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Knowledge-augmented Methods for Natural Language Processing (SpringerBriefs in Computer Science)
by Meng Jiang Bill Yuchen Lin Shuohang Wang Yichong Xu Wenhao Yu Chenguang ZhuOver the last few years, natural language processing has seen remarkable progress due to the emergence of larger-scale models, better training techniques, and greater availability of data. Examples of these advancements include GPT-4, ChatGPT, and other pre-trained language models. These models are capable of characterizing linguistic patterns and generating context-aware representations, resulting in high-quality output. However, these models rely solely on input-output pairs during training and, therefore, struggle to incorporate external world knowledge, such as named entities, their relations, common sense, and domain-specific content. Incorporating knowledge into the training and inference of language models is critical to their ability to represent language accurately. Additionally, knowledge is essential in achieving higher levels of intelligence that cannot be attained through statistical learning of input text patterns alone. In this book, we will review recent developmentsin the field of natural language processing, specifically focusing on the role of knowledge in language representation. We will examine how pre-trained language models like GPT-4 and ChatGPT are limited in their ability to capture external world knowledge and explore various approaches to incorporate knowledge into language models. Additionally, we will discuss the significance of knowledge in enabling higher levels of intelligence that go beyond statistical learning on input text patterns. Overall, this survey aims to provide insights into the importance of knowledge in natural language processing and highlight recent advances in this field.
Komplexe Mannigfaltigkeiten (essentials)
by Klaus FritzscheNach einer Einführung in die holomorphen Funktionen von mehreren Veränderlichen wird die Welt der komplexen Mannigfaltigkeiten vorgestellt, insbesondere Untermannigfaltigkeiten, analytische Mengen und tangentiale Strukturen. Weitere Themen sind komplexe Vektorbündel, Liegruppen und Quotientenstrukturen. Wichtigste Beispiele sind die Steinschen Mannigfaltigkeiten, sowie die projektiv-algebraischen Mengen mit ihrer Beziehung zur algebraischen Geometrie.
Korteweg–de Vries Flows with General Initial Conditions (Mathematical Physics Studies)
by Shinichi KotaniLarge numbers of studies of the KdV equation have appeared since the pioneering paper by Gardner, Greene, Kruskal, and Miura in 1967. Most of those works have employed the inverse spectral method for 1D Schrödinger operators or an advanced Fourier analysis. Although algebraic approaches have been discovered by Hirota–Sato and Marchenko independently, those have not been fully investigated and analyzed. The present book offers a new approach to the study of the KdV equation, which treats decaying initial data and oscillating data in a unified manner. The author’s method is to represent the tau functions introduced by Hirota–Sato and developed by Segal–Wilson later in terms of the Weyl–Titchmarsh functions (WT functions, in short) for the underlying Schrödinger operators. The main result is stated by a class of WT functions satisfying some of the asymptotic behavior along a curve approaching the spectrum of the Schrödinger operators at +∞ in an order of -(n-1/2)for the nth KdV equation. This class contains many oscillating potentials (initial data) as well as decaying ones. Especially bounded smooth ergodic potentials are included, and under certain conditions on the potentials, the associated Schrödinger operators have dense point spectrum. This provides a mathematical foundation for the study of the soliton turbulence problem initiated by Zakharov, which was the author’s motivation for extending the class of initial data in this book. A large class of almost periodic potentials is also included in these ergodic potentials. P. Deift has conjectured that any solutions to the KdV equation starting from nearly periodic initial data are almost periodic in time. Therefore, our result yields a foundation for this conjecture. For the reader’s benefit, the author has included here (1) a basic knowledge of direct and inverse spectral problem for 1D Schrödinger operators, including the notion of the WT functions; (2)Sato’s Grassmann manifold method revised by Segal–Wilson; and (3) basic results of ergodic Schrödinger operators.
