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The book contains three parts: Spectral theory of large dimensional random matrices; Applications to wireless communications; and Applications to finance. In the first part, we introduce some basic theorems of spectral analysis of large dimensional random matrices that are obtained under finite moment conditions, such as the limiting spectral distributions of Wigner matrix and that of large dimensional sample covariance matrix, limits of extreme eigenvalues, and the central limit theorems for linear spectral statistics. In the second part, we introduce some basic examples of applications of random matrix theory to wireless communications and in the third part, we present some examples of Applications to statistical finance.

Based on the author's teaching experience of Calculus along with a touch of applications of Calculus in other fields such as computer science, engineering, this book provides the practical examples that bring motivation to students to learn Calculus.

Einstein's Special Relativity (E-SR) is the cornerstone of physics. De Sitter invariant SR (dS/AdS-SR) is a natural extension of E-SR, hence it relates to the foundation of physics.

The material for these volumes has been selected from 20 years of examination questions for graduate students at the University of California at Berkeley, Columbia University, University of Chicago, MIT, SUNY at Buffalo, Princeton University and the University of Wisconsin.