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WJEC GCSE Maths Intermediate: Revision Guide
by Gareth Cole Keith Pledger Joe PetranExam Board: WJECLevel: GCSESubject: MathematicsFirst Teaching: September 2015First Exam: June 2017Maximise your students' grade potential with a step-by-step approach that builds confidence through topic summaries, worked examples and exam-style questions; developed specifically for the new Mathematics specifications, with leading Assessment Consultant Keith Pledger.- Identify areas of improvement to focus on through diagnostic tests for each topic.- Develop exam skills and techniques with skills-focused exam-style questions and exam advice on common pitfalls.- Build understanding and confidence with clear explanations of each topic covering all the key information needed to succeed.- Consolidate revision with 'two weeks to go' summaries for each topic.
WJEC GCSE Maths Intermediate: Revision Guide
by Gareth Cole Keith Pledger Joe PetranExam Board: WJECLevel: GCSESubject: MathematicsFirst Teaching: September 2015First Exam: June 2017Maximise your students' grade potential with a step-by-step approach that builds confidence through topic summaries, worked examples and exam-style questions; developed specifically for the new Mathematics specifications, with leading Assessment Consultant Keith Pledger.- Identify areas of improvement to focus on through diagnostic tests for each topic.- Develop exam skills and techniques with skills-focused exam-style questions and exam advice on common pitfalls.- Build understanding and confidence with clear explanations of each topic covering all the key information needed to succeed.- Consolidate revision with 'two weeks to go' summaries for each topic.
WJEC Level 2 Certificate in Additional Mathematics
by Andrew GintyStretch and challenge students with this introduction to higher level mathematics. Including plenty of practice activities and worked examples, this book bridges the gap from GCSE to A-level, building students' reasoning and problem-solving skills in preparation for the next step.- Develop understanding of mathematics with discussion points, thought-provoking activities and rigorous exercise questions- Build confidence with notes on how prior knowledge can be applied to tackle new concepts- Develop problem-solving skills with step-by-step worked examples and practice questions- Be aware of potential misunderstandings with common pitfalls noted throughout the text- Check progress using a checklist of key points and learning outcomes at the end of each chapter- Help students to achieve their potential with two practice papers at the end of the bookAnswers to exercise questions are at the back of the book and online, alongside full worked solutions and mark schemes for the practice papers
WJEC Mathematics for A2 Level: Pure And Applied Revision Guide
by Stephen DoyleWritten by bestselling author Stephen Doyle, this student book will engage and motivate you throughout the course. // Endorsed by WJEC offering high quality support you can trust. // Thorough coverage of all the topics in the A2 Level Applied specification. // Extra support for the problem solving and unstructured questions in the specification. // Plenty of examples with worked answers throughout to enable you to check your understanding as you progress through the course. // Answers to questions are provided in order to check your work.
WJEC Mathematics for A2 Level: Pure And Applied Revision Guide
by Stephen DoyleWritten by bestselling author Stephen Doyle, this student book will engage and motivate you throughout the course. // Endorsed by WJEC offering high quality support you can trust. // Thorough coverage of all the topics in the A2 Level Pure specification. // Extra support for the problem solving and unstructured questions in the specification. // Plenty of examples with worked answers throughout to enable you to check your understanding as you progress through the course. // Answers to questions are provided in order to check your work.
WJEC Mathematics for AS Level: Applied
by Stephen DoyleWritten by bestselling author Stephen Doyle, this student book will engage and motivate you throughout the course. // Endorsed by WJEC offering high quality support you can trust. // Thorough coverage of all the topics in the AS Level Applied specification. // Extra support for the problem solving and unstructured questions in the specification. // Plenty of examples with worked answers throughout to enable you to check your understanding as you progress through the course. // Answers to questions are provided in order to check your work.