Kurt Gödel: Metamathematisches Genie
by William D. BrewerZu seinen Lebzeiten war Kurt Gödel außerhalb der Fachwelt der Mathematiker, Philosophen und theoretischen Physiker kaum bekannt. Zu Beginn seiner Karriere schuf er beeindruckende Arbeiten zur Vollständigkeit und Beweisbarkeit formaler logischer Systeme, die zu seiner Dissertation und seiner Habilitations-schrift wurden und ihn unter Fachleuten weltberühmt machten. Seine Unvoll-ständigkeitssätze läuteten das Ende der formal-logischen Programme der Logizisten (Russell et al.) und der Formalisten (Hilbert et al.) ein. Später erzielte er auch signifikante Ergebnisse in der Mengenlehre. Nach seiner Emigration in die USA (Princeton), widmete er sich mehr der Philosophie, dem Leitmotiv seines Lebens, und er fand auch eine einzigartige Lösung zu Einsteins Feld-gleichungen der Gravitation, sein “Gödel-Universum“. Dieses Buch beschreibt sowohl den Gödel, der ein genialer Wissenschaftler war, und der gewagte und neuartige Hypothesen zu den Fundamenten der Mathe-matik und Physik hervorbrachte, ‒ als auch den Gödel, der ein perfekter Rationalist war, aber sein Alltagsleben nur mit Mühe meistern konnte und zeitlebens unter Depressionen, Angstneurosen und Hypochondrie litt. Ein Leben voller Paradoxen, in dem er trotz all seiner psychischen Probleme Beachtliches leistete und zu einem Vorbild für viele jüngere Wissenschaftler wurde. Das Buch liefert den Kontext zu seinen Errungenschaften, die ein verblüffend breites Spektrum intellektueller Unternehmungen darstellen, und zu seiner zunehmenden Geisteskrankheit; und es zeigt, wie er eine lange und erfolgreiche Karriere mit Hilfe seiner loyalen Ehefrau Adele und einigen seiner Freunde durchlaufen konnte. Dies ist eine faszinierende Geschichte der wissen-schaftlichen Genialität und der menschlichen Natur.
Lagrangian and Hamiltonian Mechanics: A Modern Approach with Core Principles and Underlying Topics
by José Rachid MohallemThis book serves as a textbook for an analytical mechanics course, a fundamental subject of physics, that pays special attention to important topics that are not discussed in most standard textbooks. Readers are provided with a clear understanding of topics that are usually inaccessible to the undergraduate level and that are critical to learning Lagrangian and Hamiltonian mechanics. Each chapter also includes worked problems and solutions, as well as additional exercises for readers to try. This book begins with the fundamentals of analytical mechanics, concisely introducing readers to the calculus of variations, Hamilton’s Principle, and Lagrange’s equations. While presenting readers with these core topics, the author uses an intuitive approach to delve into essential questions, such as where Galilean invariance lies in Lagrangian mechanics and how Hamilton’s Principle of Least Action encompasses Newton’s three laws, interesting conclusions that often go unnoticed. Infact, Hamilton’s principle is taken throughout as the very origin of classical physical laws, and the choice of appropriate Lagrangians in each case as the real theoretical challenge, meaning that forms of Lagrangian which differ from the standard one are not mere curiosities but, instead, the general rule. This book clarifies common misunderstandings that students face when learning the subject and formally rationalizes concepts that are often difficult to grasp. In addition, the final chapter provides an introduction to a Lagrangian field theory for those interested in learning more advanced topics. Ideal for upper undergraduate and graduate students, this book seeks to teach the intrinsic meaning of the principles and equations taught in an analytical mechanics course and convey their usefulness as powerful theoretical instruments of modern physics.
Landslide: Application of Geostatistical and Geospatial Modeling (Advances in Natural and Technological Hazards Research #52)
by Rajib Shaw Uday Chatterjee Subodh Chandra Pal Gopal Krishna Panda Asish SahaThe book illustrates a geospatial and geostatistical approach to data analysis, modeling, risk assessment, and visualization, as well as landslide hazard management in the hilly region. This book investigates cutting-edge methodologies based on open source software and R statistical programming and modeling in current decision-making procedures, with a particular emphasis on recent advances in data mining techniques and robust modeling in torrential rainfall and earthquake induced landslide hazard.
