This book is a concise, self-contained introduction to abstract algebra which stresses its unifying role in geometry and number theory. There is a strong emphasis on historical motivation- both to trace abstract concepts to their concrete roots, but also to show the power of new ideas to solve old problems. This approach shows algebra as an integral part of mathematics and makes this text more informative to both beginners and experts than others. Classical results of geometry and number theory are used to motivate and illustrate algebraic techniques, and classical algebra itself is used to motivate the problem of solvability by radicals and its solution via Galois theory.
Mathematics from the Visual World, taught by veteran Teaching Company Professor Michael Starbird of The University of Texas at Austin, takes Plato's dictum to heart and introduces you to the terms, concepts, and astonishing power of geometry. In 24 richly illustrated lectures, you learn that geometry is everywhere. It is the key to scientific disciplines from cosmology to chemistry. It is central to art and architecture. It provides deep insights into algebra, calculus, and other mathematical fields. And it is stunning to contemplate in its beauty.
Geometric Mechanics and Symmetry: From Finite to Infinite Dimensions (Texts in Applied and Engineering Mathematics N 12)
Classical mechanics, one of the oldest branches of science, has undergone a long evolution, developing hand in hand with many areas of mathematics, including calculus, differential geometry, and the theory of Lie groups and Lie algebras. The modern formulations of Lagrangian and Hamiltonian mechanics, in the coordinate-free language of differential geometry, are elegant and general. They pre a unifying framework for many seemingly disparate physical systems, such as n-particle systems, rigid bodies, fluids and other continua, and electromagnetic and quantum systems. text.
Added by: honhungoc | Karma: 8660.27 | Black Hole | 7 October 2010
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Curious and Interesting Geometry
A companion volume to the author's "Dictionary of Curious and Interesting Numbers", which focuses on arithmetic and number theory. The entries in this book cover curves, topology, tilings and all branches of plane and three-dimensional geometry, from Euclid to fractals.
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This book offers a new treatment of the topic, one which is designed to make differential geometry an approachable subject for advanced undergraduates. Professor McCleary considers the historical development of non-Euclidean geometry, placing differential geometry in the context of geometry students will be familiar with from high school. The text serves as both an introduction to the classical differential geometry of curves and surfaces and as a history of a particular surface, the non-Euclidean or hyperbolic plane.
