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Lectures on the Calculus of Variations (Dover Books on Mathematics)
by Oskar BolzaThis pioneering modern treatise on the calculus of variations studies the evolution of the subject from Euler to Hilbert. The text addresses basic problems with sufficient generality and rigor to offer a sound introduction for serious study. It provides clear definitions of the fundamental concepts, sharp formulations of the problems, and rigorous demonstrations of their solutions. Many examples are solved completely, and systematic references are given for each theorem upon its first appearance. Initial chapters address the first and second variation of the integral, and succeeding chapters cover the sufficient conditions for an extremum of the integral and Weierstrass's theory of the problem in parameter-representation; Kneser's extension of Weierstrass's theory to cover the case of variable end-points; and Weierstrass's theory of the isoperimetric problems. The final chapter presents a thorough proof of Hilbert's existence theorem.
Lectures on the Coupling Method
by Torgny LindvallAn important tool in probability theory and its applications, the coupling method is primarily used in estimates of total variation distances. The method also works well in establishing inequalities, and it has proven highly successful in the study of Markov and renewal process asymptotics. This text represents a detailed, comprehensive examination of the method and its broad variety of applications. Readers progress from simple to advanced topics, with end-of-discussion notes that reinforce the preceding material. Topics include renewal theory, Markov chains, Poisson approximation, ergodicity, and Strassen's theorem. A practical and easy-to-use reference, this volume will accommodate the diverse needs of professionals in the fields of statistics, mathematics, and operational research, as well as those of teachers and students.
Lectures on the Mechanical Foundations of Thermodynamics (SpringerBriefs in Physics)
by Michele CampisiThis brief provides a modern pedagogical exposition of the mechanical approach to statistical mechanics initiated by Boltzmann with his early works (1866-1871). Despite the later contribution by Helmholtz, Boltzmann himself (1884-1887), Gibbs, P. Hertz, and Einstein, the mechanical approach remained almost unknown to the modern reader, in favour of the celebrated combinatorial approach, developed by Boltzmann himself during his probabilistic turn (1876-1884). The brief constitutes an ideal continuation of a graduate course of classical mechanics and requires knowledge of basic calculus in many dimension (including differential forms), thermodynamics, probability theory, besides Hamiltonian mechanics. The cornerstone of the whole presentation is the ergodic hypothesis. Special attention is devoted to Massieu potentials (the Legendre transforms of the entropy) which are most natural in statistical mechanics, and also allow for a more direct treatment of the topic of ensemble equivalence.
Lectures on the Nearest Neighbor Method
by Luc Devroye Gérard BiauThis text presents a wide-ranging and rigorous overview of nearest neighbor methods, one of the most important paradigms in machine learning. Now in one self-contained volume, this book systematically covers key statistical, probabilistic, combinatorial and geometric ideas for understanding, analyzing and developing nearest neighbor methods. Gérard Biau is a professor at Université Pierre et Marie Curie (Paris). Luc Devroye is a professor at the School of Computer Science at McGill University (Montreal).
Lectures on the Philosophy of Mathematics
by Joel David HamkinsAn introduction to the philosophy of mathematics grounded in mathematics and motivated by mathematical inquiry and practice.In this book, Joel David Hamkins offers an introduction to the philosophy of mathematics that is grounded in mathematics and motivated by mathematical inquiry and practice. He treats philosophical issues as they arise organically in mathematics, discussing such topics as platonism, realism, logicism, structuralism, formalism, infinity, and intuitionism in mathematical contexts. He organizes the book by mathematical themes--numbers, rigor, geometry, proof, computability, incompleteness, and set theory--that give rise again and again to philosophical considerations.
