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.

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.

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.

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.

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.

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.

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.