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Learning to Teach Mathematics in the Secondary School: A companion to school experience (Learning to Teach Subjects in the Secondary School Series)
by David Pimm Sue Johnston-Wilder Clare LeeLearning to Teach Mathematics in the Secondary School combines theory and practice to present a broad introduction to the opportunities and challenges of teaching mathematics in the secondary school classroom. This fourth edition has been fully updated to reflect the latest changes to the curriculum and research in the field, taking into account key developments in teacher training and education, including examinations and assessment. Written specifically with the new and student teacher in mind, the book covers a wide range of issues related to the teaching of mathematics, such as: why we teach mathematics the place of mathematics in the National Curriculum planning, teaching and assessing for mathematics learning how to communicate mathematically using digital technology to advance mathematical learning working with students with special educational needs post-16 teaching the importance of professional development the affective dimension when learning mathematics, including motivation, confidence and resilience Already a major text for many university teaching courses, this revised edition features a glossary of useful terms and carefully designed tasks to prompt critical reflection and support thinking and writing up to Masters Level. Issues of professional development are also examined, as well as a range of teaching approaches and styles from whole-class strategies to personalised learning, helping you to make the most of school experience, during your training and beyond. Designed for use as a core textbook, Learning to Teach Mathematics in the Secondary School provides essential guidance and advice for all those who aspire to be effective mathematics teachers.
Learning to Teach Mathematics, Second Edition
by Maria GouldingRefreshed with new research, this second edition links the practical experience gained in school placements with the theoretical background surrounding it. Guidance is drawn from accounts of experiences in actual classrooms, giving students and newly qualified teachers practical ideas for planning and evaluating pupils' learning and insights into their own development as new teachers.
Learning with Uncertainty
by Xizhao Wang Junhai ZhaiLearning with uncertainty covers a broad range of scenarios in machine learning, this book mainly focuses on: (1) Decision tree learning with uncertainty, (2) Clustering under uncertainty environment, (3) Active learning based on uncertainty criterion, and (4) Ensemble learning in a framework of uncertainty. The book starts with the introduction to uncertainty including randomness, roughness, fuzziness and non-specificity and then comprehensively discusses a number of key issues in learning with uncertainty, such as uncertainty representation in learning, the influence of uncertainty on the performance of learning system, the heuristic design with uncertainty, etc. <P><P>Most contents of the book are our research results in recent decades. The purpose of this book is to help the readers to understand the impact of uncertainty on learning processes. It comes with many examples to facilitate understanding. The book can be used as reference book or textbook for researcher fellows, senior undergraduates and postgraduates majored in computer science and technology, applied mathematics, automation, electrical engineering, etc.
Leases for Lives: Life Contingent Contracts and the Emergence of Actuarial Science in Eighteenth-Century England
by David R. BellhouseMany historians of insurance have commented on the disconnect between the rise of English life insurance companies in the early eighteenth century and the mathematics behind the sound pricing of life insurance products that was developed at about the same time. Insurance and annuity promoters typically ignored this mathematical work. Bellhouse explores this issue, and shows that the early mathematical work was not motivated by insurance but instead by the fair valuation of life contingent contracts related to property. Even the work of the mathematician James Dodson in the creation of the Equitable Life Assurance Society, offering sound actuarially based premiums, did not change the industry in any significant way. The tipping point was a crisis in 1770 in which the philosopher and mathematician Richard Price, as well as other mathematicians, showed that a dozen or more recently formed annuity societies could not meet their financial obligations and were inviable.
Least Squares Data Fitting with Applications
by Per Christian Hansen Víctor Pereyra Godela SchererA lucid explanation of the intricacies of both simple and complex least squares methods.As one of the classical statistical regression techniques, and often the first to be taught to new students, least squares fitting can be a very effective tool in data analysis. Given measured data, we establish a relationship between independent and dependent variables so that we can use the data predictively. The main concern of Least Squares Data Fitting with Applications is how to do this on a computer with efficient and robust computational methods for linear and nonlinear relationships. The presentation also establishes a link between the statistical setting and the computational issues.In a number of applications, the accuracy and efficiency of the least squares fit is central, and Per Christian Hansen, Víctor Pereyra, and Godela Scherer survey modern computational methods and illustrate them in fields ranging from engineering and environmental sciences to geophysics. Anyone working with problems of linear and nonlinear least squares fitting will find this book invaluable as a hands-on guide, with accessible text and carefully explained problems.Included are• an overview of computational methods together with their properties and advantages• topics from statistical regression analysis that help readers to understand and evaluate the computed solutions• many examples that illustrate the techniques and algorithmsLeast Squares Data Fitting with Applications can be used as a textbook for advanced undergraduate or graduate courses and professionals in the sciences and in engineering.