WJEC Mathematics for AS Level: Pure & Applied: Revision Guide
by Stephen DoyleWritten by bestselling author Stephen Doyle, this student book will engage and motivate you throughout the course. // Endorsed by WJEC offering high quality support you can trust. // Thorough coverage of all the topics in the AS Level Pure specification. // Extra support for the problem solving and unstructured questions in the specification. // Plenty of examples with worked answers throughout to enable you to check your understanding as you progress through the course. // Answers to questions are provided in order to check your work.
Wage Differentials and Economic Growth (Routledge Revivals)
by Pasquale SgroThis book, which was first published in 1980, is concerned with one particular branch of growth theory, namely descriptive growth theory. It is typically assumed in growth theory that both the factors and goods market are perfectly competitive. In particular this implies amongst other things that the reward to each factor is identical in each sector of the economy. In this book the assumption of identical factor rewards is relaxed and the implications of an intersectoral wage differential for economic growth are analysed. There is also some discussion on the short-term and long-run effects of minimum wage legislation on growth. This book will serve as key reading for students of economics.
Wahrheit, Beweis, Unendlichkeit: Eine mathematische Reise zu den vielseitigen Auswirkungen der Unendlichkeit
by John StillwellIn dem Buch erkundet der preisgekrönte Autor John Stillwell die Konsequenzen, die sich ergeben, wenn man die Unendlichkeit akzeptiert, und diese Konsequenzen sind vielseitig und überraschend. Der Leser benötigt nur wenig über die Schulmathematik hinausgehendes Hintergrundwissen; es reicht die Bereitschaft, sich mit ungewohnten Ideen auseinanderzusetzen. Stillwell führt den Leser sanft in die technischen Details von Mengenlehre und Logik ein, indem jedes Kapitel einem einzigen Gedankengang folgt, der mit einer natürlichen mathematischen Frage beginnt und dann anhand einer Abfolge von historischen Antworten nachvollzogen wird. Auf diese Weise zeigt der Autor, wie jede Antwort ihrerseits zu neuen Fragen führt, aus denen wiederum neue Begriffe und Sätze entstehen.Jedes Kapitel endet mit einem Abschnitt „Historischer Hintergrund“, der das Thema in den größeren Zusammenhang der Mathematik und ihrer Geschichte einordnet.
Wahrscheinliche Algebra: Stochastische Matrizen in Beispielen und Anwendungen
by Olaf ManzDieses kompakte Buch gibt eine verständliche, anwendungsnahe Einführung in stochastische Matrizen anhand von Beispielen aus dem Alltag. Zur Einführung untersuchen wir zunächst die Verbreitung von Gerüchten. Anschließend setzen wir Mäuse in Irrgärten aus und verstecken darin Mausefallen. Als Pendant gehen wir in freier Wildbahn nach Füchsen auf die Jagd. Wir kümmern uns auch um Themen des alltäglichen Lebens wie die Gesundheit, die Vererbung, die Ausbildung, das Konsumverhalten und den Sport. Wir verfolgen den Ruin von Glücksspielern, schauen uns aber auch das faire Mischen von Spielkarten näher an. Abschließend sind wir mit Jim Knopf zu einer Reise durch Lummerland verabredet. Dabei beobachten wir die Warteschlangen, die sich vor Lukas, dem Lokomotivführer und seiner Lok Emma bilden. Wir kümmern uns auch um die Reparaturplanung der Loks und werfen hierzu einen Blick in Emmas Lokschuppen und Ersatzteillager. Das Buch eignet sich durch den lockeren Stil insbesondere auch für Nichtmathematiker.
Wahrscheinlichkeit – Mathematische Theorie und praktische Bedeutung: Grundlagen der Wahrscheinlichkeitsrechnung hinterfragt (essentials)
by Rüdiger StegenIn diesem Buch werden grundlegende Begriffe und Methoden der Wahrscheinlichkeitsrechnung kritisch hinterfragt. Zunächst wird geklärt, welche Beziehung zwischen den Wahrscheinlichkeiten in der Umgangssprache, der angewandten Stochastik und den Kolmogoroffschen Axiomen besteht. Dann werden typische Aufgaben mit Hilfe des Urnenmodells gelöst. Schließlich werden bedingte Wahrscheinlichkeiten, das (empirische) Gesetz der großen Zahlen sowie Kombinationen mehrerer Wahrscheinlichkeiten eines Ereignisses behandelt.
