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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.
Wohlstand ohne Kinder?
by Golo Henseke Matthias Czechl Thusnelda TivigDie Autoren gehen von drei möglichen Strategien zur Bewältigung der Folgen des demografischen Wandels aus und untersuchen eine davon eingehend: die Erhöhung der Kinderzahl. Sie beantworten die Frage, warum die Geburtenziffer in Deutschland als zu gering erachtet wird und klären damit komplizierte Zusammenhänge zwischen Demographie und Wachstum auf. Anschließend untersuchen sie anhand vergleichender Studien, welche Rahmenbedingungen einer höheren Kinderzahl zuträglich wären. Daraus leiten die Autoren Handlungsempfehlungen an die Politik ab.
Wohnen und Gesundheit im Alter (Vechtaer Beiträge zur Gerontologie)
by Andrea Teti Harald Künemund Enno Nowossadeck Judith FuchsVor dem Hintergrund der demographischen Entwicklung unserer Gesellschaft nimmt der Open-Access-Sammelband die Wohnsituation älterer Menschen unter besonderer Berücksichtigung der gesundheitlichen Situation in den Blick. Lebensqualität, Wohlbefinden, Teilhabe sowie Autonomie und Selbstbestimmung älterer Menschen stehen dabei im Mittelpunkt.
Women and Migration in Rural Europe: Labour Markets, Representations and Policies (New Geographies of Europe)
by Karin WiestFundamental societal changes in the globalising European countryside impact women's migration decisions. The chapters in this volume represent diverse attempts to explain women's movements from rural areas, taking prevailing labour market conditions as well as gender relations into account. Utilising empirical findings from countries including Austria, Germany, Hungary, Poland, Romania and Spain, this collection particularly aims to build bridges between research following the 'cultural turn' and functionalist explanations which refer to material and practiced ruralities. The international range of contributors to Women and Migration in Rural Europe focus on societal constructions of gender and rurality, and in doing so, address various female perspectives on rural life. The analysis of the different working and living conditions in different parts of rural Europe reveals distinct obstacles but also prospects for young women. Importantly, the book includes policy implications with respect to the challenges of demographic change, questions of gender equality and women's contribution to rural development.
Women in Analysis and PDE (Trends in Mathematics #5)
by Marianna Chatzakou Michael Ruzhansky Diana StoevaSince 2019 Ghent Analysis & PDE Center (GAPC) has been organising international workshops, conferences, seminars, and other scientific events covering a wide range of pioneering topics in Analysis and PDEs. In the winter of 2023, the GAPC decided to collect and publish mathematical results presented by women mathematician hosted at the center. This collection, in the form short papers, presented in the current book offers a wide range of state of art in Analysis and PDEs and disseminates the scientific discoveries of GAPC’s visitors and members to scientists outside of the center. The short papers published in current volume in the subseries Research Perspectives Ghent Analysis and PDE Center within the book series Trends in Mathematics are peer-reviewed written versions of the talks presented by women at GAPC events and are grouped accordingly. The current volume is strictly speaking in the realm of pure mathematics, but aims to be of interest not only to scientists in the field, butalso to anyone who has an interest to other applied sciences that Analysis and PDEs have applications to. The collection will also include the talks given at the two workshops "Women in Generalised Functions", organised in 2022 and 2023.
Women in Industrial and Systems Engineering: Key Advances and Perspectives on Emerging Topics (Women in Engineering and Science)
by Alice E. SmithThis book presents a diversity of innovative and impactful research in the field of industrial and systems engineering (ISE) led by women investigators. After a Foreword by Margaret L. Brandeau, an eminent woman scholar in the field, the book is divided into the following sections: Analytics, Education, Health, Logistics, and Production. Also included is a comprehensive biography on the historic luminary of industrial engineering, Lillian Moeller Gilbreth. Each chapter presents an opportunity to learn about the impact of the field of industrial and systems engineering and women’s important contributions to it. Topics range from big data analysis, to improving cancer treatment, to sustainability in product design, to teamwork in engineering education. A total of 24 topics touch on many of the challenges facing the world today and these solutions by women researchers are valuable for their technical innovation and excellence and their non-traditional perspective. Found within each author’s biography are their motivations for entering the field and how they view their contributions, providing inspiration and guidance to those entering industrial engineering.
