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Stochastik ohne Zufall und Wahrscheinlichkeit: Die Mathematik der relativen Anteile (essentials)
by Rüdiger StegenIn diesem Buch wird Grundlegendes der Stochastik wie Kolmogoroffsche Axiome, Erwartungswerte, bedingte Wahrscheinlichkeiten, stochastische Unabhängigkeit, Satz von Bayes oder Satz von der totalen Wahrscheinlichkeit nicht mit „Zufall“ und „Wahrscheinlichkeit“, sondern mit „relativer Anteil“ formuliert. Drei Interpretationen relativer Anteile werden näher betrachtet: Freude, Macht und Wahrscheinlichkeit. Anhand vieler Beispiele wird gezeigt, dass die angewandte Stochastik nicht nur allgemeiner und umfassender, sondern auch einfacher und anschaulicher wird, wenn man sie auf relativen Anteilen statt auf Zufall und Wahrscheinlichkeit aufbaut.
Stochastische Modelle der aktuariellen Risikotheorie: Eine mathematische Einführung (Masterclass)
by Riccardo GattoDieses Buch führt mathematisch präzise in die stochastischen Modelle ein, die bei der Bewertung von Schadensbeträgen für Versicherungen von besonderer Bedeutung sind. Abgedeckt werden Modelle für kleine und große Schadensbeträge, Modelle für extreme Ereignisse, Risikomaße, sowie die stochastischen Prozesse der aktuariellen Risikotheorie: Zählprozesse, zusammengesetzte Prozesse, Erneuerungsprozesse und Poisson-Prozesse. Zentrales Thema ist die Bestimmung der Ruinwahrscheinlichkeit des Versicherers. In diesem Zusammenhang werden analytische Lösungen, asymptotische Approximationen sowie numerische Algorithmen wie die Monte-Carlo-Simulation vorgestellt. Gute Grundkenntnisse in der Wahrscheinlichkeitstheorie werden vorausgesetzt, doch ein Anhang mit den wichtigsten Resultaten erleichtert die Lektüre dieses Buches. Das Buch ist geeignet für fortgeschrittene Bachelor- oder Masterstudierende der Mathematik oder Statistik mit entsprechender Vertiefungsrichtung. Darüber hinaus richtet es sich an Kandidaten, die das Diplom der Schweizerischen Aktuarvereinigung (SAV) erwerben oder sich auf das Diplom der Society of Actuaries (SOA) vorbereiten möchten. Auch praktizierende Versicherungsmathematiker, die ihre technischen Kenntnisse vertiefen wollen, werden angesprochen. Die vorliegende zweite Auflage enthält theoretische Ergänzungen, insbesondere Resultate über die Fluktuationen der Summe und der zusammengesetzten Summe, d.h. des Gesamtschadensbetrages einer Periode. Darüber hinaus erleichtern nun neue Aufgaben verschiedener Schwierigkeitsgrade und mit ausführlichen Lösungen das Selbststudium.
Stochastische Paradoxien (essentials)
by Heinz Klaus StrickIn diesem essential beschreibt Heinz Klaus Strick anhand von zahlreichen Beispielen aus verschiedenen Teilgebieten der Wahrscheinlichkeitsrechnung und Statistik, warum es bei stochastischen Fragestellungen immer wieder dazu kommt, dass Aussagen über Wahrscheinlichkeiten paradox erscheinen, also scheinbar im Widerspruch zu den eigenen Vorstellungen über Zufallsvorgänge stehen. Dabei stellt sich heraus, dass es sich in solchen Fällen oft nur um die Verwechslung von Wahrscheinlichkeiten oder um falsche Modellierungen von zufallsbedingten Vorgängen handelt. Nach der Lektüre des essentials werden der Leserin/dem Leser mit Sicherheit manche Phänomene nicht mehr „paradox“ vorkommen.
Stochastische partielle Differentialgleichungen (essentials)
by Stefan TappeDieses essential bietet eine prägnante und gute verständliche Einführung in die Theorie der stochastischen partiellen Differentialgleichungen. Wir werden die dafür benötigten mathematischen Hilfsmittel wie das Bochner-Integral, das Itô-Integral und die Itô-Formel kennenlernen. Anschließend werden wir die relevanten Lösungskonzepte besprechen, Existenz- und Eindeutigkeitsresultate präsentieren und diese anhand von Anwendungsbeispielen erläutern.