Wahrscheinlichkeitsrechnung für Dummies (Für Dummies)
by Deborah J. RumseyDie Wahrscheinlichkeitsrechnung wird in der Schule oft nur beiläufig behandelt, dabei handelt es sich um ein besonders spannendes und alltagstaugliches Teilgebiet der Mathematik. Für alle, die über dieses Thema noch etwas mehr erfahren wollen oder müssen, erklärt Deborah Rumsey verständlich und mit Humor, was sie unbedingt wissen sollten. Egal ob Kontingenztabelle, zentraler Grenzwertsatz, Stichproben-, Binomial- oder Poissonverteilung, in diesem Buch lernen Sie, was es ist und wie Sie es anwenden. Zu jedem Kapitel finden Sie online eine Übungsaufgabe samt Lösung, um das Gelernte zu festigen. Auch Tipps zu praktischen Anwendungen - ob bei der Arbeit oder am Pokertisch - kommen nicht zu kurz. So finden Sie in diesem Buch alles, was Sie über Wahrscheinlichkeitsrechnung unbedingt wissen sollten.
Wahrscheinlichkeitsrechnung und Statistik: Eine Einführung für Verständnis, Intuition und Überblick
by Lukas MeierDieses Lehrbuch führt in die zentralen Begriffe und Konzepte der Wahrscheinlichkeitsrechnung, der beschreibenden sowie der schließenden Statistik ein. Der Fokus liegt dabei auf einem intuitiven Verständnis der grundlegenden Konzepte, Zusammenhänge und Methoden. Trotzdem wird der Stoff mathematisch präzise präsentiert. Innerhalb jedes Kapitels finden Sie verschiedene didaktische Elemente, die Ihnen den Zugang und das Verständnis, aber auch die Orientierung deutlich erleichtern:Kurzübersicht der wichtigsten Begriffe am KapitelanfangAnschauliche Erklärungen und BeispieleZentrale Sachverhalte und DefinitionenWarnungen vor häufigen MissverständnissenSeparate Textabschnitte zur IntuitionGrafische oder tabellarische Übersichten am KapitelendeAm Ende der meisten Abschnitte finden Sie kurze Lernkontrollen – hier können Sie Ihr Wissen überprüfen, indem Sie verschiedene Aussagen als wahr oder falsch einordnen. Die Lösungen finden Sie im Anhang, je nach Schwierigkeitsgrad mit kurzem Lösungsweg. Am Ende der Kapitel finden Sie außerdem Verständnisfragen, die noch einmal die wichtigsten Inhalte abfragen und so Ihren Lernfortschritt zeigen.
Walking with Christiaan Huygens: From Archimedes' Influence to Unsung Contributions in Modern Science (History of Physics)
by Enders Anthony Robinson Tijmen Jan MoserDutch scientist Christiaan Huygens (1629-1695) left an indelible mark on the fields of mathematics, physics, astronomy, and geophysics. Despite his groundbreaking contributions, history has often overlooked his pivotal role. While two of the most famous achievements in physics are Newton’s theory of gravity and Einstein’s general theory of relativity, less well-known is that Huygens provided central elements to these theories. This book stands to correct that deficit. For example, we show how Huygens used symmetry arguments to derive conservation laws for momentum and for energy, and what Einstein later called the principle of equivalence to derive the formula for centrifugal force. In 1689, Huygens visited Newton. Together, they walked the streets of London. Newton had recently finished his masterpiece, Principia, expounding his laws of motion and the law of universal gravitation. Huygens had essentially completed his life’s work by then, building on Archimedes, Leonardo da Vinci, Galileo, Descartes, Fermat, Pascal and his own ingenuity. He had established fame as an instrument maker (telescope, pendulum clock, planetarium). He had invented the 31 tone system. He had pioneered the first principles of remote sensing. He had discovered the rings of Saturn. He had formulated the wave theory of light. What would walking with Christiaan reveal? This book gives the result in nine chapters, namely: spontaneous order, the speed of light, Huygens’ principle, the telescope, the pendulum clock, Huygens-Fresnel principle, special relativity, centrifugal force, and curvature. In addition, there is a chapter titled What Huygens could have written on diffraction, and a chapter titled Huygens and Geophysics. Mentally walking with Christiaan, browsing his collected works — a true treasure trove for puzzle enthusiasts — and rethinking his ideas creates a vivid impression of scientific life in the 17th century, an appreciation that it is remarkably similar to ours, and an understanding of Huygens' significant and lasting contributions to science.