Leavitt Path Algebras
by Mercedes Siles Molina Gene Abrams Pere AraThis book offers a comprehensive introduction by three of the leading experts in the field, collecting fundamental results and open problems in a single volume. Since Leavitt path algebras were first defined in 2005, interest in these algebras has grown substantially, with ring theorists as well as researchers working in graph C*-algebras, group theory and symbolic dynamics attracted to the topic. Providing a historical perspective on the subject, the authors review existing arguments, establish new results, and outline the major themes and ring-theoretic concepts, such as the ideal structure, Z-grading and the close link between Leavitt path algebras and graph C*-algebras. The book also presents key lines of current research, including the Algebraic Kirchberg Phillips Question, various additional classification questions, and connections to noncommutative algebraic geometry. Leavitt Path Algebras will appeal to graduate students and researchers working in the field and related areas, such as C*-algebras and symbolic dynamics. With its descriptive writing style, this book is highly accessible.
Leavitt Path Algebras and Classical K-Theory (Indian Statistical Institute Series)
by Roozbeh Hazrat A. A. Ambily B. SuryThe book offers a comprehensive introduction to Leavitt path algebras (LPAs) and graph C*-algebras. Highlighting their significant connection with classical K-theory—which plays an important role in mathematics and its related emerging fields—this book allows readers from diverse mathematical backgrounds to understand and appreciate these structures. The articles on LPAs are mostly of an expository nature and the ones dealing with K-theory provide new proofs and are accessible to interested students and beginners of the field. It is a useful resource for graduate students and researchers working in this field and related areas, such as C*-algebras and symbolic dynamics.
Leben in Exklusionssphären: Perspektiven auf Wohnangebote für Menschen mit komplexem Unterstützungsbedarf
by Martin F. ReichsteinIm Bereich wohnbezogener Hilfen für Menschen mit sogenannter geistiger Behinderung treten systemisch und systematisch ,Exklusionssphären‘ in Form von hochspezialisierten Angeboten sowie ,Resteinrichtungen‘ auf. Hiervon sind aktuell Menschen mit komplexen Unterstützungsbedarfen besonders betroffen. Der Autor untersucht am Beispiel von Menschen mit sogenannter geistiger Behinderung und herausforderndem Verhalten, schwerer bzw. mehrfacher Beeinträchtigung sowie fortgeschrittenem bzw. hohem Lebensalter explorativ das Entstehen von ,Exklusionssphären‘ sowie deren Auswirkungen auf die individuelle Lebensqualität und die persönlichen Sozialräume betroffener Personen.
Lebensqualität pflegebedürftiger älterer Menschen: Eine Längsschnittstudie unter Berücksichtigung des Pflegeheimeinzugs
by Romana WinklerRomana Winkler untersucht den Einfluss des Pflegeheimeinzugs sowie ausgewählter Aspekte sozialer Ungleichheit auf die Lebensqualität pflege- und betreuungsbedürftiger älterer Menschen in Österreich. Dies erfolgt durch eine Längsschnittstudie beim Einzug in das Pflegeheim sowie eine und zwölf Wochen danach, und zwar durch eine Mehrebenenanalyse, die strukturelle Unterschiede zwischen Pflegeheimen mitberücksichtigt. Detailliert analysiert die Autorin Einflussfaktoren auf die Gesamt-Lebensqualität und Teilbereiche sowie Gründe für eine Verbesserung bzw. Verschlechterung. Sie liefert Anregungen für weitere Forschungsaktivitäten und konkrete Handlungsempfehlungen für die Praxis.
Lebensversicherungsmathematik: Basiswissen zur Technik der deutschen Lebensversicherung
by Jens KahlenbergDieses Buch gibt eine ausführliche und verständliche Einführung in die Technik der deutschen Lebensversicherung. Nach einer allgemeinen Einleitung werden die Rechnungsgrundlagen Zins, Biometrie und Kosten, die Berechnung von Prämien, Leistungen und Reserven sowie die Überschussbeteiligung erläutert. Über diese klassische Lebensversicherungsmathematik hinaus geht der Autor detailliert auf die Darstellung fondsgebundener Tarife ein und beschreibt auch das komplexe Teilgebiet der Berufsunfähigkeitsversicherung in aller Tiefe. Zudem werden Aspekte der Pflegeversicherung sowie Fragestellungen des Jahresabschlusses und der Bilanzierung behandelt. Zahlreiche Übungsaufgaben inklusive Lösungen unterstützen das Selbststudium und veranschaulichen die versicherungstechnischen Vorgehensweisen. Ein umfassender Anhang mit biometrischen Rechnungsgrundlagen, mathematischen Grundformeln, Wörterbuch und Symbolverzeichnis rundet das Werk ab.