Lectures on the Poisson Process (Institute of Mathematical Statistics Textbooks #7)
by Mathew Penrose Günter LastThe Poisson process, a core object in modern probability, enjoys a richer theory than is sometimes appreciated. This volume develops the theory in the setting of a general abstract measure space, establishing basic results and properties as well as certain advanced topics in the stochastic analysis of the Poisson process. Also discussed are applications and related topics in stochastic geometry, including stationary point processes, the Boolean model, the Gilbert graph, stable allocations, and hyperplane processes. Comprehensive, rigorous, and self-contained, this text is ideal for graduate courses or for self-study, with a substantial number of exercises for each chapter. Mathematical prerequisites, mainly a sound knowledge of measure-theoretic probability, are kept in the background, but are reviewed comprehensively in the appendix. The authors are well-known researchers in probability theory; especially stochastic geometry. Their approach is informed both by their research and by their extensive experience in teaching at undergraduate and graduate levels.
Lectures on the Random Field Ising Model: From Parisi-Sourlas Supersymmetry to Dimensional Reduction (SpringerBriefs in Physics)
by Slava RychkovThis book is about the Random Field Ising Model (RFIM) – a paradigmatic spin model featuring a frozen disordering field. The focus is on the second-order phase transition between the paramagnetic and ferromagnetic phases, and the associated critical exponents. The book starts by summarizing the current knowledge about the RFIM from experiments, numerical simulations and rigorous mathematical results. It then reviews the classic theoretical works from the 1970’s which suggested a property of dimensional reduction – that the RFIM critical exponents should be the same as for the ordinary, non-disordered, Ising model of lower dimensionality, and related this an emergent Parisi-Sourlas supersymmetry. As is now known, these remarkable properties only hold when the spatial dimensionality of the model is larger than a critical dimension. The book presents a method to estimate the critical dimension, using standard tools such as the replica trick and perturbative renormalization group, whose result is in agreement with the numerical simulations. Some more elementary steps in the derivations are left as exercises for the readers. This book is of interest to researchers, PhD students and advanced master students specializing in statistical field theory.
Lectures on Urban Economics
by Jan K. BruecknerA rigorous but nontechnical treatment of major topics in urban economics. Lectures on Urban Economics offers a rigorous but nontechnical treatment of major topics in urban economics. To make the book accessible to a broad range of readers, the analysis is diagrammatic rather than mathematical. Although nontechnical, the book relies on rigorous economic reasoning. In contrast to the cursory theoretical development often found in other textbooks, Lectures on Urban Economics offers thorough and exhaustive treatments of models relevant to each topic, with the goal of revealing the logic of economic reasoning while also teaching urban economics. Topics covered include reasons for the existence of cities, urban spatial structure, urban sprawl and land-use controls, freeway congestion, housing demand and tenure choice, housing policies, local public goods and services, pollution, crime, and quality of life. Footnotes throughout the book point to relevant exercises, which appear at the back of the book. These 22 extended exercises (containing 125 individual parts) develop numerical examples based on the models analyzed in the chapters. Lectures on Urban Economics is suitable for undergraduate use, as background reading for graduate students, or as a professional reference for economists and scholars interested in the urban economics perspective.
Lectures on Urban Economics
by Brueckner Jan K.Lectures on Urban Economics offers a rigorous but nontechnical treatment of major topics in urban economics. To make the book accessible to a broad range of readers, the analysis is diagrammatic rather than mathematical. Although nontechnical, the book relies on rigorous economic reasoning. In contrast to the cursory theoretical development often found in other textbooks, Lectures on Urban Economics offers thorough and exhaustive treatments of models relevant to each topic, with the goal of revealing the logic of economic reasoning while also teaching urban economics. Topics covered include reasons for the existence of cities, urban spatial structure, urban sprawl and land-use controls, freeway congestion, housing demand and tenure choice, housing policies, local public goods and services, pollution, crime, and quality of life. Footnotes throughout the book point to relevant exercises, which appear at the back of the book. These 22 extended exercises (containing 125 individual parts) develop numerical examples based on the models analyzed in the chapters. Lectures on Urban Economics is suitable for undergraduate use, as background reading for graduate students, or as a professional reference for economists and scholars interested in the urban economics perspective.
