GEOMETRIC GEMS (V2)
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Our physical world is embedded in a geometric environment. Plane geometry has many amazing wonders beyond those that are briefly touched on at school. The quadrilateral, one of the basic instruments in geometry, has a plethora of unexpected curiosities. The authors present these in an easily understood fashion, requiring nothing more than the very basics of school geometry to appreciate these curiosities and their justifications or proofs.
The book is intended to be widely appreciated by a general audience, and their love for geometry should be greatly enhanced through exploring these many unexpected relationships in geometry. Geometric Gems is also suitable for mathematics teachers, to enhance the education of their students with these highly motivating quadrilateral properties.
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Sample Chapter(s)
Introduction
Contents:
About the Authors
Acknowledgments
Introduction
Quadrilateral Curiosities
Proofs of Quadrilateral Curiosities
Toolbox
Index
Readership: The book is intended for the general readership, mathematics teachers, and mathematicians interested in extending their appreciation for geometry.
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Geometric Analysis on Real Analytic Manifold
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This monograph provides some useful tools for performing global geometric analysis on real analytic manifolds. At the core of the methodology of the book is a variety of descriptions for the topologies for the space of real analytic sections of a real analytic vector bundle and for the space of real analytic mappings between real analytic manifolds. Among the various descriptions for these topologies is a development of geometric seminorms for the space of real analytic sections. To illustrate the techniques in the book, a number of fundamental constructions in differential geometry are shown to induce continuous mappings on spaces of real analytic sections and mappings.
Aimed at researchers at the level of Doctoral students and above, the book introduces the reader to the challenges and opportunities of real analytic analysis and geometry.
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