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"Mathematics, Geometry "
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Geometry : a very short introduction
Provides a fresh modern introduction to geometry, an ancient branch of mathematics with important applications. It takes readers from Euclidean and non-Euclidean geometries, to curved spaces, and the geometry of space-time inside a black hole, and outlines the role geometry plays in the broader context of science and art.
Book
Mathematical Theory of Optics
This title is part of UC Press's Voices Revived program, which commemorates University of California Press's mission to seek out and cultivate the brightest minds and give them voice, reach, and impact. Drawing on a backlist dating to 1893, Voices Revived makes high-quality, peer-reviewed scholarship accessible once again using print-on-demand technology. This title was originally published in 1964.
eBook
Beautiful geometry
\"If you've ever thought that mathematics and art don't mix, this stunning visual history of geometry will change your mind. As much a work of art as a book about mathematics, Beautiful Geometry presents more than sixty exquisite color plates illustrating a wide range of geometric patterns and theorems, accompanied by brief accounts of the fascinating history and people behind each. With artwork by Swiss artist Eugen Jost and text by acclaimed math historian Eli Maor, this unique celebration of geometry covers numerous subjects, from straightedge-and-compass constructions to intriguing configurations involving infinity. The result is a delightful and informative illustrated tour through the 2,500-year-old history of one of the most important and beautiful branches of mathematics\"-- Provided by publisher.
Book
Topology Optimization Design of Heterogeneous Materials and Structures
This book pursues optimal design from the perspective of mechanical properties and resistance to failure caused by cracks and fatigue.The book abandons the scale separation hypothesis and takes up phase-field modeling, which is at the cutting edge of research and is of high industrial and practical relevance.
eBook
Imaginary Elements in Geometry
A remarkable fact in mathematics is the accordance between algebra and geometry: since the time of Descartes it is possible to express geometric phenomena in terms of numbers.And after doing calculations with these numbers, we can draw geometric conclusions from them.
eBook
Noncommutative Geometry
The series de Gruyter Studies in Mathematics was founded in 1982 by the late Professor Heinz Bauer and Professor Peter Gabriel. The series publishes monographs and textbooks in mathematics and its applications. Apart from covering important areas of current interest, a major aim is to make topics of an interdisciplinary nature accessible to the non-specialist. Each volume undergoes peer review using a double-blind reviewing process.
eBook
Barcode entropy of geodesic flows
We introduce and study the barcode entropy for geodesic flows of closed Riemannian manifolds, which measures the exponential growth rate of the number of not-too-short bars in the Morse-theoretic barcode of the energy functional. We prove that the barcode entropy bounds from below the topological entropy of the geodesic flow and, conversely, bounds from above the topological entropy of any hyperbolic compact invariant set. As a consequence, for Riemannian metrics on surfaces, the barcode entropy is equal to the topological entropy. A key to the proofs and of independent interest is a crossing energy theorem for gradient flow lines of the energy functional.
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