Stochastische Prozesse und Finanzmathematik (Masterclass)
by Ludger RüschendorfDas Buch gibt eine Einführung in weiterführende Themengebiete der stochastischen Prozesse und der zugehörigen stochastischen Analysis und verbindet diese mit einer fundierten Darstellung von Grundlagen der Finanzmathematik. Es ist inhaltlich weitreichend und legt gleichzeitig viel Wert auf gute Lesbarkeit, Motivation und Erklärung der behandelten Sachverhalte. Finanzmathematische Fragestellungen werden zunächst im Rahmen diskreter Modelle eingeführt und dann auf zeitstetige Modelle übertragen. Die grundlegende Konstruktion des stochastischen Integrals und die zugehörige Martingaltheorie liefern fundamentale Methoden der Theorie stochastischer Prozesse zur Konstruktion von geeigneten stochastischen Modellen der Finanzmathematik, z.B. mit Hilfe von stochastischen Differentialgleichungen. Zentrale Resultate der stochastischen Analysis wie Itô -Formel, Satz von Girsanov und Martingaldarstellungssätze erhalten in der Finanzmathematik grundlegende Bedeutung, z.B. für die risiko-neutrale Bewertungsformel (Black-Scholes Formel) oder die Frage nach der Hedgebarkeit von Optionen und der Vollständigkeit von Marktmodellen. Kapitel zur Bewertung von Optionen in vollständigen und nichtvollständigen Märkten und zur Bestimmung optimaler Hedgingstrategien schließen die Thematik ab.Vorausgesetzt werden fortgeschrittene Kenntnisse der Wahrscheinlichkeitstheorie, insbesondere zu zeitdiskreten Prozessen (Martingale, Markov-Ketten) sowie zeitstetigen Prozessen (Brownsche Bewegung, Lévy-Prozesse, Prozesse mit unabhängigen Zuwächsen, Markovprozesse). Das Buch ist somit für fortgeschrittene Studierende als begleitende Lektüre sowie für Dozenten als Grundlage für eigene Lehrveranstaltungen geeignet.
Stochastische Szenariosimulation in der Unternehmenspraxis: Risikomodellierung, Fallstudien, Umsetzung in R
by Frank Romeike Manfred StallingerDas Buch zeigt, wie Unternehmen durch die Anwendung der stochastischen Szenariosimulation ein wirksames und effizientes Risikomanagement umsetzen können. Die einfache Darstellung der Grundbegriffe und Methoden der Stochastik, ergänzt um Beispiele und Fallstudien aus der Praxis, geben dem Leser ein praxiserprobtes Toolkit an Instrumenten für die praktische Umsetzung mit auf den Weg.Die Autoren führen zunächst in die faszinierende Welt des Zufalls ein und erklären die Grundbegriffe der deskriptiven und auch für das Risikomanagement wichtigen Inferenzstatistik. Anschließend geben sie einen Einblick in erforderliche Wahrscheinlichkeitsverteilungen mit deren Risikomaße und Anwendung in der Praxis und beschreiben Verfahren der Risikoaggregation und der Effizienzbewertung von Risiko-Abmilderungsmaßnahmen. Diese Einführung wird begleitet durch konkrete Fallbeispiele, die in der Programmumgebung „R“ umgesetzt wurden.Ergänzend zur Einführung in die spannende Welt der Stochastik werden in einem separaten Kapitel typische Fallstudien aus der Praxis präsentiert. Die Beispiele werden als Sourcecode in der Programmiersprache „R“ für eine praktische Anwendung sowohl im Buch als auch in elektronischer Form von den Autoren zum Download bereitgestellt.
The Stock-Flow Consistent Approach
by Marc Lavoie Gennaro ZezzaSelected essays from the eminent economist, Wynne Godley, tracing the development of his work and illuminating the key theories and models that made his name. Essays focus not only on the stock-flow coherent approach, but also lay out Godley's views about the European Union and the stability of its monetary policy.