Walter Gautschi, Volume 1
by Claude Brezinski Ahmed SamehWalter Gautschi has written extensively on topics ranging from special functions, quadrature and orthogonal polynomials to difference and differential equations, software implementations, and the history of mathematics. He is world renowned for his pioneering work in numerical analysis and constructive orthogonal polynomials, including a definitive textbook in the former, and a monograph in the latter area.<P><P> This three-volume set, Walter Gautschi: Selected Works with Commentaries, is a compilation of Gautschi’s most influential papers and includes commentaries by leading experts. The work begins with a detailed biographical section and ends with a section commemorating Walter’s prematurely deceased twin brother. This title will appeal to graduate students and researchers in numerical analysis, as well as to historians of science.<P><P> Selected Works with Commentaries, Vol. 1<P> - Numerical Conditioning<P> - Special Functions<P> - Interpolation and Approximation<P> Selected Works with Commentaries, Vol. 2<P> - Orthogonal Polynomials on the Real Line<P> - Orthogonal Polynomials on the Semicircle<P> - Chebyshev Quadrature<P> - Kronrod and Other Quadratures<P> - Gauss-type Quadrature<P> Selected Works with Commentaries, Vol. 3<P> - Linear Difference Equations<P> - Ordinary Differential Equations<P> - Software<P> - History and Biography<P> - Miscellanea<P> - Works of Werner Gautschi<P>
Walter Gautschi, Volume 2
by Claude Brezinski Ahmed SamehWalter Gautschi has written extensively on topics ranging from special functions, quadrature and orthogonal polynomials to difference and differential equations, software implementations, and the history of mathematics. He is world renowned for his pioneering work in numerical analysis and constructive orthogonal polynomials, including a definitive textbook in the former, and a monograph in the latter area.<P><P> This three-volume set, Walter Gautschi: Selected Works with Commentaries, is a compilation of Gautschi’s most influential papers and includes commentaries by leading experts. The work begins with a detailed biographical section and ends with a section commemorating Walter’s prematurely deceased twin brother. This title will appeal to graduate students and researchers in numerical analysis, as well as to historians of science.<P><P> Selected Works with Commentaries, Vol. 1<P> - Numerical Conditioning<P> - Special Functions<P> - Interpolation and Approximation<P> Selected Works with Commentaries, Vol. 2<P> - Orthogonal Polynomials on the Real Line<P> - Orthogonal Polynomials on the Semicircle<P> - Chebyshev Quadrature<P> - Kronrod and Other Quadratures<P> - Gauss-type Quadrature<P> Selected Works with Commentaries, Vol. 3<P> - Linear Difference Equations<P> - Ordinary Differential Equations<P> - Software<P> - History and Biography<P> - Miscellanea<P> - Works of Werner Gautschi<P>
Walter Gautschi, Volume 3
by Claude Brezinski Ahmed SamehWalter Gautschi has written extensively on topics ranging from special functions, quadrature and orthogonal polynomials to difference and differential equations, software implementations, and the history of mathematics. He is world renowned for his pioneering work in numerical analysis and constructive orthogonal polynomials, including a definitive textbook in the former, and a monograph in the latter area. This three-volume set, Walter Gautschi: Selected Works with Commentaries, is a compilation of Gautschi’s most influential papers and includes commentaries by leading experts. The work begins with a detailed biographical section and ends with a section commemorating Walter’s prematurely deceased twin brother. This title will appeal to graduate students and researchers in numerical analysis, as well as to historians of science.<P><P> Selected Works with Commentaries, Vol. 1<P> - Numerical Conditioning<P> - Special Functions<P> - Interpolation and Approximation<P> Selected Works with Commentaries, Vol. 2<P> - Orthogonal Polynomials on the Real Line<P> - Orthogonal Polynomials on the Semicircle<P> - Chebyshev Quadrature<P> - Kronrod and Other Quadratures<P> - Gauss-type Quadrature<P> Selected Works with Commentaries, Vol. 3<P> - Linear Difference Equations<P> - Ordinary Differential Equations<P> - Software<P> - History and Biography<P> - Miscellanea<P> - Works of Werner Gautschi<P>
