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AuthorNaber, Gregory L. author
TitleTopology, Geometry, and Gauge Fields [electronic resource] : Foundations / by Gregory L. Naber
ImprintNew York, NY : Springer New York : Imprint: Springer, 1997
Connect tohttp://dx.doi.org/10.1007/978-1-4757-2742-5
Descript XVIII, 396 p. online resource

SUMMARY

Mathematics is playing an ever more important role in the physical and biological sciences, provoking a blurring of boundaries between scientific disciplines and a resurgence of interest in the modern as well as the clasยญ sical techniques of applied mathematics. This renewal of interest, both in research and teaching, has led to the establishment of the series: Texts in Applied Mathematics (TAM). The development ofnewcourses is a natural consequence of a high levelof excitement on the research frontier as newer techniques, such as numerical and symbolic computer systems, dynamical systems, and chaos, mix with and reinforce the traditional methods of applied mathematics. Thus, the purpose of this textbook series is to meet the current and future needs of these advances and encourage the teaching of new courses. TAM will publish textbooks suitable for use in advanced undergraduate and beginning graduate courses, and will complement the Applied matheยญ matical Sciences (AMS) series, which will focus on advanced textbooks and research level monographs. Preface In Egypt, geometry was created to measure the land. Similar motivations, on a somewhat larger scale, led Gauss to the intrinsic differential geometry of surfaces in space. Newton created the calculus to study the motion of physical objects (apples, planets, etc.) and Poincare was similarly impelled toward his deep and far-reaching topological view of dynamical systems


CONTENT

0 Physical and Geometrical Motivation -- 1 Topological Spaces -- 2 Homotopy Groups -- 3 Principal Bundles -- 4 Differentiable Manifolds and Matrix Lie Groups -- 5 Gauge Fields and Instantons -- Appendix SU (2) and SO (3) -- References -- Symbols


Mathematics Geometry Topology Mathematics Topology Geometry



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