Lectures on Visco-Plastic Fluid Mechanics (CISM International Centre for Mechanical Sciences #583)
by Guillaume Ovarlez Sarah HormoziThe book is designed for advanced graduate students as well as postdoctoral researchers across several disciplines (e.g., mathematics, physics and engineering), as it provides them with tools and techniques that are essential in performing research on the flow problems of visco-plastic fluids. The following topics are treated: analysis of classical visco-plastic fluid modelsmathematical modeling of flows of visco-plastic fluidscomputing flows of visco-plastic fluidsrheology of visco-plastic fluids and visco-plastic suspensionsapplication of visco-plastic fluids in engineering sciencescomplex flows of visco-plastic fluids.
Lee de Forest
by Mike AdamsThe life-long inventor, Lee de Forest invented the three-element vacuum tube used between 1906 and 1916 as a detector, amplifier, and oscillator of radio waves. Beginning in 1918 he began to develop a light valve, a device for writing and reading sound using light patterns. While he received many patents for his process, he was initially ignored by the film industry. In order to promote and demonstrate his process he made several hundred sound short films, he rented space for their showing; he sold the tickets and did the publicity to gain audiences for his invention. Lee de Forest officially brought sound to film in 1919. Lee De Forest: King of Radio, Television, and Film is about both invention and early film making; de Forest as the scientist and producer, director, and writer of the content. This book tells the story of de Forest's contribution in changing the history of film through the incorporation of sound. The text includes primary source historical material, U.S. patents and richly-illustrated photos of Lee de Forest's experiments. Readers will greatly benefit from an understanding of the transition from silent to audio motion pictures, the impact this had on the scientific community and the popular culture, as well as the economics of the entertainment industry.
The Lefschetz Properties
by Junzo Watanabe Yasuhide Numata Toshiaki Maeno Hideaki Morita Akihito Wachi Tadahito HarimaThis is a monograph which collects basic techniques, major results and interesting applications of Lefschetz properties of Artinian algebras. The origin of the Lefschetz properties of Artinian algebras is the Hard Lefschetz Theorem, which is a major result in algebraic geometry. However, for the last two decades, numerous applications of the Lefschetz properties to other areas of mathematics have been found, as a result of which the theory of the Lefschetz properties is now of great interest in its own right. It also has ties to other areas, including combinatorics, algebraic geometry, algebraic topology, commutative algebra and representation theory. The connections between the Lefschetz property and other areas of mathematics are not only diverse, but sometimes quite surprising, e.g. its ties to the Schur-Weyl duality. This is the first book solely devoted to the Lefschetz properties and is the first attempt to treat those properties systematically.
Left to Their Own Devices: How Digital Natives Are Reshaping the American Dream
by Julie M. AlbrightA sociologist explores the many ways that digital natives' interaction with technology has changed their relationship with people, places, jobs, and other stabilizing structures and created a new way of life that is at odds with the American Dream of past generations.Digital natives are hacking the American Dream. Young people brought up with the Internet, smartphones, and social media are quickly rendering old habits, values, behaviors, and norms a distant memory--creating the greatest generation gap in history. In this eye-opening book, digital sociologist Julie M. Albright looks at the many ways in which younger people, facilitated by technology, are coming "untethered" from traditional aspirations and ideals, and asks: What are the effects of being disconnected from traditional, stabilizing social structures like churches, marriage, political parties, and long-term employment? What does it mean to be human when one's ties to people, places, jobs, and societal institutions are weakened or broken, displaced by digital hyper-connectivity? Albright sees both positives and negatives. On the one hand, mobile connectivity has given digital nomads the unprecedented opportunity to work or live anywhere. But, new threats to well-being are emerging, including increased isolation, anxiety, and loneliness, decreased physical exercise, ephemeral relationships, fragmented attention spans, and detachment from the calm of nature.In this time of rapid, global, technologically driven change, this book offers fresh insights into the unintended societal and psychological implications of lives exclusively lived in a digital world.