Stokes–Darcy Equations: Analytic And Numerical Analysis (Advances in Mathematical Fluid Mechanics)
by Ulrich WilbrandtThis book offers a thorough guide starting from fundamental functional analysis leading to the coupling of Stokes and Darcy equations, including numerical analysis and scientific computing. Almost all intermediate results are given with complete, rigorous proofs, including theorems which can be rarely found in the literature such that this book serves well as a reference on the topic. Special care is taken to analyze the difficult cases of non-smooth interfaces which are not completely enclosed in one subdomain, i.e, intersect with the outer boundary. This can hardly be found in the literature. Additionally, known and new subdomain iterative methods are introduced, analyzed and applied to standard examples as well as one example motivated by a geoscientific setting.
Stories of Innovation for the Millennial Generation: The Lynceus Long View
by Piero FormicaThe Lycneus's Longview uses the reality of fictional stories to help inspire the Millennial Generation.
The Story of Algebraic Numbers in the First Half of the 20th Century: From Hilbert to Tate (Springer Monographs in Mathematics)
by Władysław NarkiewiczThe book is aimed at people working in number theory or at least interested in this part of mathematics. It presents the development of the theory of algebraic numbers up to the year 1950 and contains a rather complete bibliography of that period. The reader will get information about results obtained before 1950. It is hoped that this may be helpful in preventing rediscoveries of old results, and might also inspire the reader to look at the work done earlier, which may hide some ideas which could be applied in contemporary research.
The Story of More: How We Got to Climate Change and Where to Go from Here
by Hope JahrenFrom the bestselling author of Lab Girl comes a slim, urgent missive on the defining issue of our time: here is Hope Jahren on climate change, our timeless pursuit of more, and how the same human ambition that got us here can also be our salvation.Hope Jahren is an award-winning geobiologist, a brilliant writer, and one of the seven billion people with whom we share this earth. The Story of More is her impassioned open letter to humanity as we stand at the crossroads of survival and extinction. Jahren celebrates the long history of our enterprising spirit--which has tamed wild crops, cured diseases, and sent us to the moon--but also shows how that spirit has created excesses that are quickly warming our planet to dangerous levels. In short, highly readable chapters, she takes us through the science behind the key inventions--from electric power to large-scale farming and automobiles--that, even as they help us, release untenable amounts of carbon dioxide into the atmosphere. She explains the current and projected consequences of greenhouse gases--from superstorms to rising sea levels--and shares the science-based tools that could help us fight back. At once an explainer on the mechanisms of warming and a capsule history of human development, The Story of More illuminates the link between our consumption habits and our endangered earth. It is the essential pocket primer on climate change that will leave an indelible impact on everyone who reads it.
The Story of More: How We Got to Climate Change and Where to Go from Here
by Hope Jahren&“Hope Jahren is the voice that science has been waiting for.&” —Nature &“A superb account of the deadly struggle between humanity and what may prove the only life-bearing planet within ten light years, written in a brilliantly sardonic and conversational style.&” —E. O. Wilson&“Hope Jahren asks the central question of our time: how can we learn to live on a finite planet? The Story of More is thoughtful, informative, and—above all—essential.&” —Elizabeth Kolbert, author of The Sixth ExtinctionHope Jahren is an award-winning scientist, a brilliant writer, a passionate teacher, and one of the seven billion people with whom we share this earth. In The Story of More, she illuminates the link between human habits and our imperiled planet. In concise, highly readable chapters, she takes us through the science behind the key inventions—from electric power to large-scale farming to automobiles—that, even as they help us, release greenhouse gases into the atmosphere like never before. She explains the current and projected consequences of global warming—from superstorms to rising sea levels—and the actions that we all can take to fight back. At once an explainer on the mechanisms of global change and a lively, personal narrative given to us in Jahren&’s inimitable voice, The Story of More is the essential pocket primer on climate change that will leave an indelible impact on everyone who reads it.
