firstly I have included a series of exercises at the end of each chapter. Some of these exercises are fairly easy and should help the reader to understand the basic concepts, others are more advanced and cover additional material. Secondly a new chapter titled “Asymptotic Bounds for the Number of Rational Places” has been added. This chapter contains a detailed presentation of the asymptotic theory of function ?elds over ?nite ?elds, including the explicit construction of some asymptotically good and optimal towers. Based on these towers, a complete and self-contained proof of the Tsfasman-Vladut-Zink Theorem is given. This theorem is perhaps the most beautiful application of function ?elds to coding theory. The codes which are constructed from algebraic function ?elds were ?rst introduced by V. D. Goppa. Accordingly I referred to them in the ?rst edition as geometric Goppa codes. Since this terminology has not generally been - cepted in the literature, I now use the more common term algebraic geometry codes or AG codes. I would like to thank Alp Bassa, Arnaldo Garcia, Cem Guneri, ¨ Sevan Harput and Alev Topuzo? glu for their help in preparing the second edition.

For a brief period during the latter part of World War II, Nevill F. Mott led a theoretical group at Fort Halstead in the United Kingdom that tackled scientific issues related to pressing war-time concerns. Among later awards and honors, Mott was knighted and a recipient of the Nobel Prize. While at Fort Halstead, he undertook an effort to theoretically describe the statistical fragmentation of munitions subjected to intense explosive loading. Mott`s original internal reports contain seminal theoretical concepts on the physics and statistics of dynamic fracture and fragmentation, which have provided the inspiration for numerous later modeling efforts and engineering formulae. Some of his most forward-looking thoughts on the micromechanical and molecular aspects of fracture are included in these publications. The present book surveys the theoretical analysis put forth by Mott with particular focus on his efforts to characterize the size and distribution of fragments resulting from a dynamic fragmentation event. Copies of the original internal reports of Mott and his co-workers are included. The book also pursues additional theoretical analysis with the intent of delving further into the physical ideas and unfinished analysis implicit in Mott`s original studies. This book will be of interest to all scientists and engineers concerned with the dynamic fracture and fragmentation of solid bodies subject to intense transient loads imparted by explosive detonation and high-velocity impact from both the historical and modern perspective.

This book covers the dominant theoretical approaches to the approximate solution of hard combinatorial optimization and enumeration problems. It contains elegant combinatorial theory, useful and interesting algorithms, and deep results about the intrinsic complexity of combinatorial problems. Its clarity of exposition and excellent selection of exercises will make it accessible and appealing to all those with a taste for mathematics and algorithms.Richard Karp,University Professor, University of California at BerkeleyFollowing the development of basic combinatorial optimization techniques in the 1960s and 1970s, a main open question was to develop a theory of approximation algorithms. In the 1990s, parallel developments in techniques for designing approximation algorithms as well as methods for proving hardness of approximation results have led to a beautiful theory. The need to solve truly large instances of computationally hard problems, such as those arising from the Internet or the human genome project, has also increased interest in this theory. The field is currently very active, with the toolbox of approximation algorithm design techniques getting always richer.It is a pleasure to recommend Vijay Vazirani's well-written and comprehensive book on this important and timely topic.I am sure the reader will find it most useful both as an introduction to approximability as well as a reference to the many aspects of approximation algorithms.Laszlo Lovasz, Senior Researcher, Microsoft Research

There is growing recognition of the need to address the fragility of digital information, on which our society heavily depends for smooth operation in all aspects of daily life. This has been discussed in many books and articles on digital preservation, so why is there a need for yet one more? Because, for the most part, those other publications focus on documents, images and webpages – objects that are normally rendered to be simply displayed by software to a human viewer. Yet there are clearly many more types of digital objects that may need to be preserved, such as databases, scientific data and software itself.David Giaretta, Director of the Alliance for Permanent Access,  and his contributors explain why the tools and techniques used for preserving rendered objects are inadequate for all these other types of digital objects, and they provide the concepts, techniques and tools that are needed. The book is structured in three parts. The first part is on theory, i.e., the concepts and techniques that are essential for preserving digitally encoded information. The second part then shows practice, i.e., the use and validation of these tools and techniques. Finally, the third part concludes by addressing how to judge whether money is being well spent, in terms of effectiveness and cost sharing.Various examples of digital objects from many sources are used to explain the tools and techniques presented. The presentation style mainly aims at practitioners in libraries, archives and industry who are either directly responsible for preservation or who need to prepare for audits of their archives. Researchers in digital preservation and developers of preservation tools and techniques will also find valuable practical information here. Researchers creating digitally encoded information of all kinds will also need to be aware of these topics so that they can help to ensure that their data is usable and can be valued by others now and in thefuture.To further assist the reader, the book is supported by many hours of videos and presentations from the CASPAR project and by a set of open source software.