Lateral Solutions to Mathematical Problems (AK Peters/CRC Recreational Mathematics Series)
by Desmond MacHaleLateral Solutions to Mathematical Problems offers a fresh approach to mathematical problem solving via lateral thinking. Lateral thinking has long been used informally by good mathematics teachers and lecturers to spice up their material and interest their students in the more artistic aspects of mathematical problem solving. In this book, the author attempts to carry out this process formally, with reference to specific, non-technical problems that are easily understood and explained at an intermediate level.This book is appropriate for interested high school students, undergraduates and postgraduates, looking for relief from technical material and also looking for insight into the methodology of mathematics; for teachers and lecturers looking for a novel approach to course material; and anyone interested in both mathematics and lateral thinking.
LATIN 2024: 16th Latin American Symposium, Puerto Varas, Chile, March 18–22, 2024, Proceedings, Part II (Lecture Notes in Computer Science #14579)
by José A. Soto Andreas WieseThis book constitutes the proceedings of the 16th Latin American Symposium on Theoretical Informatics, LATIN 2042, which took place in Puerto Varas, Chile, in March 2024. The 44 papers presented in this volume were carefully reviewed and selected from 93 submissions. They were organized in topical sections as follows:Part I: Algorithms and Data Structures; Approximation and Online Algorithms; Complexity Theory; Part II: Combinatorics and Graph Theory; Parameterized Algorithms; Automata Theory and Formal Languages; and Game Theory and Fairness.
LATIN 2024: 16th Latin American Symposium, Puerto Varas, Chile, March 18–22, 2024, Proceedings, Part I (Lecture Notes in Computer Science #14578)
by José A. Soto Andreas WieseThis book constitutes the proceedings of the 16th Latin American Symposium on Theoretical Informatics, LATIN 2042, which took place in Puerto Varas, Chile, in March 2024. The 44 papers presented in this volume were carefully reviewed and selected from 93 submissions. They were organized in topical sections as follows:Part I: Algorithms and Data Structures; Approximation and Online Algorithms; Complexity Theory; Part II: Combinatorics and Graph Theory; Parameterized Algorithms; Automata Theory and Formal Languages; and Game Theory and Fairness.
Leading in Analytics: The Seven Critical Tasks for Executives to Master in the Age of Big Data (Wiley and SAS Business Series)
by Joseph A. CazierA step-by-step guide for business leaders who need to manage successful big data projects Leading in Analytics: The Critical Tasks for Executives to Master in the Age of Big Data takes you through the entire process of guiding an analytics initiative from inception to execution. You’ll learn which aspects of the project to pay attention to, the right questions to ask, and how to keep the project team focused on its mission to produce relevant and valuable project. As an executive, you can’t control every aspect of the process. But if you focus on high-impact factors that you can control, you can ensure an effective outcome. This book describes those factors and offers practical insight on how to get them right. Drawn from best-practice research in the field of analytics, the Manageable Tasks described in this book are specific to the goal of implementing big data tools at an enterprise level. A dream team of analytics and business experts have contributed their knowledge to show you how to choose the right business problem to address, put together the right team, gather the right data, select the right tools, and execute your strategic plan to produce an actionable result. Become an analytics-savvy executive with this valuable book. Ensure the success of analytics initiatives, maximize ROI, and draw value from big data Learn to define success and failure in analytics and big data projects Set your organization up for analytics success by identifying problems that have big data solutions Bring together the people, the tools, and the strategies that are right for the jobBy learning to pay attention to critical tasks in every analytics project, non-technical executives and strategic planners can guide their organizations to measurable results.