Storytelling with Data: A Data Visualization Guide for Business Professionals
by Cole Nussbaumer KnaflicDon't simply show your data—tell a story with it! Storytelling with Data teaches you the fundamentals of data visualization and how to communicate effectively with data. You'll discover the power of storytelling and the way to make data a pivotal point in your story. The lessons in this illuminative text are grounded in theory, but made accessible through numerous real-world examples—ready for immediate application to your next graph or presentation. Storytelling is not an inherent skill, especially when it comes to data visualization, and the tools at our disposal don't make it any easier. This book demonstrates how to go beyond conventional tools to reach the root of your data, and how to use your data to create an engaging, informative, compelling story. Specifically, you'll learn how to: Understand the importance of context and audience Determine the appropriate type of graph for your situation Recognize and eliminate the clutter clouding your information Direct your audience's attention to the most important parts of your data Think like a designer and utilize concepts of design in data visualization Leverage the power of storytelling to help your message resonate with your audience Together, the lessons in this book will help you turn your data into high impact visual stories that stick with your audience. Rid your world of ineffective graphs, one exploding 3D pie chart at a time. There is a story in your data—Storytelling with Data will give you the skills and power to tell it!
Storytelling with Data in Healthcare
by Kevin Masick Eric BouillonWith the constant evolution of change in healthcare from both a technology and governmental perspective, it is imperative to take a step back and view the big picture. Relying on hunches or beliefs is no longer sustainable, so avoid jumping to conclusions and making decisions without thoroughly understanding the statistics being analyzed. The triple aim of statistics is a conceptual model laying the foundation for improving healthcare outcomes through statistics. This foundation is: know your numbers; develop behavioral interventions; and set goals to drive change.With the availability of electronic data sources, the quantity and quality of data have grown exponentially to the point of information overload. Translating all this data into words that tell a meaningful story is overwhelming. This book takes the reader on a journey that navigates through this data to tell a story that everyone can understand and use to drive improvement. Readers will learn to tell a narrative story based on data, to develop creative, innovative and effective solutions to improve processes and outcomes utilizing the authors’ tools. Topics include mortality and readmission, patient experience, patient safety survey, governmental initiatives, CMS Star Rating and Hospital Compare.Storytelling with Data in Healthcare combines methodology and statistics in the same course material, making it coherent and easier to put into practice. It uses storytelling as a tool for knowledge acquisition and retention and will be valuable for courses in nursing schools, medical schools, pharmacy schools or any healthcare profession that has a research design or statistics course offered to students. The book will be of interest to researchers, academics, healthcare professionals, and students in the fields of healthcare management and operations as well as statistics and data visualization.
Straight Lines, Parallel Lines, Perpendicular Lines (Young Math Books)
by Mannis Charosh Enrico ArnoUsing an imaginative approach to basic principles, this book invites the reader to explore, to understand, and to enjoy the principles of mathematics.
Straightforward Statistics: Bowen: Straightforward Statistics + Sage Ibm® Spss® Statistics V23. 0 Student Version
by Chieh-Chen BowenStraightforward Statistics by Chieh-Chen Bowen is written in plain language and connects material in a clear, logical manner to help students across the social and behavioral sciences develop a “big picture” understanding of foundational statistics. Each new chapter is purposefully connected with the previous chapter for a gradual accrual of knowledge from simple to more complex concepts—this effective, cumulative approach to statistics through logical transitions eases students into statistics and prepares them for success in more advanced quantitative coursework and their own research.
Straightforward Statistics: Bowen: Straightforward Statistics + Sage Ibm® Spss® Statistics V23. 0 Student Version
by Chieh-Chen BowenStraightforward Statistics by Chieh-Chen Bowen is written in plain language and connects material in a clear, logical manner to help students across the social and behavioral sciences develop a “big picture” understanding of foundational statistics. Each new chapter is purposefully connected with the previous chapter for a gradual accrual of knowledge from simple to more complex concepts—this effective, cumulative approach to statistics through logical transitions eases students into statistics and prepares them for success in more advanced quantitative coursework and their own research.