The Legacy of Alladi Ramakrishnan in the Mathematical Sciences
by Krishnaswami Alladi John R. Klauder Calyampudi R. RaoIn the spirit of Alladi Ramakrishnan's profound interest and contributions to three fields of science -- Mathematics, Statistics, and Physics -- this volume contains invited surveys and research articles from prominent members of these communities who also knew Ramakrishnan personally and greatly respected his influence in these areas of science. Historical photos, telegrams, and biographical narratives of Alladi Ramakrishnan's illustrious career of special interest are included as well.
The Legacy of Felix Klein (ICME-13 Monographs)
by Hans-Georg Weigand William McCallum Marta Menghini Michael Neubrand Gert SchubringThis open access book provides an overview of Felix Klein’s ideas, highlighting developments in university teaching and school mathematics related to Klein’s thoughts, stemming from the last century. It discusses the meaning, importance and the legacy of Klein’s ideas today and in the future, within an international, global context. Presenting extended versions of the talks at the Thematic Afternoon at ICME-13, the book shows that many of Klein’s ideas can be reinterpreted in the context of the current situation, and offers tips and advice for dealing with current problems in teacher education and teaching mathematics in secondary schools. It proves that old ideas are timeless, but that it takes competent, committed and assertive individuals to bring these ideas to life. Throughout his professional life, Felix Klein emphasised the importance of reflecting upon mathematics teaching and learning from both a mathematical and a psychological or educational point of view. He also strongly promoted the modernisation of mathematics in the classroom, and developed ideas on university lectures for student teachers, which he later consolidated at the beginning of the last century in the three books on elementary mathematics from a higher standpoint.
The Legacy of Tatjana Afanassjewa: Philosophical Insights from the Work of an Original Physicist and Mathematician (Women in the History of Philosophy and Sciences #7)
by Jos Uffink Giovanni Valente Charlotte Werndl Lena ZuchowskiThis book presents a collection of essays that explore the life and works of Tatjana Afanassjewa (1876–1964), a Russian–Dutch physicist–mathematician. Readers will discover a scientist whose work on the foundations of thermodynamics significantly influenced the field itself as well as the philosophy of physics. This book highlights the philosophical consequences of her work in physics and mathematics and discusses historical aspects of her writings on the foundations of physics. In addition, it features English translations and critical reviews of key selections from her texts.First and foremost, the book highlights the numerous contributions that Afanassjewa made to the field. In particular, the authors examine her work on the foundations of thermodynamics and statistical physics, starting in the 1920s and extending to 1956, well after the untimely death of her husband in 1933. They also explore her almost entirely forgotten work on the didactics of mathematics. In addition, they discuss her influential collaboration with her husband, the Austrian physicist Paul Ehrenfest (1880–1933).The portrait that emerges is that of a highly original physicist and mathematician, whose legacy continues to influence scientists and philosophers today and whose lesser-known works deserve more attention than they have received. Readers will find a rich body of work that continues to this day to yield insights into the foundations of physics and mathematics.
Lehr-Lern-Labore: Konzepte und deren Wirksamkeit in der MINT-Lehrpersonenbildung
by Burkhard Priemer Jürgen RothAn verschiedenen Hochschulen werden in den MINT-Fächern Schülerlabore in die Lehrpersonenbildung integriert. In diesen - als Lehr-Lern-Labore bezeichneten - Einrichtungen werden MINT-Lernumgebungen für Schülerinnen und Schüler, Veranstaltungen der Lehrpersonenbildung und an vielen Standorten auch fachdidaktische Forschung fruchtbar miteinander verknüpft. Das Ziel ist dabei, evidenzbasiert innovative Lehrkonzepte für Schule und Hochschule zu entwickeln und zu implementieren. In diesem Band werden Lehr-Lern-Labore zunächst allgemein beschrieben und dann durch zahlreiche Beispiele von Konzepten verschiedener Hochschulstandorte illustriert. Darüber hinaus wird berichtet, welche Wirksamkeit Lehr-Lern-Labore bei der Förderung von Kompetenzen zukünftiger Lehrpersonen haben und wie Studierende diese Einrichtungen wahrnehmen. Die vorgestellten Forschungsergebnisse, die aus einem Verbund von sechs Hochschulen stammen, sollen durch diesen Band weiteren Standorten zugänglich gemacht werden. Dieses Buch richtet sich an Studierende und Dozierende der Lehrpersonenbildung in Hochschulen - insbesondere in den MINT-Fachdidaktiken - sowie an Personen in Schule und Referendariat.