Wandering Towards a Goal: How Can Mindless Mathematical Laws Give Rise To Aims And Intention? (The Frontiers Collection)
by Anthony Aguirre Brendan Foster Zeeya MeraliThis collection of prize-winning essays addresses the controversial question of how meaning and goals can emerge in a physical world governed by mathematical laws. What are the prerequisites for a system to have goals? What makes a physical process into a signal? Does eliminating the homunculus solve the problem? The three first-prize winners, Larissa Albantakis, Carlo Rovelli and Jochen Szangolies tackle exactly these challenges, while many other aspects (agency, the role of the observer, causality versus teleology, ghosts in the machine etc.) feature in the other award winning contributions. All contributions are accessible to non-specialists.These seventeen stimulating and often entertaining essays are enhanced versions of the prize-winning entries to the FQXi essay competition in 2017.The Foundational Questions Institute, FQXi, catalyzes, supports, and disseminates research on questions at the foundations of physics and cosmology, particularly new frontiers and innovative ideas integral to a deep understanding of reality, but unlikely to be supported by conventional funding sources.
War Games: A History of War on Paper
by Philipp Von Hilgers Ross BenjaminFor centuries, both mathematical and military thinkers have used game-like scenarios to test their visions of mastering a complex world through symbolic operations. By the end of World War I, mathematical and military discourse in Germany simultaneously discovered the game as a productive concept. Mathematics and military strategy converged in World War II when mathematicians designed fields of operation. In this book, Philipp von Hilgers examines the theory and practice of war games through history, from the medieval game boards, captured on parchment, to the paper map exercises of the Third Reich. Von Hilgers considers how and why war games came to exist: why mathematical and military thinkers created simulations of one of the most unpredictable human activities on earth. Von Hilgers begins with the medieval rythmomachia, or Battle of Numbers, then reconstructs the ideas about war and games in the baroque period. He investigates the role of George Leopold von Reiswitz's tactical war game in nineteenth-century Prussia and describes the artifact itself: a game board--topped table with drawers for game implements. He explains Clausewitz's emphasis on the "fog of war" and the accompanying element of incalculability, examines the contributions of such thinkers as Clausewitz, Leibniz, Wittgenstein, and von Neumann, and investigates the war games of the German military between the two World Wars. Baudrillard declared this to be the age of simulacra; war games stand contrariwise as simulations that have not been subsumed in absolute virtuality.
War Stories from the Drug Survey: How Culture, Politics, and Statistics Shaped the National Survey on Drug Use and Health
by Joseph GfroererThe primary data driver behind US drug policy is the National Survey on Drug Use and Health. This insider history traces the evolution of the survey and how the survey has interacted with the political and social climate of the country, from its origins during the Vietnam War to its role in the war on drugs. <P><P>The book includes first-hand accounts that explain how the data was used and misused by political leaders, why changes were made in the survey design, and what challenges researchers faced in communicating statistical principles to policymakers and leaders. It also makes recommendations for managing survey data collection and reporting in the context of political pressures and technological advances. <P><P>Survey research students and practitioners will learn practical lessons about questionnaire design, mode effects, sampling, nonresponse, weighting, editing, imputation, statistical significance, and confidentiality. The book also includes common-language explanations of key terms and processes to help data users understand the point of view of survey statisticians.