This concise survey describes the requirements on materials operating in high-temperature environments and the processes that increase the temperature capability of metals, ceramics, and composites. The major part deals with the applicable materials and their specific properties, with one entire chapter devoted to coatings. Written for engineering and science students, researchers, and managers in industry.

Topics include Bayesian updating, conjugate and reference priors, Bayesian point and interval estimates, Bayesian asymptotics and empirical Bayes methods.

Der Lehrbuch-Klassiker zur Einführung in die Sozialpsychologie stellt das beliebte Grundlagenfach der Psychologie lebendig, bunt und anschaulich vor: Jemanden lieben, miteinander streiten, zusammen arbeiten, gemeinsam lernen – das Leben steckt voller Sozialpsychologie, denn das vielseitige Fachgebiet beschäftigt sich damit, wie Gedanken, Gefühle und Verhalten von Menschen durch die Anwesenheit anderer Menschen beeinflusst werden.

This standard textbook on modern graph theory combines the authority of a classic with the engaging freshness of style that is the hallmark of active mathematics. It covers the core material of the subject, with concise yet complete proofs, while offering glimpses of more advanced methods in each field via one or two deeper results.This is a major new edition. Among many other improvements, it offers additional tools for applying the regularity lemma, brings the tangle theory of graph minors up to the cutting edge of current research, and addresses new topics such as chi-boundedness in perfect graph theory.The book can be used as a reliable text for an introductory graduate course and is also suitable for self-study.From the reviews:“Deep, clear, wonderful. This is a serious book about the heart of graph theory. It has depth and integrity.” Persi Diaconis & Ron Graham, SIAM Review“The book has received a very enthusiastic reception, which it amply deserves. A masterly elucidation of modern graph theory.” Bulletin of the Institute of Combinatorics and its Applications“Succeeds dramatically ... a hell of a good book.” MAA Reviews“ ... like listening to someone explain mathematics.” Bulletin of the AMS

The main theme is the integration of the theory of linear PDE and the theory of finite difference and finite element methods. For each type of PDE, elliptic, parabolic, and hyperbolic, the text contains one chapter on the mathematical theory of the differential equation, followed by one chapter on finite difference methods and one on finite element methods. The chapters on elliptic equations are preceded by a chapter on the two-point boundary value problem for ordinary differential equations. Similarly, the chapters on time-dependent problems are preceded by a chapter on the initial-value problem for ordinary differential equations. There is also one chapter on the elliptic eigenvalue problem and eigenfunction expansion. The presentation does not presume a deep knowledge of mathematical and functional analysis. The required background on linear functional analysis and Sobolev spaces is reviewed in an appendix. The book is suitable for advanced undergraduate and beginning graduate students of applied mathematics and engineering.

Understanding and employing cryptography has become central for securing virtually any digital application, whether user app, cloud service, or even medical implant.Heavily revised and updated, the long-awaited second edition of Understanding Cryptography follows the unique approach of making modern cryptography accessible to a broad audience, requiring only a minimum of prior knowledge. After introducing basic cryptography concepts, this seminal textbook covers nearly all symmetric, asymmetric, and post-quantum cryptographic algorithms currently in use in applications—ranging from cloud computing and smart phones all the way to industrial systems, block chains, and cryptocurrencies.Topics and features:Opens with a foreword by cryptography pioneer and Turing Award winner, Ron RivestHelps develop a comprehensive understanding of modern applied cryptographyProvides a thorough introduction to post-quantum cryptography consisting of the three standardized cipher familiesIncludes for every chapter a comprehensive problem set, extensive examples, and a further-reading discussionCommunicates, using a unique pedagogical approach, the essentials about foundations and use in practice, while keeping mathematics to a minimumSupplies up-to-date security parameters for all cryptographic algorithmsIncorporates chapter reviews and discussion on such topics as historical and societal contextThis must-have book is indispensable as a textbook for graduate and advanced undergraduate courses, as well as for self-study by designers and engineers.The authors have more than 20 years’ experience teaching cryptography at various universities in the US and Europe. In addition to being renowned scientists, they have extensive experience with applying cryptography in industry, fromwhich they have drawn important lessons for their teaching.

