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Wednesday, September 30

Math: Geometry of the Hyperbolic Plane, Math in India, Cryptography, and the History of Math

New books in Brooks Library are taking new spins, publishing recent theories, and chronicling the history of math will interest both Mathematicians and Physicists alike.

Hyperbolic Geometry (BOOK): by James W. Anderson

The geometry of the hyperbolic plane has been an active and fascinating field of mathematical inquiry for most of the past two centuries. This second edition of Hyperbolic Geometry has been thoroughly rewritten and updated. Chapter 4 focuses on planar models of hyperbolic plane that arise from complex analysis and looks at the connections between planar hyperbolic geometry and complex analysis.

This book is writ

ten primarily for third or fourth year undergraduate students with some calculus knowledge. It contains new exercises with solutions and is ideal for self-study or as a classroom text.

Mathematics in India (BOOK): by Kim Plofker

Mathematics in India presents an accessible, readable, and well-informed treatment of the history of India's mathematical traditions. It includes topics discussed little to date: the social setting of the mathematicians, the textual practices learned in Sanskrit, and the realm of observational and timekeeping practices. The survey of the Kerala school and the later life of Indian mathematics are detailed, unique, and valuable.—Christopher Minkowski, University of Oxford

Number Theory in Science and Communication: With Applications in Cryptography, Physics, Digital Information, Computing, and Self-similarity (BOOK): by Manfred Robert Schroeder

"A lighthearted and readable volume with a wide range of applications to which the author has been a productive contributor - useful mathematics given outside the formalities of theorem and proof"—Scientific American

The Mathematics of the Heavens and the Earth: The Early History of Trigonometry (BOOK): by Glen van Brummelen

There does not seem to have been a book-length history of trigonometry in English before this fine book. Van Brummelen takes us from the unnamed Egyptians and Babylonians who created trigonometry to the subject's first few centuries in Europe. In between, he deftly traces how it was studied by the astronomers Hipparchus and Ptolemy in classical Greece, and later by a host of scholars in India and the Islamic world. —John H. Conway, coauthor of "The Book of Numbers"

The Oxford Handbook of the History of Mathematics (BOOK): edited by Eleanor Robson and Jacqueline Stedall

This Handbook explores the history of mathematics under a series of themes which raise new questions about what mathematics has been and what it has meant to practice it. It addresses questions of who creates mathematics, who uses it, and how. A broader understanding of mathematical practitioners naturally leads to a new appreciation of what counts as a historical source. Material and oral evidence is drawn upon as well as an unusual array of textual sources. Further, the ways in which people have chosen to express themselves are as historically meaningful as the contents of the mathematics they have produced. Mathematics is not a fixed and unchanging entity. New questions, contexts, and applications all influence what counts as productive ways of thinking. Because the history of mathematics should interact constructively with other ways of studying the past, the contributors to this book come from a diverse range of intellectual backgrounds in anthropology, archaeology, art history, philosophy, and literature, as well as history of mathematics more traditionally understood.

The thirty-six self-contained, multifaceted chapters, each written by a specialist, are arranged under three main headings: 'Geographies and Cultures', 'Peoples and Practices', and 'Interactions and Interpretations'. Together they deal with the mathematics of 5000 years, but without privileging the past three centuries, and an impressive range of periods and places with many points of cross-reference between chapters. The key mathematical cultures of North America, Europe, the Middle East, India, and China are all represented here as well as areas which are not often treated in mainstream history of mathematics, such as Russia, the Balkans, Vietnam, and South America.


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