by Nirmala Prakash (Visiting Scientist, Massachusetts Institute of Technology, USA)

Table of Contents (64k)
Preface (51k)
Chapter 1: Complex Functions, Riemann Surfaces, and Two-Dimensional Conformal Field Theory (An Introduction)
Chapter 1.1: Complex Functions (357k)
Chapter 1.2: Complex Structures on a Manifold, Kahler Metric (267k)
Chapter 1.3: Riemann Surfaces (1,077k)
Chapter 1.4: The Two-Dimensional Conformal Field Theory (422k)

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.

• Complex Functions, Riemann Surfaces and Two-Dimensional Conformal Field Theory (an Introduction)
• Elements of Group Theory and Group Representations
• A Primer on Operators
• Basics of Algebras and Related Concepts
• Infinite-Dimensional Algebras
• The Role of Symmetry in Physics and Mathematics
• All That's Super — An Introduction
• Gravitation, Relativity and Black Holes
• Basics of Quantum Theory
• Theory of Yang–Mills and the Yang–Mills–Higgs Mechanism
• Strings and Superstrings (Elementary Aspects)