War in Economic Theories over Time: Assessing the True Economic, Social and Political Costs (Palgrave Studies in the History of Economic Thought)
by Renata AllioThis book offers the first systematic analysis of economic thought concerning war. It retraces debates on war from the formation of European states, the rise of Mercantilism, to Colonialism, Imperialism, the World Wars and the Cold War. Allio shows different economic perspectives from which it is possible to study war as a tool to achieve economic ends: causes, consequences, costs, funding methods, and effects on the economic status of the state and on the well-being of citizens. Examining interpretations from Smith, Hobson, Keynes, Kalecki, Stiglitz and many more, this important volume addresses the economic implications of war from the perspectives of many who bore the costs of wars in reality.
War, Humanitarian Crises, Population Displacement, and Fertility: A Review of Evidence
by Kenneth HillIncludes statistical data.
War, Violence, and Population
by James TynerGrounded in theory and research, this book offers a spatial perspective on how and why populations are regulated and disciplined by mass violence and why these questions matter for scholars concerned about social justice. James Tyner focuses on how states and other actors use acts of brutality to manage, administer, and control space for political and economic purposes. He shows how demographic analyses of fertility, mortality, and migration cannot be complete without taking war and genocide into account. Stark, in-depth case studies provide a powerful and provocative basis for retheorizing population geography.
Warped Passages: Unraveling the Mysteries of the Universe's Hidden Dimensions
by Lisa RandallThe universe has many secrets. It may hide additional dimensions of space other than the familier three we recognize. There might even be another universe adjacent to ours, invisible and unattainable . . . for now.Warped Passages is a brilliantly readable and altogether exhilarating journey that tracks the arc of discovery from early twentieth-century physics to the razor's edge of modern scientific theory. One of the world's leading theoretical physicists, Lisa Randall provides astonishing scientific possibilities that, until recently, were restricted to the realm of science fiction. Unraveling the twisted threads of the most current debates on relativity, quantum mechanics, and gravity, she explores some of the most fundamental questions posed by Nature—taking us into the warped, hidden dimensions underpinning the universe we live in, demystifying the science of the myriad worlds that may exist just beyond our own.
Was für ein Zufall!: Zum Ursprung von Unvorhersehbarkeit, Komplexität, Krisen und Zeit
by Bernhard WeßlingWarum sind so viele Ereignisse nicht vorhersehbar, glückliche Zufälle ebensowenig wie Katastrophen? Erleben wir eine neue Zeit der Polykrise? Angeblich so schlimm wie noch nie dagewesen, ist das belegbar? Aber was genau sind Krisen eigentlich? Und was haben sie mit der Komplexität der Welt zu tun? Sehr einfach und verständlich beantwortet der Autor diese und weitere Fragen im unterhaltsamen Plauderton, unterlegt mit knallharten Fakten, Daten und Berechnungen. Diese 2. und umfassend erweiterte Auflage ist im besten Sinne ein populärwissenschaftliches Buch und mischt sich zugleich in aktuelle gesellschaftliche Debatten ein: Wie können wir nachhaltig mit der Klimakrise umgehen? Nachhaltig nicht als leere Phrase. Denn Nachhaltigkeit kann objektiv beurteilt werden! Aber nach welchen Kriterien? Dazu entführt uns Bernhard Weßling auf eine Entdeckungsreise zu neuesten Erkenntnissen der modernen Chemie, Quantenphysik, Biologie und Kosmologie. Auf der Grundlage anerkannter Naturgesetze konfrontiert er uns mit neuen überraschenden Gedanken: Zufall, Komplexität und Krisen sind miteinander verwandt – gemeinsame Wurzel ist die Entropie. Sie erweist sich als lebensnah verständlich und sinnvoll anwendbar. Und ganz passend leitet der Autor daraus eine bestechende Hypothese ab zu der Menschheitsfrage: Was ist die Zeit?