Straightforward Statistics: Understanding the Tools of Research
by Glenn Geher Sara HallStraightforward Statistics: Understanding the Tools of Research is a clear and direct introduction to statistics for the social, behavioral, and life sciences. <p><p>Based on Glenn Geher's extensive experience teaching undergraduate statistics, this book provides a narrative presentation of the core principles that provide the foundation for modern-day statistics. With step-by-step guidance on the nuts and bolts of computing these statistics, the book includes detailed tutorials how to use state-of-the-art software, SPSS, to compute the basic statistics employed in modern academic and applied research. Across 13 succinct chapters, this text presents statistics using a conceptual approach along with information on the relevance of the different tools in different contexts and summaries of current research examples. <p><p> Students should find this book easy useful and engaging in its presentation while instructors should find it detailed, comprehensive, accessible, and helpful in complementing a basic course in statistics.
Straightforward Statistics with Excel®
by Chieh-Chen BowenWritten in an accessible and clear manner, Straightforward Statistics with Excel® 2e by Chieh-Chen Bowen helps students across the social and behavioral sciences gradually build their skills to develop a better understanding of the world around them. Each chapter purposefully connects with the previous chapter for a gradual accrual of knowledge from simple to more complex concepts. This effective, cumulative approach to statistics through logical transitions eases students into statistics and prepares them for success in more advanced quantitative coursework and their own research. The second edition now features Excel instructions and exercises throughout so students can use this widely-available and applied software for statistics. This book is designed to walk the reader through statistics at a steady but gentle pace, providing pop quizzes throughout every chapter so readers can check their knowledge along the way. By gradually stepping up difficulty in each chapter, students generate a solid foundation and are prepared for the next chapters. Straightforward Statistics with Excel looks at the big picture so that the basic statistical concepts connect to everyday and relevant research examples in multiple ways. Throughout the book the reader is reminded of what they need to be able to recall with "You Must Remember This" boxes. A rich source of practical resources are located at the end of chapters beginning with " What You Learned," followed by three sets of exercises so students can immediately apply their knowledge. The new edition features a reorganized presentation of material, starting with measures of central tendency, separating this from measures of variability so students better understand the differences. A more thorough presentation of one-sample and dependent samples t-tests gives students a stronger foundation in these crucial tests in statistics. New examples and studies complete the update, with a focus on simplicity. Throughout, the book makes use of Excel instructions and screenshots so students can take statistics with them through research projects and into the world beyond academia.
Straightforward Statistics with Excel®
by Chieh-Chen BowenWritten in an accessible and clear manner, Straightforward Statistics with Excel® 2e by Chieh-Chen Bowen helps students across the social and behavioral sciences gradually build their skills to develop a better understanding of the world around them. Each chapter purposefully connects with the previous chapter for a gradual accrual of knowledge from simple to more complex concepts. This effective, cumulative approach to statistics through logical transitions eases students into statistics and prepares them for success in more advanced quantitative coursework and their own research. The second edition now features Excel instructions and exercises throughout so students can use this widely-available and applied software for statistics. This book is designed to walk the reader through statistics at a steady but gentle pace, providing pop quizzes throughout every chapter so readers can check their knowledge along the way. By gradually stepping up difficulty in each chapter, students generate a solid foundation and are prepared for the next chapters. Straightforward Statistics with Excel looks at the big picture so that the basic statistical concepts connect to everyday and relevant research examples in multiple ways. Throughout the book the reader is reminded of what they need to be able to recall with "You Must Remember This" boxes. A rich source of practical resources are located at the end of chapters beginning with " What You Learned," followed by three sets of exercises so students can immediately apply their knowledge. The new edition features a reorganized presentation of material, starting with measures of central tendency, separating this from measures of variability so students better understand the differences. A more thorough presentation of one-sample and dependent samples t-tests gives students a stronger foundation in these crucial tests in statistics. New examples and studies complete the update, with a focus on simplicity. Throughout, the book makes use of Excel instructions and screenshots so students can take statistics with them through research projects and into the world beyond academia.
