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Author: William Byers
Publisher: Princeton University Press
ISBN: 0691145997
Category : Mathematics
Languages : en
Pages : 424
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Book Description
To many outsiders, mathematicians appear to think like computers, grimly grinding away with a strict formal logic and moving methodically--even algorithmically--from one black-and-white deduction to another. Yet mathematicians often describe their most important breakthroughs as creative, intuitive responses to ambiguity, contradiction, and paradox. A unique examination of this less-familiar aspect of mathematics, How Mathematicians Think reveals that mathematics is a profoundly creative activity and not just a body of formalized rules and results. Nonlogical qualities, William Byers shows, play an essential role in mathematics. Ambiguities, contradictions, and paradoxes can arise when ideas developed in different contexts come into contact. Uncertainties and conflicts do not impede but rather spur the development of mathematics. Creativity often means bringing apparently incompatible perspectives together as complementary aspects of a new, more subtle theory. The secret of mathematics is not to be found only in its logical structure. The creative dimensions of mathematical work have great implications for our notions of mathematical and scientific truth, and How Mathematicians Think provides a novel approach to many fundamental questions. Is mathematics objectively true? Is it discovered or invented? And is there such a thing as a "final" scientific theory? Ultimately, How Mathematicians Think shows that the nature of mathematical thinking can teach us a great deal about the human condition itself.
Author: William Byers
Publisher: Princeton University Press
ISBN: 0691145997
Category : Mathematics
Languages : en
Pages : 424
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Book Description
To many outsiders, mathematicians appear to think like computers, grimly grinding away with a strict formal logic and moving methodically--even algorithmically--from one black-and-white deduction to another. Yet mathematicians often describe their most important breakthroughs as creative, intuitive responses to ambiguity, contradiction, and paradox. A unique examination of this less-familiar aspect of mathematics, How Mathematicians Think reveals that mathematics is a profoundly creative activity and not just a body of formalized rules and results. Nonlogical qualities, William Byers shows, play an essential role in mathematics. Ambiguities, contradictions, and paradoxes can arise when ideas developed in different contexts come into contact. Uncertainties and conflicts do not impede but rather spur the development of mathematics. Creativity often means bringing apparently incompatible perspectives together as complementary aspects of a new, more subtle theory. The secret of mathematics is not to be found only in its logical structure. The creative dimensions of mathematical work have great implications for our notions of mathematical and scientific truth, and How Mathematicians Think provides a novel approach to many fundamental questions. Is mathematics objectively true? Is it discovered or invented? And is there such a thing as a "final" scientific theory? Ultimately, How Mathematicians Think shows that the nature of mathematical thinking can teach us a great deal about the human condition itself.
Author: Shane P. Desselle
Publisher: MDPI
ISBN: 3039365436
Category : Medical
Languages : en
Pages : 196
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Book Description
This book provides research and commentary on pharmacy technicians. It demonstrates how the re-design of pharmacy workflow to incorporate more responsibilities for technicians will free up pharmacist time to provide direct patient care. It also highlights that doing so can be accomplished without compromising—and often even improving upon—patient safety. The book also sheds light on employer needs and on new paradigms in pharmacy technician certification, education, and training. However, it also demonstrates the need for improvements in this area, as well as improvements in pharmacy technician quality of work life, advancement opportunities, and wages. Taken together, the papers in this book demonstrate how the results of recent studies help pave the road for the continued evolution of pharmacy care and the optimal deployment of pharmacy workforce personnel.
Author: Israel Kleiner
Publisher: Springer Science & Business Media
ISBN: 0817646841
Category : Mathematics
Languages : en
Pages : 175
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Book Description
This book explores the history of abstract algebra. It shows how abstract algebra has arisen in attempting to solve some of these classical problems, providing a context from which the reader may gain a deeper appreciation of the mathematics involved.
Author: Giuliana B. Prato
Publisher: Routledge
ISBN: 1317174674
Category : Social Science
Languages : en
Pages : 237
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Book Description
While the anthropological field initially shied away from the debate on multiculturalism, it has been widely discussed within the fields of political theory, social policy, cultural studies and law. Beyond Multiculturalism is the first volume of its kind to offer a comparative, worldwide view of multiculturalism, considering both traditional multicultural/multiethnic societies and those where cultural pluralism is relatively new. Its varied case studies focus on the intersections and relationships between cultural groups in everyday life using employment, identity, consumption, language, legislation and policy making to show the unique contribution anthropologists can bring to multiculturalism studies. Their work will be of great interest to scholars of race, ethnicity, migration, urban studies and social and cultural geography.
Author: Joseph Albert Wolf
Publisher: American Mathematical Soc.
ISBN: 0821842897
Category : Mathematics
Languages : en
Pages : 408
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Book Description
This study starts with the basic theory of topological groups, harmonic analysis, and unitary representations. It then concentrates on geometric structure, harmonic analysis, and unitary representation theory in commutative spaces.
Author: Steven George Krantz
Publisher: American Mathematical Soc.
