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Wissenschaft, Zahlen und Politik
by Markus J. PrutschDiese Studie untersucht die dynamische Beziehung zwischen Wissenschaft, Zahlen und Politik. Was können wissenschaftliche Erkenntnisse realistischerweise in und für die Politik tun? Der Band leistet einen Beitrag zu dieser Debatte, indem er sich auf die Rolle von "Zahlen" als Mittel konzentriert, mit dem Wissen ausgedrückt wird und durch das dieses Wissen in den politischen Bereich übertragen werden kann. Ausgehend von der Annahme, dass Zahlen ständig aktiv geschaffen, übersetzt und verwendet werden und dass sie in ihren jeweiligen Kontexten interpretiert werden müssen, wird untersucht, wie Zahlen und Quantifizierungen "politisch nutzbar" gemacht werden, indem ihre Produktion, ihr Übergang in die Sphäre der Politik und ihre letztendliche Verwendung darin untersucht werden. Zu den zentralen Fragen, die behandelt werden, gehören: Auf welche Weise beeinflussen wissenschaftliche Erkenntnisse die politische Entscheidungsfindung in der heutigen Welt? Wie und warum hat Quantifizierung in der demokratischen Politik eine so wichtige Rolle gespielt? Was leisten wissenschaftliche Erkenntnisse und Zahlen in der Politik?
Within Our Reach
by Lisbeth SchorrIn this solidly researched book, the authors demonstrate that the knowledge and techniques exist to decrease the incidence of welfare dependency, poor single-parent families and alienated, uneducated youth. In addition to providing a detailed account of the problem, they describe twenty-four programs that have proved successful in changing the lives of seriously disadvantaged children.From the Trade Paperback edition.
Without Words: Mathematical Puzzles to Confound and Delight
by James TantonAll real life mathematics is problem solving. And all those fascinated by puzzles are problem solvers at heart. But thinking mathematically is a skill we have to learn and one which it is easy to forget. Recreational mathematicians and students can practise problem solving in different ways. In this book solving puzzles is practised in a different way from most books they will have seen before:• Readers get no clues to what the puzzle is about• They may take hours or even days to work out what is being asked of them• Even after that, some problems may have no solutionThe result of this challenge is a really challenging book that will fascinate anyone interested in puzzles and recreational mathematicians in particular. This volume contains 36 puzzles ranging from quite easy to more difficult. The sister volume More Without Words: Mathematical Puzzles to Confound and Delight is also available – containing 36 more puzzles with more easy and fewer testing ones.
Wittgenstein, Mathematics and World (History of Analytic Philosophy)
by Bob ClarkThis book uses Ludwig Wittgenstein's philosophical methodology to solve a problem that has perplexed thinkers for thousands of years: 'how come (abstract) mathematics applies so wonderfully well to the (concrete, physical) world?' The book is distinctive in several ways. First, it gives the reader a route into understanding important features of Wittgenstein's writings and lectures by using his methodology to tackle this long-standing and seemingly intractable philosophical problem. More than this, though, it offers an outline of important (sometimes little-known) aspects of the development of mathematical thought through the ages, and an engagement of Wittgenstein's philosophy with this and with contemporary philosophy of mathematics on its own terms. A clear overview of all this in the context of Wittgenstein's philosophy of mathematics is interesting in its own right; it is also just what is needed to solve the problem of mathematics and world.
WITTGENSTEINIAN: Looking at the World from the Viewpoint of Wittgenstein's Philosophy (The Frontiers Collection)
by Shyam Wuppuluri Newton Da Costa“Tell me," Wittgenstein once asked a friend, "why do people always say, it was natural for man to assume that the sun went round the earth rather than that the earth was rotating?" His friend replied, "Well, obviously because it just looks as though the Sun is going round the Earth." Wittgenstein replied, "Well, what would it have looked like if it had looked as though the Earth was rotating?” What would it have looked like if we looked at all sciences from the viewpoint of Wittgenstein’s philosophy? Wittgenstein is undoubtedly one of the most influential philosophers of the twentieth century. His complex body of work has been analysed by numerous scholars, from mathematicians and physicists, to philosophers, linguists, and beyond. This volume brings together some of his central perspectives as applied to the modern sciences and studies the influence they may have on the thought processes underlying science and on the world view it engenders. The contributions stem from leading scholars in philosophy, mathematics, physics, economics, psychology and human sciences; all of them have written in an accessible style that demands little specialist knowledge, whilst clearly portraying and discussing the deep issues at hand.
Wittgenstein’s Annotations to Hardy’s Course of Pure Mathematics: An Investigation of Wittgenstein’s Non-Extensionalist Understanding of the Real Numbers (Nordic Wittgenstein Studies #7)
by Juliet Floyd Felix MühlhölzerThis monograph examines the private annotations that Ludwig Wittgenstein made to his copy of G.H. Hardy’s classic textbook, A Course of Pure Mathematics. Complete with actual images of the annotations, it gives readers a more complete picture of Wittgenstein’s remarks on irrational numbers, which have only been published in an excerpted form and, as a result, have often been unjustly criticized. The authors first establish the context behind the annotations and discuss the historical role of Hardy’s textbook. They then go on to outline Wittgenstein’s non-extensionalist point of view on real numbers, assessing his manuscripts and published remarks and discussing attitudes in play in the philosophy of mathematics since Dedekind. Next, coverage focuses on the annotations themselves. The discussion encompasses irrational numbers, the law of excluded middle in mathematics and the notion of an “improper picture," the continuum of real numbers, and Wittgenstein’s attitude toward functions and limits.
