This book's title can be misleading. I would say it is more of an advanced textbook on the mathematics that is a foundation for computer science than a foundational book on the mathematics of computer science. I think this misreading of the title and thus the book's content is what is behind much of the heartache that readers have when trying to tackle it. This book expands on the "Mathematical Preliminaries" portion of "The Art of Computer Programming" series of books by Knuth, and thus this book has a style much like that series of books. The book is complete and clear, but it is also densely packed with lots of theory and proofs and will require much effort and time to understand well. It is really not meant to be an applied mathematics textbook at all. I show the table of contents next. Note that there are exercises at the conclusion of each chapter with solutions in the back of the book. However, most of the exercises are not so simple that you can just glimpse at the solution and figure out how to get from A to B. I recommend it if you have the time. It can really bring out thoughts and the beauty of mathematics that you may not have considered before.<br><br>1. Recurrent Problems.<br>The Tower of Hanoi.<br>Lines in the Plane.<br>The Josephus Problem.<br>Exercises.<br><br>2. Sums.<br>Notation.<br>Sums and Recurrences.<br>Manipulation of Sums.<br>Multiple Sums.<br>General Methods.<br>Finite and Infinite Calculus.<br>Infinite Sums.<br>Exercises.<br><br>3. Integer Functions.<br>Floors and Ceilings.<br>Floor/Ceiling Applications.<br>Floor/Ceiling Recurrences.<br>'mod': The Binary Operation.<br>Floor/Ceiling Sums.<br>Exercises.<br><br>4. Number Theory.<br>Divisibility.<br>Factorial Factors.<br>Relative Primality.<br>'mod': The Congruence Relation.<br>Independent Residues.<br>Additional Applications.<br>Phi and Mu.<br>Exercises.<br><br>5. Binomial Coefficients.<br>Basic Identities.<br>Basic Practice.<br>Tricks of the Trade.<br>Generating Functions.<br>Hypergeometric Functions.<br>Hypergeometric Transformations.<br>Partial Hypergeometric Sums.<br>Mechanical Summation.<br>Exercises.<br><br>6. Special Numbers.<br>Stirling Numbers.<br>Eulerian Numbers.<br>Harmonic Numbers.<br>Harmonic Summation.<br>Bernoulli Numbers.<br>Fibonacci Numbers.<br>Continuants.<br>Exercises.<br><br>7. Generating Functions.<br>Domino Theory and Change.<br>Basic Maneuvers.<br>Solving Recurrences.<br>Special Generating Functions.<br>Convolutions.<br>Exponential Generating Functions.<br>Dirichlet Generating Functions.<br>Exercises.<br><br>8. Discrete Probability.<br>Definitions.<br>Mean and Variance.<br>Probability Generating Functions.<br>Flipping Coins.<br>Hashing.<br>Exercises.<br><br>9. Asymptotics.<br>A Hierarchy.<br>O Notation.<br>O Manipulation.<br>Two Asymptotic Tricks.<br>Euler's Summation Formula.<br>Final Summations.<br>Exercises.<br><br>A. Answers to Exercises.<br>B. Bibliography.