Lehrerkompetenzen zum Unterrichten mathematischer Modellierung: Konzepte und Transfer (Realitätsbezüge im Mathematikunterricht)
by Rita Borromeo Ferri Werner BlumIm vorliegenden Band wird verdeutlicht, welche Kompetenzen Lehrkräfte haben sollten, um Schülerinnen und Schülern im Unterricht mathematisches Modellieren zu vermitteln. Im ersten Teil des Buches liegt der Fokus auf den zum Unterrichten von Modellierung in der Schule nötigen Lehrerkompetenzen. Dabei werden auch Möglichkeiten zur Förderung solcher Kompetenzen aufgezeigt. Im zweiten Teil des Buches stehen Konzepte für die Lehreraus- und -fortbildung im Vordergrund, die angehenden und praktizierenden Lehrkräften jene Kompetenzen vermitteln können. Lehrende in Schule und Hochschule wie auch Studierende des Lehramts finden in diesem Buch zahlreiche Anregungen aus Forschung und Praxis zu Lehrerkompetenzen in Bezug auf Modellieren und zu deren Erwerb.
Lehrinnovationen in der Hochschulmathematik: praxisrelevant – didaktisch fundiert – forschungsbasiert (Konzepte und Studien zur Hochschuldidaktik und Lehrerbildung Mathematik)
by Rolf Biehler Andreas Eichler Reinhard Hochmuth Stefanie Rach Niclas SchaperDieses Buch stellt praxisnahe Innovationen für Lehrveranstaltungen zur Mathematik an Hochschulen vor und richtet sich sowohl an Mathematiklehrende wie auch an Forschende in der Hochschuldidaktik Mathematik. Die Innovationen umfassen hierbei einen weiten Bereich mathematischer Lehrveranstaltungen in verschiedenen Studiengängen – von Wirtschaftswissenschaften über Ingenieurwissenschaften bis zum Lehramts- und Fachmathematikstudium. Die Lehrinnovationen wurden im Kompetenzzentrum Hochschuldidaktik Mathematik (khdm), einer gemeinsamen Einrichtung der Universitäten Hannover, Kassel und Paderborn, auf wissenschaftlicher Grundlage konzipiert, in Veranstaltungen erprobt, evaluiert und weiterentwickelt.Im ersten Teil des Bandes stehen fachlich-fachdidaktische Analysen im Vordergrund, die Grundlagen für eine Vermittlung verschiedener Fachthemen wie z. B. Folgenkonvergenz und Signaltheorie bilden. Im Teil „Schnittstellenaktivitäten“ werden erprobte Konzepte dazu vorgestellt, wie im Lehramts- und Ingenieurstudium auch in den mathematischen Fachvorlesungen Verbindungen zur Fachdidaktik bzw. Ingenieurwissenschaft hergestellt werden können. Zusätzlich wird gezeigt, dass geeignete Aufgaben die Motivation der Studierenden verbessern und die verschiedenen Studienstränge besser verknüpfen. Ein Schwerpunkt des dritten Teiles „Mathematikvorkurse“ liegt auf der Integration digitaler Angebote (Einbindung von interaktiven Apps, Lernvideos, digitales Assessment mit STACK). Im vierten Teil des Bandes geht es um die Förderung mathematikspezifischer Arbeitsweisen und insbesondere um Vorschläge zur Neugestaltung von Vorlesungen und Übungsgruppen, die auf eine stärkere kognitive Aktivierung und erfolgreichere Lernprozesse der Studierenden zielen. Außerdem stehen Veranstaltungen im Fokus, die neben der Vermittlung fachlicher Inhalte auch die Vermittlung mathematischer Arbeitsweisen explizit ins Zentrum rücken, z. B. das selbstregulierte Nacharbeiten von Vorlesungen oder das selbstständige Beweisen.