ISBN: 9780821872598
Category : Mathematics
Languages : en
Pages : 324
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Book Description
Mathematicians are expected to publish their work: in journals, conference proceedings, and books. It is vital to advancing their careers. Later, some are asked to become editors. However, most mathematicians are trained to do mathematics, not to publish it. But here, finally, for graduate students and researchers interested in publishing their work, Steven G. Krantz, the respected author of several "how-to" guides in mathematics, shares his experience as an author, editor, editorial board member, and independent publisher. This new volume is an informative, comprehensive guidebook to publishing mathematics. Krantz describes both the general setting of mathematical publishing and the specifics about all the various publishing situations mathematicians may encounter. As with his other books, Krantz's style is engaging and frank. He gives advice on how to get your book published, how to get organized as an editor, what to do when things go wrong, and much more. He describes the people, the language (including a glossary), and the process of publishing both books and journals. Steven G. Krantz is an accomplished mathematician and an award-winning author. He has published more than 130 research articles and 45 books. He has worked as an editor of several book series, research journals, and for the Notices of the AMS. He is also the founder of the Journal of Geometric Analysis. Other titles available from the AMS by Steven G. Krantz are How to Teach Mathematics, A Primer of Mathematical Writing, A Mathematician's Survival Guide, and Techniques of Problem Solving.
Author: Julian Havil
Publisher: Princeton University Press
ISBN: 1400837383
Category : Mathematics
Languages : en
Pages : 213
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Book Description
Math—the application of reasonable logic to reasonable assumptions—usually produces reasonable results. But sometimes math generates astonishing paradoxes—conclusions that seem completely unreasonable or just plain impossible but that are nevertheless demonstrably true. Did you know that a losing sports team can become a winning one by adding worse players than its opponents? Or that the thirteenth of the month is more likely to be a Friday than any other day? Or that cones can roll unaided uphill? In Nonplussed!—a delightfully eclectic collection of paradoxes from many different areas of math—popular-math writer Julian Havil reveals the math that shows the truth of these and many other unbelievable ideas. Nonplussed! pays special attention to problems from probability and statistics, areas where intuition can easily be wrong. These problems include the vagaries of tennis scoring, what can be deduced from tossing a needle, and disadvantageous games that form winning combinations. Other chapters address everything from the historically important Torricelli's Trumpet to the mind-warping implications of objects that live on high dimensions. Readers learn about the colorful history and people associated with many of these problems in addition to their mathematical proofs. Nonplussed! will appeal to anyone with a calculus background who enjoys popular math books or puzzles.
Author: Satyanad Kichenassamy
Publisher: Springer Science & Business Media
ISBN: 0817643524
Category : Mathematics
Languages : en
Pages : 296
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Book Description
This four-part text beautifully interweaves theory and applications in Fuchsian Reduction. Background results in weighted Sobolev and Holder spaces as well as Nash-Moser implicit function theorem are provided. Most chapters contain a problem section and notes with references to the literature. This volume can be used as a text in graduate courses in PDEs and/or Algebra, or as a resource for researchers working with applications to Fuchsian Reduction. The comprehensive approach features the inclusion of problems and bibliographic notes.
Author: Titu Andreescu
Publisher: Springer Science & Business Media
ISBN: 1461221382
Category : Mathematics
Languages : en
Pages : 270
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Book Description
Mathematical Olympiad Challenges is a rich collection of problems put together by two experienced and well-known professors and coaches of the U.S. International Mathematical Olympiad Team. Hundreds of beautiful, challenging, and instructive problems from algebra, geometry, trigonometry, combinatorics, and number theory were selected from numerous mathematical competitions and journals. An important feature of the work is the comprehensive background material provided with each grouping of problems. The problems are clustered by topic into self-contained sections with solutions provided separately. All sections start with an essay discussing basic facts and one or two representative examples. A list of carefully chosen problems follows and the reader is invited to take them on. Additionally, historical insights and asides are presented to stimulate further inquiry. The emphasis throughout is on encouraging readers to move away from routine exercises and memorized algorithms toward creative solutions to open-ended problems. Aimed at motivated high school and beginning college students and instructors, this work can be used as a text for advanced problem- solving courses, for self-study, or as a resource for teachers and students training for mathematical competitions and for teacher professional development, seminars, and workshops.
Author: The Postclassicisms Collective
Publisher: University of Chicago Press
ISBN: 022667231X
Category : History
Languages : en
Pages : 251
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Book Description
Made up of nine prominent scholars, The Postclassicisms Collective aims to map a space for theorizing and reflecting on the values attributed to antiquity. The product of these reflections, Postclassicisms takes up a set of questions about what it means to know and care about Greco-Roman antiquity in our turbulent world and offers suggestions for a discipline in transformation, as new communities are being built around the study of the ancient Greco-Roman world. Structured around three primary concepts—value, time, and responsibility—and nine additional concepts, Postclassicisms asks scholars to reflect upon why they choose to work in classics, to examine how proximity to and distance from antiquity has been—and continues to be—figured, and to consider what they seek to accomplish within their own scholarly practices. Together, the authors argue that a stronger critical self-awareness, an enhanced sense of the intellectual history of the methods of classics, and a greater understanding of the ethical and political implications of the decisions that the discipline makes will lead to a more engaged intellectual life, both for classicists and, ultimately, for society. A timely intervention into the present and future of the discipline, Postclassicisms will be required reading for professional classicists and students alike and a model for collaborative disciplinary intervention by scholars in other fields.
