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In "The Princeton Companion to Mathematics", Timothy Gowers - a recipient of the Fields Medal, the most esteemed prize in mathematics - presents a unique reference for anyone with a serious interest in mathematics. Nearly two hundred entries, commissioned especially for this book from the world's leading mathematicians, introduce basic mathematical tools and vocabulary; trace the development of modern mathematics; define essential terms and concepts and put them in context; explain core ideas in major areas of mathematics; describe the achievements of scores of famous mathematicians; discuss the impact of mathematics on other disciplines such as biology, finance, and music - and much, much more.
Unparalleled in its depth of coverage, "The Princeton Companion to Mathematics" surveys the most active and exciting branches of pure mathematics in areas such as number theory, algebra, analysis, geometry, combinatorics, logic, probability, theoretical computer science, and mathematical physics, providing the context and broad perspective that are vital at a time of increasing specialization in the field. Packed with information and presented in an accessible style, this is an indispensable resource for undergraduate and graduate students in mathematics, as well as for researchers and scholars seeking to understand areas outside their specialties. It features nearly 200 entries, organized thematically and written by an international team of distinguished contributors. It presents the major ideas and branches of pure mathematics in a clear, accessible style.It defines and explains important mathematical concepts, methods, theorems, and open problems. It introduces the language of mathematics and the goals of mathematical research. It covers number theory, algebra, analysis, geometry, logic, probability, and more. It traces the history and development of modern mathematics. It discusses more than ninety-five mathematicians whose achievements influenced those working today. It explores the influence of mathematics on other disciplines such as biology, communication theory, finance, medical statistics, and music. It includes bibliographies, cross-references, and a comprehensive index.
Timothy Gowers is the Rouse Ball Professor of Mathematics at the University of Cambridge. He received the Fields Medal in 1998, and is the author of "Mathematics: A Very Short Introduction". June Barrow-Green is lecturer in the history of mathematics at the Open University. Imre Leader is professor of pure mathematics at the University of Cambridge.