Leibniz Algebras: Structure and Classification
by Shavkat Ayupov Bakhrom Omirov Isamiddin RakhimovLeibniz Algebras: Structure and Classification is designed to introduce the reader to the theory of Leibniz algebras. Leibniz algebra is the generalization of Lie algebras. These algebras preserve a unique property of Lie algebras that the right multiplication operators are derivations. They first appeared in papers of A.M Blokh in the 1960s, under the name D-algebras, emphasizing their close relationship with derivations. The theory of D-algebras did not get as thorough an examination as it deserved immediately after its introduction. Later, the same algebras were introduced in 1993 by Jean-Louis Loday , who called them Leibniz algebras due to the identity they satisfy. The main motivation for the introduction of Leibniz algebras was to study the periodicity phenomena in algebraic K-theory. Nowadays, the theory of Leibniz algebras is one of the more actively developing areas of modern algebra. Along with (co)homological, structural and classification results on Leibniz algebras, some papers with various applications of the Leibniz algebras also appear now. However, the focus of this book is mainly on the classification problems of Leibniz algebras. Particularly, the authors propose a method of classification of a subclass of Leibniz algebras based on algebraic invariants. The method is applicable in the Lie algebras case as well. Features: Provides a systematic exposition of the theory of Leibniz algebras and recent results on Leibniz algebras Suitable for final year bachelor's students, master's students and PhD students going into research in the structural theory of finite-dimensional algebras, particularly, Lie and Leibniz algebras Covers important and more general parts of the structural theory of Leibniz algebras that are not addressed in other texts
Leibniz and the Structure of Sciences: Modern Perspectives on the History of Logic, Mathematics, Epistemology (Boston Studies in the Philosophy and History of Science #337)
by Vincenzo De RisiThe book offers a collection of essays on various aspects of Leibniz’s scientific thought, written by historians of science and world-leading experts on Leibniz. The essays deal with a vast array of topics on the exact sciences: Leibniz’s logic, mereology, the notion of infinity and cardinality, the foundations of geometry, the theory of curves and differential geometry, and finally dynamics and general epistemology. Several chapters attempt a reading of Leibniz’s scientific works through modern mathematical tools, and compare Leibniz’s results in these fields with 19th- and 20th-Century conceptions of them. All of them have special care in framing Leibniz’s work in historical context, and sometimes offer wider historical perspectives that go much beyond Leibniz’s researches. A special emphasis is given to effective mathematical practice rather than purely epistemological thought. The book is addressed to all scholars of the exact sciences who have an interest in historical research and Leibniz in particular, and may be useful to historians of mathematics, physics, and epistemology, mathematicians with historical interests, and philosophers of science at large.
Leibniz on Binary: The Invention of Computer Arithmetic
by Lloyd Strickland Harry R. LewisThe first collection of Leibniz&’s key writings on the binary system, newly translated, with many previously unpublished in any language.The polymath Gottfried Wilhelm Leibniz (1646–1716) is known for his independent invention of the calculus in 1675. Another major—although less studied—mathematical contribution by Leibniz is his invention of binary arithmetic, the representational basis for today&’s digital computing. This book offers the first collection of Leibniz&’s most important writings on the binary system, all newly translated by the authors with many previously unpublished in any language. Taken together, these thirty-two texts tell the story of binary as Leibniz conceived it, from his first youthful writings on the subject to the mature development and publication of the binary system. As befits a scholarly edition, Strickland and Lewis have not only returned to Leibniz&’s original manuscripts in preparing their translations, but also provided full critical apparatus. In addition to extensive annotations, each text is accompanied by a detailed introductory &“headnote&” that explains the context and content. Additional mathematical commentaries offer readers deep dives into Leibniz&’s mathematical thinking. The texts are prefaced by a lengthy and detailed introductory essay, in which Strickland and Lewis trace Leibniz&’s development of binary, place it in its historical context, and chart its posthumous influence, most notably on shaping our own computer age.
