Why science? : to know, to understand, and to rely on results / Roger G. Newton.

Includes bibliographical references (pages 85-86) and index.

This volume is based on lectures given at the highly successful three-week Summer School on Geometry, Topology and Dynamics of Character Varieties held at the National University of Singapore's Institute for Mathematical Sciences in July 2010. Aimed at graduate students in the early stages of research, the edited and refereed articles comprise an excellent introduction to the subject of the program, much of which is otherwise available only in specialized texts. Topics include hyperbolic structures on surfaces and their degenerations, applications of ping-pong lemmas in various contexts, introductions to Lorenzian and complex hyperbolic geometry, and representation varieties of surface groups into PSL(2, R) and other semi-simple Lie groups. This volume will serve as a useful portal to students and researchers in a vibrant and multi-faceted area of mathematics.

Introduction; 1. We Want to Know; Looking at the Heavens; Exploratory Voyages; 2. We Want to Understand; Charles Darwin; Gregor Mendel; Louis Pasteur; Michael Faraday; Max Planck; Enrico Fermi; 3. Science; Chemistry as the Fundamental Science; How Physics Became Most Fundamental; On Reductionism; References and Further Reading; Illustration Credits; Index.

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