Learn R: As a Language (Chapman & Hall/CRC The R Series)
by Pedro J. AphaloLearning a computer language like R can be either frustrating, fun or boring. Having fun requires challenges that wake up the learner’s curiosity but also provide an emotional reward for overcoming them. The book is designed so that it includes smaller and bigger challenges, in what I call playgrounds, in the hope that all readers will enjoy their path to R fluency. Fluency in the use of a language is a skill that is acquired through practice and exploration. For students and professionals in the biological sciences, humanities and many applied fields, recognizing the parallels between R and natural languages should help them feel at home with R. The approach I use is similar to that of a travel guide, encouraging exploration and describing the available alternatives and how to reach them. The intention is to guide the reader through the R landscape of 2024 and beyond.What is new in the second edition? Text expanded by more than 25% to include additional R features and gentler and more detailed explanations Contains 24 new diagrams and flowcharts, seven new tables, and revised text and code examples for clarity All three indexes were expanded, and answers to 28 frequently asked questions added What will you find in this book? Programming concepts explained as they apply to current R Emphasis on the role of abstractions in programming Few prescriptive rules—mostly the author’s preferences together with alternatives Presentation of the R language emphasizing the “R way of doing things” Tutoring for “programming in the small” using scripts for data analysis Explanation of the differences between R proper and extensions for data wrangling The grammar of graphics is described as a language for the construction of data visualisations Examples of data exchange between R and the foreign world using common file formats Coaching to become an independent R user, capable of writing original scripts and solving future challenges
Lectures in Knot Theory: An Exploration of Contemporary Topics (Universitext)
by Józef H. Przytycki Rhea Palak Bakshi Dionne Ibarra Gabriel Montoya-Vega Deborah WeeksThis text is based on lectures delivered by the first author on various, often nonstandard, parts of knot theory and related subjects. By exploring contemporary topics in knot theory including those that have become mainstream, such as skein modules, Khovanov homology and Gram determinants motivated by knots, this book offers an innovative extension to the existing literature. Each lecture begins with a historical overview of a topic and gives motivation for the development of that subject. Understanding of most of the material in the book requires only a basic knowledge of topology and abstract algebra. The intended audience is beginning and advanced graduate students, advanced undergraduate students, and researchers interested in knot theory and its relations with other disciplines within mathematics, physics, biology, and chemistry.Inclusion of many exercises, open problems, and conjectures enables the reader to enhance their understanding of the subject. The use of this text for the classroom is versatile and depends on the course level and choices made by the instructor. Suggestions for variations in course coverage are included in the Preface. The lecture style and array of topical coverage are hoped to inspire independent research and applications of the methods described in the book to other disciplines of science. An introduction to the topology of 3-dimensional manifolds is included in Appendices A and B. Lastly, Appendix C includes a Table of Knots.
Lectures on Geometry (UNITEXT #158)
by Lucian Bădescu Ettore CarlettiThis is an introductory textbook on geometry (affine, Euclidean and projective) suitable for any undergraduate or first-year graduate course in mathematics and physics. In particular, several parts of the first ten chapters can be used in a course of linear algebra, affine and Euclidean geometry by students of some branches of engineering and computer science. Chapter 11 may be useful as an elementary introduction to algebraic geometry for advanced undergraduate and graduate students of mathematics. Chapters 12 and 13 may be a part of a course on non-Euclidean geometry for mathematics students. Chapter 13 may be of some interest for students of theoretical physics (Galilean and Einstein’s general relativity). It provides full proofs and includes many examples and exercises. The covered topics include vector spaces and quadratic forms, affine and projective spaces over an arbitrary field; Euclidean spaces; some synthetic affine, Euclidean and projective geometry; affine and projective hyperquadrics with coefficients in an arbitrary field of characteristic different from 2; Bézout’s theorem for curves of P^2 (K), where K is a fixed algebraically closed field of arbitrary characteristic; and Cayley-Klein geometries.
Lesson Study with Mathematics and Science Preservice Teachers: Finding the Form (WALS-Routledge Lesson Study Series)
by Sharon Dotger Gabriel Matney Jennifer Heckathorn Kelly Chandler-Olcott Miranda FoxThis insightful volume offers an overview of the fundamentals of lesson student practice in US teacher education as well as examples from math and science teacher educators using lesson study in their local contexts. The number of teacher educators using lesson study with preservice teachers is small but growing. This book is aimed at teacher educators who may want to try lesson study in university contexts without the challenge of translating the practice from the K-12 context on their own. In this volume, lesson study is broadly overviewed, attention is given to its constituent steps, and examples of lesson study in preservice contexts are shared. Given the broad array of teacher education program designs, numerous contingencies guide teacher educators in their implementation of lesson study, given their contextual affordances and limitations. The lesson study descriptions and cases in this book will support teacher educators and scholars across subject specialities and geographic lines, as they seek instructional frameworks to advance their pedagogical goals.