The main theme is the integration of the theory of linear PDE and the theory of finite difference and finite element methods. For each type of PDE, elliptic, parabolic, and hyperbolic, the text contains one chapter on the mathematical theory of the differential equation, followed by one chapter on finite difference methods and one on finite element methods. The chapters on elliptic equations are preceded by a chapter on the two-point boundary value problem for ordinary differential equations. Similarly, the chapters on time-dependent problems are preceded by a chapter on the initial-value problem for ordinary differential equations. There is also one chapter on the elliptic eigenvalue problem and eigenfunction expansion. The presentation does not presume a deep knowledge of mathematical and functional analysis. The required background on linear functional analysis and Sobolev spaces is reviewed in an appendix. The book is suitable for advanced undergraduate and beginning graduate students of applied mathematics and engineering.

The book serves as a first introduction to computer programming of scientific applications, using the high-level Python language. The exposition is example and problem-oriented, where the applications are taken from mathematics, numerical calculus, statistics, physics, biology and finance. The book teaches "Matlab-style" and procedural programming as well as object-oriented programming. High school mathematics is a required background and it is advantageous to study classical and numerical one-variable calculus in parallel with reading this book. Besides learning how to program computers, the reader will also learn how to solve mathematical problems, arising in various branches of science and engineering, with the aid of numerical methods and programming. By blending programming, mathematics and scientific applications, the book lays a solid foundation for practicing computational science.From the reviews: Langtangen … does an excellent job of introducing programming as a set of skills in problem solving. He guides the reader into thinking properly about producing program logic and data structures for modeling real-world problems using objects and functions and embracing the object-oriented paradigm. … Summing Up: Highly recommended. F. H. Wild III, Choice, Vol. 47 (8), April 2010Those of us who have learned scientific programming in Python ‘on the streets’ could be a little jealous of students who have the opportunity to take a course out of Langtangen’s Primer.” John D. Cook, The Mathematical Association of America, September 2011This book goes through Python in particular, and programming in general, via tasks that scientists will likely perform. It contains valuable information for students new to scientific computing and would be the perfect bridge between an introduction to programming and an advanced course on numerical methods or computational science.Alex Small,IEEE, CiSE Vol. 14 (2), March /April 2012  “This fourth edition is a wonderful, inclusive textbook that covers pretty much everything one needs to know to go from zero to fairly sophisticated scientific programming in Python…” Joan Horvath, Computing Reviews, March 2015

Shafarevich's Basic Algebraic Geometry has been a classic and universally used introduction to the subject since its first appearance over 40 years ago. As the translator writes in a prefatory note, ``For all [advanced undergraduate and beginning graduate] students, and for the many specialists in other branches of math who need a liberal education in algebraic geometry, Shafarevich’s book is a must.''The second volume is in two parts: Book II is a gentle cultural introduction to scheme theory, with the first aim of putting abstract algebraic varieties on a firm foundation; a second aim is to introduce Hilbert schemes and moduli spaces, that serve as parameter spaces for other geometric constructions. Book III discusses complex manifolds and their relation with algebraic varieties, Kähler geometry and Hodge theory. The final section raises an important problem in uniformising higher dimensional varieties that has been widely studied as the ``Shafarevich conjecture''.The style of  Basic Algebraic Geometry 2 and its minimal prerequisites make it to a large extent independent of  Basic Algebraic Geometry 1, and accessible to beginning graduate students in mathematics and in theoretical physics.

Introducing the finite element method as a general computational method for solving partial differential equations approximately, this book goes on to cover important applications including diffusion and transport phenomena, solid and fluid mechanics and more.

special pulses of light which have the wonderful property of being able to heal after perturbation. The book will take you from the physical basics of ray and beam optics, explain fiber structure and the functions of optical elements, and bring you to the forefront of both applications and research.