Lebenswirklichkeiten des Alter(n)s: Vielfalt, Heterogenität, Ungleichheit
by Werner Schneider Stephanie StadelbacherAlter(n) ist eine gesellschaftliche Konstruktion, die sich abhängig von soziokulturellen und sozialstrukturellen Rahmenbedingungen auf der einen Seite und lebensweltlichen Bezügen, Interaktions- und Beziehungssystemen auf der anderen Seite realisiert. Im Sammelband soll ein Blick in die verschiedenen Lebenswelten der Älterwerdenden und Alten im Sinne von gesellschaftlich gerahmten, sozial gestalteten und subjektiv wahrgenommenen Wirklichkeiten des Alter(n)s in unserer Gesellschaft geworfen werden. Als relevante lebensweltliche Bereiche werden hier Gesundheit, Arbeit (und Freizeit), Wohnen, Familie/soziale Beziehungen, Sozialraum, soziales Engagement bis hin zu Pflege und Lebensende betrachtet. In den Beiträgen sollen Gegenwartsanalysen und mögliche Zukunftsszenarien zum Älterwerden und Altsein in unserer Gesellschaft skizziert werden.
Lebesgue Integral (Compact Textbooks in Mathematics)
by Liviu C. FlorescuThis book presents a compact and self-contained introduction to the theory of measure and integration. The introduction into this theory is as necessary (because of its multiple applications) as difficult for the uninitiated. Most measure theory treaties involve a large amount of prerequisites and present crucial theoretical challenges. By taking on another approach, this textbook provides less experienced readers with material that allows an easy access to the definition and main properties of the Lebesgue integral. The book will be welcomed by upper undergraduate/early graduate students who wish to better understand certain concepts and results of probability theory, statistics, economic equilibrium theory, game theory, etc., where the Lebesgue integral makes its presence felt throughout. The book can also be useful to students in the faculties of mathematics, physics, computer science, engineering, life sciences, as an introduction to a more in-depth study of measure theory.
Lebesgue Integration (Dover Books on Mathematics)
by J. H. WilliamsonThis concise introduction to Lebesgue integration is geared toward advanced undergraduate math majors and may be read by any student possessing some familiarity with real variable theory and elementary calculus. The self-contained treatment features exercises at the end of each chapter that range from simple to difficult. The approach begins with sets and functions and advances to Lebesgue measure, including considerations of measurable sets, sets of measure zero, and Borel sets and nonmeasurable sets. A two-part exploration of the integral covers measurable functions, convergence theorems, convergence in mean, Fourier theory, and other topics. A chapter on calculus examines change of variables, differentiation of integrals, and integration of derivatives and by parts. The text concludes with a consideration of more general measures, including absolute continuity and convolution products.
Lebesgue Points and Summability of Higher Dimensional Fourier Series
by Ferenc WeiszThis monograph presents the summability of higher dimensional Fourier series, and generalizes the concept of Lebesgue points. Focusing on Fejér and Cesàro summability, as well as theta-summation, readers will become more familiar with a wide variety of summability methods. Within the theory of higher dimensional summability of Fourier series, the book also provides a much-needed simple proof of Lebesgue’s theorem, filling a gap in the literature. Recent results and real-world applications are highlighted as well, making this a timely resource. The book is structured into four chapters, prioritizing clarity throughout. Chapter One covers basic results from the one-dimensional Fourier series, and offers a clear proof of the Lebesgue theorem. In Chapter Two, convergence and boundedness results for the lq-summability are presented. The restricted and unrestricted rectangular summability are provided in Chapter Three, as well as the sufficient and necessary condition for the norm convergence of the rectangular theta-means. Chapter Four then introduces six types of Lebesgue points for higher dimensional functions. Lebesgue Points and Summability of Higher Dimensional Fourier Series will appeal to researchers working in mathematical analysis, particularly those interested in Fourier and harmonic analysis. Researchers in applied fields will also find this useful.