Liberty's Grid: A Founding Father, a Mathematical Dreamland, and the Shaping of America
by Amir AlexanderThe surprising history behind a ubiquitous facet of the United States: the gridded landscape. Seen from an airplane, much of the United States appears to be a gridded land of startling uniformity. Perpendicular streets and rectangular fields, all precisely measured and perfectly aligned, turn both urban and rural America into a checkerboard landscape that stretches from horizon to horizon. In evidence throughout the country, but especially the West, the pattern is a hallmark of American life. One might consider it an administrative convenience—an easy way to divide land and lay down streets—but it is not. The colossal grid carved into the North American continent, argues historian and writer Amir Alexander, is a plan redolent with philosophical and political meaning. In 1784 Thomas Jefferson presented Congress with an audacious scheme to reshape the territory of the young United States. All western lands, he proposed, would be inscribed with a single rectilinear grid, transforming the natural landscape into a mathematical one. Following Isaac Newton and John Locke, he viewed mathematical space as a blank slate on which anything is possible and where new Americans, acting freely, could find liberty. And if the real America, with its diverse landscapes and rich human history, did not match his vision, then it must be made to match it. From the halls of Congress to the open prairies, and from the fight against George III to the Trail of Tears, Liberty’s Grid tells the story of the battle between grid makers and their opponents. When Congress endorsed Jefferson’s plan, it set off a struggle over American space that has not subsided. Transcendentalists, urban reformers, and conservationists saw the grid not as a place of possibility but as an artificial imposition that crushed the human spirit. Today, the ideas Jefferson associated with the grid still echo through political rhetoric about the country’s founding, and competing visions for the nation are visible from Manhattan avenues and Kansan pastures to Yosemite’s cliffs and suburbia’s cul-de-sacs. An engrossing read, Liberty’s Grid offers a powerful look at the ideological conflict written on the landscape.
Limitarianism: The Case Against Extreme Wealth
by Ingrid Robeyns"A powerful case for limitarianism—the idea that we should set a maximum on how much resources one individual can appropriate. A must-read!" —Thomas Piketty, bestselling author of Capital in the Twenty-First CenturyAn original, bold, and convincing argument for a cap on wealth by the philosopher who coined the term "limitarianism."How much money is too much? Is it ethical, and democratic, for an individual to amass a limitless amount of wealth, and then spend it however they choose? Many of us feel that the answer to that is no—but what can we do about it?Ingrid Robeyns has long written and argued for the principle she calls "limitarianism"—or the need to limit extreme wealth. This idea is gaining momentum in the mainstream – with calls to "tax the rich" and slogans like "every billionaire is a policy failure"—but what does it mean in practice?Robeyns explains the key reasons to support the case against extreme wealth: It keeps the poor poor and inequalities growingIt&’s often dirty moneyIt undermines democracyIt&’s one of the leading causes of climate changeNobody actually deserves to be a millionaireThere are better things to do with excess moneyThe rich will benefit, tooThis will be the first authoritative trade book to unpack the concept of a cap on wealth, where to draw the line, how to collect the excess and what to do with the money. In the process, Robeyns will ignite an urgent debate about wealth, one that calls into question the very forces we live by (capitalism and neoliberalism) and invites us to a radical reimagining of our world.