Leibniz und die moderne Naturwissenschaft (Wissenschaft und Philosophie – Science and Philosophy – Sciences et Philosophie)
by Jürgen JostWas hat ein Gelehrter des 17.Jahrhunderts noch für die heutigen Naturwissenschaften zu sagen? Eine ganze Menge, so zeigt sich in diesem Buch. Gottfried Wilhelm Leibniz (1646-1716) war ein Universalgenie, und ihm gelangen bahnbrechende Leistungen in fast allen Gebieten der Wissenschaft, insbesondere in der Philosophie (Relativität von Raum und Zeit), der Mathematik (Infinitesimalrechnung, Determinantentheorie, binäres Zahlsystem, Konstruktion einer Rechenmaschine), der Logik (Prädikaten- und Modallogik, Konzept der möglichen Welten), der Physik (Energieerhaltung und Aktionsprinzip), der Erd- und Menschheitsgeschichte, der Rechtswissenschaft und der Theologie. Diese Leistungen waren aber nicht isoliert, sondern eingebettet in ein umfassendes System, das auf dem Satz vom Widerspruch, dem Satz vom zureichenden Grunde und dem Kontinuitätsprinzip beruhte. Erst durch das Verständnis dieses Systems erschließen sich die Einheit und die Spannweite seines Denkens. Jürgen Jost, der wie nur wenige andere die verschiedenen Wissenschaften überblickt, konfrontiert dieses leibnizsche System mit den Ansätzen, Denkweisen und Ergebnissen der heutigen Naturwissenschaften, insbesondere der Quantenphysik, der Relativitätstheorie und Kosmologie, der modernen Logik, der Evolutionsbiologie und der Hirnforschung. Es zeigt sich, dass das leibnizsche System in vieler Hinsicht noch aktuell ist und sich bewährt, aber auch in manchen Positionen revidiert werden muss. Hieraus ergeben sich neue Einsichten sowohl in das leibnizsche System als auch in die heutigen Naturwissenschaften.
Leistungseffekte beim verschachtelten und geblockten Lernen mittels Lernvideos auf Tablets: Eine empirische Untersuchung an Schülerinnen und Schülern der fünften Jahrgangsstufe (Mathematikdidaktik im Fokus)
by Maria AfroozAuslöser der vorliegenden Forschungsstudie sind die Aktualität des Forschungsthemas sowie die mangelnden empirischen Untersuchungen im Mathematikunterricht und im Zusammenhang mit digitalen Medien: Das verschachtelte Lernen als ein neuer, kognitionspsychologischer Forschungsansatz in der Mathematikdidaktik erschwert kurzfristig das Lernen, führt jedoch langfristig zu besseren Leistungen der Lernenden. Die innovative Studie vereint den Ansatz des verschachtelten Lernens mit den selbst entwickelten Lernvideos, welche optimal im Mathematikunterricht integriert werden können.
The Lemonade War (Into Reading, Trade Book #2)
by Jacqueline DaviesNIMAC-sourced textbook <p><p> Fourth-grader Evan Treski is people-smart. He’s good at talking with people, even grownups. His younger sister, Jessie, on the other hand, is math-smart, but not especially good with people. So when the siblings’ lemonade stand war begins, there really is no telling who will win—or even if their fight will ever end. Brimming with savvy marketing tips for making money at any business, definitions of business terms, charts, diagrams, and even math problems, this fresh, funny, emotionally charged novel subtly explores how arguments can escalate beyond anyone’s intent.