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This book presents the basics of mathematics that are needed for learning the physics of today. It describes briefly the theories of groups and operators, finite- and infinite-dimensional algebras, concepts of symmetry and supersymmetry, and then delineates their relations to theories of relativity and black holes, classical and quantum physics, electroweak fields and Yang-Mills. It concludes with a chapter on (the complex theory of) strings and superstrings and their link to black holes — an idea that fascinates both the physicist and the mathematician.
Sample Chapter(s)
Chapter 1.1: Complex Functions (357 KB)
Chapter 1.2: Complex Structures on a Manifold, Kahler Metric (267 KB)
Chapter 1.3: Riemann Surfaces (1,077 KB)
Chapter 1.4: The Two-Dimensional Conformal Field Theory (422 KB)
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