Limits of AI - theoretical, practical, ethical (Technik im Fokus)
by Klaus Mainzer Reinhard KahleArtificial intelligence is a key technology with great expectations in science, industry, and everyday life. This book discusses both the perspectives and the limitations of this technology. This concerns the practical, theoretical, and conceptual challenges that AI has to face. In an early phase of symbolic AI, AI focused on formal programs (e.g., expert systems), in which rule-based knowledge was processed with the help of symbolic logic. Today, AI is dominated by statistics-based machine learning methods and Big Data. While this sub-symbolic AI is extremely successful (e.g., chatbots like ChatGPT), it is often not transparent. The book argues for explainable and reliable AI, in which the logical and mathematical foundations of AI-algorithms become understandable and verifiable.
Linear Algebra for Earth Scientists
by J. Douglas Walker Noah M. McLeanLinear Algebra for Earth Scientists is written for undergraduate and graduate students in Earth and Environmental sciences. It is intended to give students enough background in linear algebra to work with systems of equations and data in geology, hydrology, geophysics, or whatever part of the Earth Sciences they engage with.The book does not presuppose any extensive prior knowledge of linear algebra. Instead, the book builds students up from a low base to a working understanding of the sub t that they can apply to their work, using many familiar examples in the geosciences.Features Suitable for students of Earth and Environmental Sciences Minimal prerequisites — written in a way that is accessible and engaging for those without a mathematical background All material presented with examples and applications to the Earth Sciences
Linear Algebra in Data Science (Compact Textbooks in Mathematics)
by Peter Zizler Roberta La HayeThis textbook explores applications of linear algebra in data science at an introductory level, showing readers how the two are deeply connected. The authors accomplish this by offering exercises that escalate in complexity, many of which incorporate MATLAB. Practice projects appear as well for students to better understand the real-world applications of the material covered in a standard linear algebra course. Some topics covered include singular value decomposition, convolution, frequency filtering, and neural networks. Linear Algebra in Data Science is suitable as a supplement to a standard linear algebra course.
Linear Models and the Relevant Distributions and Matrix Algebra: A Unified Approach Volume 2
by David A. HarvilleLinear Models and the Relevant Distributions and Matrix Algebra: A Unified Approach, Volume 2 covers several important topics that were not included in the first volume. The second volume complements the first, providing detailed solutions to the exercises in both volumes, thereby greatly enhancing its appeal for use in advanced statistics programs. This volume can serve as a valuable reference. It can also serve as a resource in a mathematical statistics course for use in illustrating various theoretical concepts in the context of a relatively complex setting of great practical importance. Together with the first volume, this volume provides a largely self-contained treatment of an important area of statistics and should prove highly useful to graduate students and others. Key Features: Includes solutions to the exercises from both the first and second volumes Includes coverage of several topics not covered in the first volume Highly valuable as a reference book for graduate students and researchers
Linear Partial Differential and Difference Equations and Simultaneous Systems with Constant or Homogeneous Coefficients (Mathematics and Physics for Science and Technology)
by Luis Manuel Braga da Costa Campos Luís António Raio VilelaLinear Partial Differential and Difference Equations and Simultaneous Systems: With Constant or Homogeneous Coefficients is part of the series "Mathematics and Physics for Science and Technology," which combines rigorous mathematics with general physical principles to model practical engineering systems with a detailed derivation and interpretation of results. Volume V presents the mathematical theory of partial differential equations and methods of solution satisfying initial and boundary conditions, and includes applications to: acoustic, elastic, water, electromagnetic and other waves; the diffusion of heat, mass, and electricity; and their interactions. This is the third book of the volume.The book starts with six different methods of solution of linear partial differential equations (p.d.e.) with constant coefficients. One of the methods, namely characteristic polynomial, is then extended to a further five classes, including linear p.d.e. with homogeneous power coefficients and finite difference equations and simultaneous systems of both (simultaneous partial differential equations [s.p.d.e.] and simultaneous finite difference equations [s.f.d.e.]). The applications include detailed solutions of the most important p.d.e. in physics and engineering, including the Laplace, heat, diffusion, telegraph, bar, and beam equations. The free and forced solutions are considered together with boundary, initial, asymptotic, starting, and other conditions.The book is intended for graduate students and engineers working with mathematical models and can be applied to problems in mechanical, aerospace, electrical, and other branches of engineering dealing with advanced technology, and also in the physical sciences and applied mathematics.