Martin Zenck porträtiert den 2024 verstorbenen Wolfgang Rihm als einen kosmopolitischen Komponisten, der auf der Welthaftigkeit der Musik und auf der Freiheit des Komponierens kompromisslos besteht. Der Autor legt eine breite Darstellung des Rihm’schen Œuvres vor: der Lieder, der Instrumentalmusik, des sakralen Werks sowie des zentralen „Nietzsche-Komplexes“ und vor allem des Musiktheaters: von der Artaud-Trilogie und der „Hamletmaschine“ nach Heiner Müller bis hin zu den Opern, die Rihm auf der Textbasis von Goethe („Proserpina“) und Hölderlin („Oedipus“) verfasst hat.Gegenüber der Deutungshoheit und kraftvoll-energetischen Sprache Rihms findet dieses Buch seinen eigenen methodischen Ansatz, indem es zwar der Selbstinterpretation des Komponisten Raum gibt, auf der anderen Seite aber das Rihm’sche Werk in einen neuen Verstehenshorizont stellt. Dazu dienen theater- und literaturwissenschaftliche Perspektiven, philosophische und produktionsästhetische Zugänge sowie die musikalische Analyse und die Untersuchung von Aufführungen und Aufnahmen.Im Zentrum des Buches steht so der Dialog zwischen dem Komponisten und seinem Interpreten Martin Zenck: die Suche nach Bedeutungsdimensionen innerhalb der Rezeption, nach einem „Sinnüberschuss“ gemäß der Rihm’schen Maxime, dass „das Werk immer mehr weiß als der Autor“.

Significant, and usually unwelcome, surprises, such as floods, financial crisis, epileptic seizures, or material rupture, are the topics of Extreme Events in Nature and Society. The book, authored by foremost experts in these fields, reveals unifying and distinguishing features of extreme events, including problems of understanding and modelling their origin, spatial and temporal extension, and potential impact. The chapters converge towards the difficult problem of anticipation: forecasting the event and proposing measures to moderate or prevent it. Extreme Events in Nature and Society will interest not only specialists, but also the general reader eager to learn how the multifaceted field of extreme events can be viewed as a coherent whole.

Pro Git (Second Edition) is your fully-updated guide to Git and its usage in the modern world.

Lankhorst and his co-authors present ArchiMate® 3.0, enterprise modelling language that captures the complexity of architectural domains and their relations and allows the construction of integrated enterprise architecture models.

He met his wife Dagmar Hilfert-Rüppell on a research trip to the dragonflies of Japan.Dagmar Hilfert-Rüppell has been studying and filming dragonflies for 30 years.

Dieses Lehrbuch erklärt alle wichtigen Themen des psychologischen Grundlagenfachs „Persönlichkeitspsychologie“ kompakt und verständlich. Zahlreiche Fallbeispiele und Praxishinweise stellen dabei den Bezug zum Alltag her, Lernziele, Kontrollfragen und weiterführende Literatur helfen bei der gezielten Prüfungsvorbereitung. Doch das Buch bietet noch viel mehr: Die begleitende Website lehrbuch-psychologie.springer.com enthält kostenlose Lerntools für Studierende sowie Lehrmaterialien für Dozierende zum Download.

Now the OPC Foundation has released a new generation of OPC specifications called OPC Unified Architecture (OPC UA).

Die deutschsprachige Gegenwartslyrik zeichnet sich durch eine intensive Rezeption und Aktualisierung des Barocks aus, deren historische Verbindungslinien die Beiträge in ihren Kontinuitäten und Diskontinuitäten, Diachronien und Anachronien nachzeichnen. Die Aufsätze zur Lyrik von u.a. Jan Wagner, Christian Lehnert, Marion Poschmann, Michael Lentz, Durs Grünbein, Monika Rinck, Kerstin Preiwuß, Martina Hefter, Pia Birkel, Ulf Stolterfoht, Nico Bleutge, Nora Gomringer und Christiane Frohmann gehen den Referenzen zum Barock dabei auf drei Ebenen nach: Im Fokus stehen Gattungspoetik und Gattungsvariation, kultur- und wissensgeschichtliche Bezüge sowie Medien- und Materialästhetik. Vor diesem Hintergrund versteht sich der Band auch als ein Beitrag zur Barockforschung der späten Moderne/Gegenwart.