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Table of Contents
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.
"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.