Lebesgue’s Theory of Integration: The Untouched Classic
by Rahul JainThis is an invaluable book that presents the original work published in French, in 1904, by Henry Leon Lebesgue, the creator of the theory of integration. Translated into English for the first time, the book offers readers a unique opportunity to explore Lebesgue’s groundbreaking ideas and delves into the mind of one of the greatest mathematicians in history. The book provides historical context and explanations that enhance readers’ comprehension and appreciation of the material. Covering a wide range of topics, from the integration before Riemann to the search for primitive functions, it offers a comprehensive understanding of Lebesgue’s theories and their significance in the field of mathematics. It inspires readers to explore further in the field, stimulates new ideas, and opens avenues for future research. The book bridges the gap between theory and practice by providing examples and applications that contributed to the development of Lebesgue integration theory. The book serves as a valuable resource for courses in analysis, measure theory, and Lebesgue integration theory, providing students with the opportunity to study the original work of Lebesgue and deepen their understanding of integration theory. It is meant for a broad audience, including advanced undergraduate and graduate students, mathematics scholars, researchers, educators, and enthusiasts, seeking a comprehensive understanding of Lebesgue’s theories and the historical development of integration theory. Mathematicians and researchers will find this book essential for its historical significance and the preservation of important mathematical literature.
Lecture Notes in Real Analysis (Compact Textbooks in Mathematics)
by Xiaochang WangThis compact textbook is a collection of the author’s lecture notes for a two-semester graduate-level real analysis course. While the material covered is standard, the author’s approach is unique in that it combines elements from both Royden’s and Folland’s classic texts to provide a more concise and intuitive presentation. Illustrations, examples, and exercises are included that present Lebesgue integrals, measure theory, and topological spaces in an original and more accessible way, making difficult concepts easier for students to understand. This text can be used as a supplementary resource or for individual study.
Lecture Notes on Geometry of Numbers (University Texts in the Mathematical Sciences)
by R. J. Hans-Gill Madhu Raka Ranjeet SehmiThis book serves as an illuminating introduction to the intricacies of the geometry of numbers. It commences by exploring basic concepts of convex sets and lattices in Euclidean space and goes on to delve into Minkowski’s fundamental theorem for convex bodies and its applications. It discusses critical determinants and successive minima before explaining the core results of packings and coverings. The text goes on to delve into the significance of renowned conjectures such as Minkowski’s conjecture regarding the product of linear forms, Watson’s conjecture, and the conjecture of Bambah, Dumir, and Hans-Gill concerning non-homogeneous minima of indefinite quadratic forms. Dedicated to Prof. R.P. Bambah on his 98th birthday, a living legend of number theory in India, this comprehensive book addresses both homogeneous and non-homogeneous problems, while sprinkling in historical insights and highlighting unresolved questions in the field. It is ideally suited for beginnersembarking on self-study as well as for use as a text for a one- or two-semester introductory course.
Lecture Notes on Newtonian Mechanics: Lessons from Modern Concepts
by Guilherme de Berredo-Peixoto Ilya L. ShapiroOne could make the claim that all branches of physics are basically generalizations of classical mechanics. It is also often the first course which is taught to physics students. The approach of this book is to construct an intermediate discipline between general courses of physics and analytical mechanics, using more sophisticated mathematical tools. The aim of this book is to prepare a self-consistent and compact text that is very useful for teachers as well as for independent study.
Lecture Notes on Numerical Methods for Hyperbolic Equations
by Elena Vázquez-CendónThis volume contains the lecture notes of the Short Course on Numerical Methods for Hyperbolic Equations (Faculty of Mathematics, University of Santiago de Compostela, Spain, 2-4 July 2011). The course was organized in recognition of Prof. Eleuterio Toro‘s contribution to education and training on numerical methods for partial differential equation
Lecture Notes on the General Theory of Relativity
by Øyvind GrønThis book is the result of more than twenty years of lecturing a master course on the General Theory of Relativity at the University of Oslo, Norway, by Dr. Øyvind Grøn. The text has been continuously updated by Dr. Grøn and is written so students can follow the deductions all the way throughout the book. The conceptual content of the general theory of relativity is presented briefly but reasonably and completely. Both bachelor students and master students will find the text useful as the manuscript is organized to easily find the topics one wants to read about, with separate lists of contents, figures, definitions, examples, and an index.
