Mathematical Methods for Physics: An Introduction to Group Theory, Topology and Geometry

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This detailed yet accessible text provides an essential introduction to the advanced mathematical methods at the core of theoretical physics. The book steadily develops the key concepts required for an understanding of symmetry principles and topological structures, such as group theory, differentiable manifolds, Riemannian geometry, and Lie algebras. Based on a course for senior undergraduate students of physics, it is written in a clear, pedagogical style and would also be valuable to students in other areas of science and engineering. The material has been subject to more than twenty years of feedback from students, ensuring that explanations and examples are lucid and considered, and numerous worked examples and exercises reinforce key concepts and further strengthen readers' understanding. This text unites a wide variety of important topics that are often scattered across different books, and provides a solid platform for more specialized study or research.

LECTURES ON ALGEBRAIC TOPOLOGY

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Algebraic Topology and basic homotopy theory form a fundamental building block for much of modern mathematics. These lecture notes represent a culmination of many years of leading a two-semester course in this subject at MIT. The style is engaging and student-friendly, but precise. Every lecture is accompanied by exercises. It begins slowly in order to gather up students with a variety of backgrounds, but gains pace as the course progresses, and by the end the student has a command of all the basic techniques of classical homotopy theory. Request Inspection Copy Sample Chapter(s) Preface Chapter 1: Singular homology Contents: Preface Singular Homology Computational Methods Cohomology and Duality Basic Homotopy Theory The Homotopy Theory of CW Complexes Vector Bundles and Principal Bundles Spectral Sequences and Serre Classes Characteristic Classes, Steenrod Operations, and Cobordism Bibliography Index Readership: Ideal for a beginning graduate course, aimed at students familiar with general topology and basic modern algebra; also good for researchers who need to use the methods of algebraic topology, in mathematics at large and in theoretical physics.