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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
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:
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