Tu, Loring W.  | Springer

0원  | 20210101  | 9780387480985

The aim of this textbook is to introduce advanced undergraduate and graduate level students - in either a mathematics or physics field of study - to manifolds. In the first section of the book, the Euclidean space and point-set topology are presented to create a smooth transition from undergraduate calculus. At a quick yet accessible pace, the text then continues to explore manifolds in terms of their relationship to tangent spaces, such as Lie groups and their Lie algebras. The focus within each chapter consists of only the most fundamental topics in manifold theory. This modesty of scope and logical organization lend clarity to the book. Examples and exercises are provided throughout the text and solutions to selected exercises are also included. A novice to manifolds needs a semester of abstract algebra and a year of real analysis. The author covers prerequisites from point-set topology in an elaborate appendix. An Introduction to Manifolds should enable students to do calculus on manifolds and recognize their applications in analysis and topology.

Tu, Loring W.  | Springer International Publishing AG

65,000원  | 20170615  | 9783319550824

Over the past one hundred years, differential geometry has proven indispensable to an understanding of the physical world, in Einstein's general theory of relativity, in the theory of gravitation, in gauge theory, and now in string theory.

Tu, Loring W.  | Springer

96,230원  | 20110614  | 9781441973993

Manifolds, the higher-dimensional analogs of smooth curves and surfaces, are fundamental objects in modern mathematics. Combining aspects of algebra, topology, and analysis, manifolds have also been applied to classical mechanics, general relativity, and quantum field theory. In this streamlined introduction to the subject, the theory of manifolds is presented with the aim of helping the reader achieve a rapid mastery of the essential topics. By the end of the book the reader should be able to compute, at least for simple spaces, one of the most basic topological invariants of a manifold, its de Rham cohomology. Along the way, the reader acquires the knowledge and skills necessary for further study of geometry and topology. The requisite point-set topology is included in an appendix of twenty pages; other appendices review facts from real analysis and linear algebra. Hints and solutions are provided to many of the exercises and problems. This work may be used as the text for a one-semester graduate or advanced undergraduate course, as well as by students engaged in self-study. Requiring only minimal undergraduate prerequisites, "Introduction to Manifolds" is also an excellent foundation for Springer's GTM 82, "Differential Forms in Algebraic Topology".