Introduction.- Doing Mathematics A Toolkit for Mathematical Reasoning.- Sets and Their Algebras The Stem Cells of Mathematics.- Numbers I The Basics of Our Number System.- Arithmetic Putting Numbers to Work.- Summations Complex Operations from Simple Components.- The Vertigo of Infinity Handling the Very Large and the Infinite.- Numbers II Building the Integers and Building with the Integers.- Recurrences Rendering Complex Structure Manageable.- Numbers III Operational Representations and Their Consequences.- The Art of Counting Combinatorics, Probability, and Statistics.- Graphs I Representing Relationships Mathematically.- Graphs II Graphs Within Computation and Communication.- Solutions to Exercises.- App. A, Pairing Functions.- App. B, A Deeper Look at the Fibonacci Numbers.- App. C, Two Recurrence-Defined Number Families.- App. D, Signed-Digit Numerals Carry-Free Addition.- App. E, The Diverse Delights of de Bruijn Networks.- List of Symbols.- References.- Index.