To design future networks that are worthy of societys trust we must put the 'discipline of computer networking on a much stronger foundation. This book rises above the considerable minutiae of todays networking technologies to emphasize the long-standing mathematical underpinnings of the field." -Professor Jennifer Rexford Department of Computer Science Princeton University "This book is exactly the one I have been waiting for the last couple of years. Recently I decided most students were already very familiar with the way the net works but were not being taught the fundamentals-the math. This book contains the knowledge for people who will create and understand future communications systems." -Professor Jon Crowcroft The Computer Laboratory University of Cambridge The Essential Mathematical Principles Required to Design Implement or Evaluate Advanced Computer Networks Students researchers and professionals in computer networking require a firm conceptual understanding of its foundations. Mathematical Foundations of Computer Networking provides an intuitive yet rigorous introduction to these essential mathematical principles and techniques. Assuming a basic grasp of calculus this book offers sufficient detail to serve as the only reference many readers will need. Each concept is described in four ways: intuitively; using appropriate mathematical notation; with a numerical example carefully chosen for its relevance to networking; and with a numerical exercise for the reader. The first part of the text presents basic concepts and the second part introduces four theories in a progression that has been designed to gradually deepen readers understanding. Within each part chapters are as self-contained as possible. The first part covers probability; statistics; linear algebra; optimization; and signals systems and transforms. Topics range from Bayesian networks to hypothesis testing and eigenvalue computation to Fourier transforms. These preliminary chapters establish a