Women in Mathematical Biology: Research Collaboration Workshop, NIMBioS, Knoxville, June 2015 (Association for Women in Mathematics Series #8)
by Laura A. Miller Anita T. LaytonInspired by the Research Collaboration Workshop for Women in Mathematical Biology, this volume contains research and review articles that cover topics ranging from models of animal movement to the flow of blood cells in the embryonic heart. Hosted by the National Institute for Mathematics and Biological Synthesis (NIMBioS), the workshop brought together women working in biology and mathematics to form four research groups that encouraged multidisciplinary collaboration and lifetime connections in the STEM field. This volume introduces many of the topics from the workshop, including the aerodynamics of spider ballooning; sleep, circadian rhythms, and pain; blood flow regulation in the kidney; and the effects of antimicrobial therapy on gut microbiota and microbiota and Clostridium difficile. Perfect for students and researchers in mathematics and biology, the papers included in this volume offer an introductory glimpse at recent research in mathematical biology.
Women in Numbers Europe
by Marie José Bertin Alina Bucur Brooke Feigon Leila SchnepsThis volume presents a collection of papers on number theory emerging from the third iteration of the international Women in Numbers conference, "Women in Numbers - Europe" (WINE), held on October 14-18, 2013 at the CIRM-Luminy mathematical conference center in France. The volume contains contributions covering a wide range of cutting-edge topics in number theory, yet emphasizing those concrete approaches that make it possible for graduate students and postdocs to begin work immediately on research problems even in highly complex subjects.
Women in Numbers Europe II: Research Directions In Number Theory (Association for Women in Mathematics Series #11)
by Irene I. Bouw Ekin Ozman Jennifer Johnson-Leung Rachel NewtonInspired by the September 2016 conference of the same name, this second volume highlights recent research in a wide range of topics in contemporary number theory and arithmetic geometry. Research reports from projects started at the conference, expository papers describing ongoing research, and contributed papers from women number theorists outside the conference make up this diverse volume. Topics cover a broad range of topics such as arithmetic dynamics, failure of local-global principles, geometry in positive characteristics, and heights of algebraic integers. The use of tools from algebra, analysis and geometry, as well as computational methods exemplifies the wealth of techniques available to modern researchers in number theory. Exploring connections between different branches of mathematics and combining different points of view, these papers continue the tradition of supporting and highlighting the contributions of women number theorists at a variety of career stages. Perfect for students and researchers interested in the field, this volume provides an easily accessible introduction and has the potential to inspire future work.
Women in Numbers Europe IV: Research Directions in Number Theory (Association for Women in Mathematics Series #32)
by Ramla Abdellatif Valentijn Karemaker Lejla SmajlovicThis volume contains research and expository content based on a wide variety of topics within modern number theory and arithmetic geometry. Research in this volume arises from or is connected with the Women in Numbers Europe (WiNE) IV conference held in summer 2022 in Utrecht, The Netherlands. The contents of this volume are of interest to professional mathematicians, graduate students, and researchers working in number theory, arithmetic geometry, and related areas.
Women in STEM in Higher Education: Good Practices of Attraction, Access and Retainment in Higher Education (Lecture Notes in Educational Technology)
by Francisco José García-Peñalvo Alicia García-Holgado Angeles Dominguez Jimena PascualThis open access book addresses challenges related to women in STEM in higher education, presenting research, experiences, studies, and good practices associated with the engagement, access, and retention of women in the STEM disciplines. It also discusses strategies implemented by universities and policymakers to reduce the existing gender gap in these areas. The chapters provide an overview of implementations in different regions of the world and provide numerous examples that can be transferred to other higher education institutions.
Women Leaders in Chaotic Environments: Examinations of Leadership Using Complexity Theory (Lecture Notes in Social Networks)
by Şefika Şule ErçetinThis book spotlights how women leaders behave in chaotic environments and features examples of women who have been key figures in determining complex socio-economic outcomes throughout history. Women leaders can be seen on many high- levels in the political arena, be they a prime minister, empress or opinion leader. From Kösem Sultan of the Ottoman Empire to Benazir Bhutto, women leaders have had an undeniable effect on modern history. Is it possible to understand the current role of women in politics in Turkey without the First Lady Emine Erdoğan? Can we analyze Europe’s future without Angela Merkel? There are many different books about women leaders' biography or memoirs of persons who worked closely with them. However, until now, no in-depth scientific analysis of such women leaders with respect to chaos and complexity theory has been available. This work represents a unique and important step towards filling this gap in research, and includes an epilogue presenting women’s leadership model visualized by an eight-pointed star.