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Graduate students, researchers, and professionals in the field of computer networking often require a firm conceptual understanding of its theoretical foundations. Knowledge of optimization, information theory, game theory, control theory, and queueing theory is assumed by research papers in the field. Yet these subjects are not taught in a typical computer science undergraduate curriculum. This leaves only two alternatives: to either study these topics on one’s own from standard texts or take a remedial course. Neither alternative is attractive. Standard texts pay little attention to computer networking in their choice of problem areas, making it a challenge to map from the text to the problem at hand, and it is inefficient to require students to take an entire course when all that is needed is an introduction to the topic. This book addresses these problems by providing a single source to learn about the mathematical foundations of computer networking. Assuming only a rudimentary grasp of calculus, the book provides an intuitive yet rigorous introduction to a wide range of mathematical topics. The topics are covered in sufficient detail so that the book will usually serve as both the first and ultimate reference. Note that the topics are selected to be complementary to those found in a typical undergraduate computer science curriculum. The book, therefore, does not cover network foundations, such as discrete mathematics, combinatorics, or graph theory. xvi Preface Each concept in the book is described in four ways: intuitively, using precise mathematical notation, providing a carefully chosen numerical example, and offering a numerical exercise to be done by the reader. This progression is designed to gradually deepen understanding. Nevertheless, the depth of coverage provided here is not a substitute for that found in standard textbooks. Rather, I hope to provide enough intuition to allow a student to grasp the essence of a research paper that uses these theoretical foundations.