Strain Gradient Plasticity-Based Modeling of Damage and Fracture
by Emilio Martínez PañedaThis book provides a comprehensive introduction to numerical modeling of size effects in metal plasticity. The main classes of strain gradient plasticity formulations are described and efficiently implemented in the context of the finite element method. A robust numerical framework is presented and employed to investigate the role of strain gradients on structural integrity assessment. The results obtained reveal the need of incorporating the influence on geometrically necessary dislocations in the modeling of various damage mechanisms. Large gradients of plastic strain increase dislocation density, promoting strain hardening and elevating crack tip stresses. This stress elevation is quantified under both infinitesimal and finite deformation theories, rationalizing the experimental observation of cleavage fracture in the presence of significant plastic flow. Gradient-enhanced modeling of crack growth resistance, hydrogen diffusion and environmentally assisted cracking highlighted the relevance of an appropriate characterization of the mechanical response at the small scales involved in crack tip deformation. Particularly promising predictions are attained in the field of hydrogen embrittlement. The research has been conducted at the Universities of Cambridge, Oviedo, Luxembourg, and the Technical University of Denmark, in a collaborative effort to understand, model and optimize the mechanical response of engineering materials.
Strain Solitons in Solids and How to Construct Them
by Alexander M. SamsonovAlthough the theory behind solitary waves of strain shows that they hold significant promise in nondestructive testing and a variety of other applications, an enigma has long persisted-the absence of observable elastic solitary waves in practice. Inspired by this apparent contradiction, Strain Solitons in Solids and How to Construct Them refines th
Strange Curves, Counting Rabbits, & Other Mathematical Explorations
by Keith BallHow does mathematics enable us to send pictures from space back to Earth? Where does the bell-shaped curve come from? Why do you need only 23 people in a room for a 50/50 chance of two of them sharing the same birthday? In Strange Curves, Counting Rabbits, and Other Mathematical Explorations, Keith Ball highlights how ideas, mostly from pure math, can answer these questions and many more. Drawing on areas of mathematics from probability theory, number theory, and geometry, he explores a wide range of concepts, some more light-hearted, others central to the development of the field and used daily by mathematicians, physicists, and engineers. Each of the book's ten chapters begins by outlining key concepts and goes on to discuss, with the minimum of technical detail, the principles that underlie them. Each includes puzzles and problems of varying difficulty. While the chapters are self-contained, they also reveal the links between seemingly unrelated topics. For example, the problem of how to design codes for satellite communication gives rise to the same idea of uncertainty as the problem of screening blood samples for disease. Accessible to anyone familiar with basic calculus, this book is a treasure trove of ideas that will entertain, amuse, and bemuse students, teachers, and math lovers of all ages.
Strange Functions in Real Analysis
by Alexander KharazishviliStrange Functions in Real Analysis, Third Edition differs from the previous editions in that it includes five new chapters as well as two appendices. More importantly, the entire text has been revised and contains more detailed explanations of the presented material. In doing so, the book explores a number of important examples and constructions of pathological functions. After introducing basic concepts, the author begins with Cantor and Peano-type functions, then moves effortlessly to functions whose constructions require what is essentially non-effective methods. These include functions without the Baire property, functions associated with a Hamel basis of the real line and Sierpinski-Zygmund functions that are discontinuous on each subset of the real line having the cardinality continuum. Finally, the author considers examples of functions whose existence cannot be established without the help of additional set-theoretical axioms. On the whole, the book is devoted to strange functions (and point sets) in real analysis and their applications.
A Strange Wilderness: The Lives of the Great Mathematicians
by Amir D. AczelThe international bestselling author of Fermat&’s Last Theorem explores the eccentric lives of history&’s foremost mathematicians. From Archimedes&’s eureka moment to Alexander Grothendieck&’s seclusion in the Pyrenees, bestselling author Amir Aczel selects the most compelling stories in the history of mathematics, creating a colorful narrative that explores the quirky personalities behind some of the most groundbreaking, influential, and enduring theorems. Alongside revolutionary innovations are incredible tales of duels, battlefield heroism, flamboyant arrogance, pranks, secret societies, imprisonment, feuds, and theft—as well as some costly errors of judgment that prove genius doesn&’t equal street smarts. Aczel&’s colorful and enlightening profiles offer readers a newfound appreciation for the tenacity, complexity, eccentricity, and brilliance of our greatest mathematicians.