Lecture Notes: Epidemiology, Evidence-based Medicine and Public Health (Lecture Notes)
by Yoav Ben-Shlomo Sara Brookes Matthew HickmanTranslating the evidence from the bedside to populations This sixth edition of the best-selling Epidemiology, Evidence-based Medicine and Public Health Lecture Notes equips students and health professionals with the basic tools required to learn, practice and teach epidemiology and health prevention in a contemporary setting. The first section, ‘Epidemiology’, introduces the fundamental principles and scientific basis behind work to improve the health of populations, including a new chapter on genetic epidemiology. Applying the current and best scientific evidence to treatment at both individual and population level is intrinsically linked to epidemiology and public health, and has been introduced in a brand new second section: ‘Evidence-based Medicine’ (EBM), with advice on how to incorporate EBM principles into your own practice. The third section, 'Public Health', introduces students to public health practice, including strategies and tools used to prevent disease, prolong life, reduce inequalities, and includes global health. Thoroughly updated throughout, including new studies and cases from around the globe, key learning features include: Learning objectives and key points in every chapter Extended coverage of critical appraisal and data interpretation A brand new self-assessment section of SAQs and ’True/False’ questions for each topic A glossary to quickly identify the meaning of key terms, all of which are highlighted for study and exam preparation Further reading suggestions on each topic Whether approaching these topics for the first time, starting a special study module or placement, or looking for a quick-reference summary, this book offers medical students, junior doctors, and public health students an invaluable collection of theoretical and practical information.
Lectures and Surveys on G2-Manifolds and Related Topics (Fields Institute Communications #84)
by Spiro Karigiannis Naichung Conan Leung Jason D. LotayThis book, one of the first on G2 manifolds in decades, collects introductory lectures and survey articles largely based on talks given at a workshop held at the Fields Institute in August 2017, as part of the major thematic program on geometric analysis. It provides an accessible introduction to various aspects of the geometry of G2 manifolds, including the construction of examples, as well as the intimate relations with calibrated geometry, Yang-Mills gauge theory, and geometric flows. It also features the inclusion of a survey on the new topological and analytic invariants of G2 manifolds that have been recently discovered. The first half of the book, consisting of several introductory lectures, is aimed at experienced graduate students or early career researchers in geometry and topology who wish to familiarize themselves with this burgeoning field. The second half, consisting of numerous survey articles, is intended to be useful to both beginners and experts in the field.
Lectures in Algebraic Combinatorics: Young's Construction, Seminormal Representations, SL(2) Representations, Heaps, Basics on Finite Fields (Lecture Notes in Mathematics #2277)
by Adriano M. Garsia Ömer EğecioğluCapturing Adriano Garsia's unique perspective on essential topics in algebraic combinatorics, this book consists of selected, classic notes on a number of topics based on lectures held at the University of California, San Diego over the past few decades. The topics presented share a common theme of describing interesting interplays between algebraic topics such as representation theory and elegant structures which are sometimes thought of as being outside the purview of classical combinatorics. The lectures reflect Garsia’s inimitable narrative style and his exceptional expository ability. The preface presents the historical viewpoint as well as Garsia's personal insights into the subject matter. The lectures then start with a clear treatment of Alfred Young's construction of the irreducible representations of the symmetric group, seminormal representations and Morphy elements. This is followed by an elegant application of SL(2) representations to algebraic combinatorics. The last two lectures are on heaps, continued fractions and orthogonal polynomials with applications, and finally there is an exposition on the theory of finite fields. The book is aimed at graduate students and researchers in the field.
Lectures in Feedback Design for Multivariable Systems
by Alberto IsidoriThis book focuses on methods that relate, in one form or another, to the "small-gain theorem". It is aimed at readers who are interested in learning methods for the design of feedback laws for linear and nonlinear multivariable systems in the presence of model uncertainties. With worked examples throughout, it includes both introductory material and more advanced topics. Divided into two parts, the first covers relevant aspects of linear-systems theory, the second, nonlinear theory. In order to deepen readers' understanding, simpler single-input-single-output systems generally precede treatment of more complex multi-input-multi-output (MIMO) systems and linear systems precede nonlinear systems. This approach is used throughout, including in the final chapters, which explain the latest advanced ideas governing the stabilization, regulation, and tracking of nonlinear MIMO systems. Two major design problems are considered, both in the presence of model uncertainties: asymptotic stabilization with a "guaranteed region of attraction" of a given equilibrium point and asymptotic rejection of the effect of exogenous (disturbance) inputs on selected regulated outputs. Much of the introductory instructional material in this book has been developed for teaching students, while the final coverage of nonlinear MIMO systems offers readers a first coordinated treatment of completely novel results. The worked examples presented provide the instructor with ready-to-use material to help students to understand the mathematical theory. Readers should be familiar with the fundamentals of linear-systems and control theory. This book is a valuable resource for students following postgraduate programs in systems and control, as well as engineers working on the control of robotic, mechatronic and power systems.
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.