Wittgenstein's Lectures on the Foundations of Mathematics, Cambridge 1939
by Cora DiamondFor several terms at Cambridge in 1939, Ludwig Wittgenstein lectured on the philosophical foundations of mathematics. A lecture class taught by Wittgenstein, however, hardly resembled a lecture. He sat on a chair in the middle of the room, with some of the class sitting in chairs, some on the floor. He never used notes. He paused frequently, sometimes for several minutes, while he puzzled out a problem. He often asked his listeners questions and reacted to their replies. Many meetings were largely conversation. These lectures were attended by, among others, D. A. T. Gasking, J. N. Findlay, Stephen Toulmin, Alan Turing, G. H. von Wright, R. G. Bosanquet, Norman Malcolm, Rush Rhees, and Yorick Smythies. Notes taken by these last four are the basis for the thirty-one lectures in this book. The lectures covered such topics as the nature of mathematics, the distinctions between mathematical and everyday languages, the truth of mathematical propositions, consistency and contradiction in formal systems, the logicism of Frege and Russell, Platonism, identity, negation, and necessary truth. The mathematical examples used are nearly always elementary.
Wittgenstein's On Certainty: Insight and Method (SpringerBriefs in Philosophy)
by Robert Greenleaf BriceThis book considers the important twentieth century Austrian philosopher, Ludwig Wittgenstein, and his conception of certainty. In his work entitled On Certainty, Wittgenstein provides not only a brilliant solution to a previously intractable philosophical problem, but also the elements of an entirely new way of approaching this and similar longstanding, apparently unresolvable, problems. In On Certainty, he re-conceives the problem of radical skepticism–the claim that we can never really be certain of anything except the contents of our own minds–as a kind of philosophical “disease” of thought. His approach to the problem, which is emphasized in the book, is similar to the treatment of disease, has two main goals: (1) bring about an awareness in the philosopher that this kind of extreme skepticism is not a methodological approach to be taken seriously, and, with this awareness, (2) an attempt to replace this radical skepticism with a practical, Common Sense framework. Implicit in Wittgenstein’s approach are a number of strategies found in a contemporary approach to psychotherapy known as Cognitive Behavioral Therapy (CBT). These strategies, along with philosophical methods and scientific practices rooted in the Scottish School of Common Sense, seek to diagnose and treat irrational thoughts and beliefs that often emerge (and re-emerge) in the discipline of philosophy. The aim of this book, then, is to provide students of philosophy with the tools necessary to adjust and reshape these irrational, self-defeating thoughts and beliefs into something new, something healthy.
Wizards, Aliens, and Starships: Physics and Math in Fantasy and Science Fiction
by Charles L. AdlerExplaining the science behind science fiction and fantasy—from the probable to the impossibleFrom teleportation and space elevators to alien contact and interstellar travel, science fiction and fantasy writers have come up with some brilliant and innovative ideas. Yet how plausible are these ideas--for instance, could Mr. Weasley's flying car in the Harry Potter books really exist? Which concepts might actually happen, and which ones wouldn’t work at all? Wizards, Aliens, and Starships delves into the most extraordinary details in science fiction and fantasy--such as time warps, shape changing, rocket launches, and illumination by floating candle--and shows readers the physics and math behind the phenomena.With simple mathematical models, and in most cases using no more than high school algebra, Charles Adler ranges across a plethora of remarkable imaginings, from the works of Ursula K. Le Guin to Star Trek and Avatar, to explore what might become reality. Adler explains why fantasy in the Harry Potter and Dresden Files novels cannot adhere strictly to scientific laws, and when magic might make scientific sense in the muggle world. He examines space travel and wonders why it isn’t cheaper and more common today. Adler also discusses exoplanets and how the search for alien life has shifted from radio communications to space-based telescopes. He concludes by investigating the future survival of humanity and other intelligent races. Throughout, he cites an abundance of science fiction and fantasy authors, and includes concise descriptions of stories as well as an appendix on Newton's laws of motion.Wizards, Aliens, and Starships will speak to anyone wanting to know about the correct--and incorrect--science of science fiction and fantasy.
WJEC GCSE Maths Foundation: Mastering Mathematics Revision Guide
by Karen Hughes Linda Mason 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- 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 Higher: Mastering Mathematics Revision Guide
by Keith Pledger Joe Petran Gareth ColeExam 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.- 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 Higher: Mastering Mathematics Revision Guide
by Keith Pledger Joe Petran Gareth ColeExam 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.- 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 GCSE Maths Intermediate: Revision Guide
by Keith Pledger Joe Petran Gareth ColeExam 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: 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.
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.