Lineare Algebra: Ein Lehrbuch über die Theorie mit Blick auf die Praxis (Springer Studium Mathematik (Bachelor))
by Volker Mehrmann Jörg LiesenDieses Lehrbuch über die Lineare Algebra deckt den gesamten Stoff der zweisemestrigen Grundvorlesung ab. Seine anschauliche und konsequent matrizenorientierte Herangehensweise ermöglicht Studierenden ein intuitives Verständnis der abstrakten Objekte. Die im Buch präsentierten vielfältigen Anwendungen und Beispiele motivieren Studierende zur intensiven Auseinandersetzung mit der Linearen Algebra als leistungsfähiges mathematisches Werkzeug. In vielen „MATLAB-Minuten“ können sich Studierende wichtige Sätze und Konzepte am Rechner erarbeiten. Alle notwendigen Vorkenntnisse werden in einer MATLAB-Kurzeinführung erläutert. Das Buch enthält zudem über 350 Übungsaufgaben, die das Erlernen des Stoffes unterstützen. Interessierte Studierende finden darüber hinaus historische Notizen zur Entwicklung des Gebiets. Für diese vierte Auflage wurde das Buch durchgesehen und ergänzt. Zu den Ergänzungen gehören insbesondere die genauere Betrachtung von Projektionen, die Herleitung der Frobenius-Normalform von Endomorphismen sowie der Beweis eines wichtigen Satzes über Matrixfunktionen basierend auf der Lösung des Hermite-Interpolationsproblems. Hinzugekommen sind außerdem mehr als 20 neue Aufgaben sowie Begriffe wie der Bidualraum, derogatorische Matrizen, Invariantenteiler und Isometrien. Der übersichtliche Aufbau und das bewährte Konzept des Lehrbuchs wurden beibehalten.
A Little Guide for Teachers: Using Student Data (A Little Guide for Teachers)
by Richard SelfridgeStudent data can be one of the most powerful tools a teacher can use to help their students to learn. In this book, Richard Selfridge offers practical advice for teachers on how to gather useful student data in the classroom and how to use these findings effectively to enhance your teaching. The Little Guide for Teachers series is little in size but BIG on all the support and inspiration you need to navigate your day-to-day life as a teacher. Authored by experts in the field Easy to dip in-and-out of Interactive activities encourage you to write into the book and make it your own Read in an afternoon or take as long as you like with it!
A Little Guide for Teachers: Using Student Data (A Little Guide for Teachers)
by Richard SelfridgeStudent data can be one of the most powerful tools a teacher can use to help their students to learn. In this book, Richard Selfridge offers practical advice for teachers on how to gather useful student data in the classroom and how to use these findings effectively to enhance your teaching. The Little Guide for Teachers series is little in size but BIG on all the support and inspiration you need to navigate your day-to-day life as a teacher. Authored by experts in the field Easy to dip in-and-out of Interactive activities encourage you to write into the book and make it your own Read in an afternoon or take as long as you like with it!
Logic-Based Benders Decomposition: Theory and Applications (Synthesis Lectures on Operations Research and Applications)
by John HookerThis book is the first comprehensive guide to logic-based Benders decomposition (LBBD), a general and versatile method for breaking large, complex optimization problems into components that are small enough for practical solution. The author introduces logic-based Benders decomposition for optimization, which substantially generalizes the classical Benders method. It can reduce solution times by orders of magnitude and allows decomposition to be applied to a much wider variety of optimization problems. On the theoretical side, this book provides a full account of inference duality concepts that underlie LBBD, as well as a description of how LBBD can be combined with stochastic and robust optimization, heuristic methods, and decision diagrams. It also clarifies the connection between LBBD and combinatorial Benders cuts for mixed integer programming. On the practical side, it explains how LBBD has been applied to a rapidly growing variety of problem domains. After describing basic theory, this book provides a comprehensive review of the rapidly growing literature that describes these applications, in each case explaining how LBBD is adapted to the problem at hand. In doing so this work provides a sourcebook of ideas for applying LBBD to new problems as they arise.