About the Author
Introduction
First Steps
Then, The Babylonians, Egyptians, and The Greeks
And Elsewhere
Axioms
Definitions and Properties
Addition
Properties of Addition – Proof Based on Axioms
The Associative Law
The Law of Substitution
The Commutative Law
What is Mathematics: A First Look
The Law of Cancellation
Summary So Far
Sets – Definitions and Properties
Simple Logic
A Note About Infinity
Definitions and Properties
A new relationship: Less–Equals
Some Terminology
Multiplication
What is Easy, What is Hard, and Mathematical Insight
Algebra, Variables, Unknowns, and How Mathematics is Not Computer Science
Some Interesting Sums
Representing Whole Numbers
Summary So Far
Equivalence Relations and Equivalence Classes
Definitions and Properties
Generalization and the Nature of Mathematics – Foreshadowing Abstract Algebra
Applied Mathematics: A Simple Example
Subtraction
A Note on Proof
Substitution and Cancellation Laws in Z
Integer Division and Remainders
A Note on Mathematical Insight
Summary So Far
Definitions and Properties
Denseness and Distance in the Rational Numbers
Cardinality of the Rational Numbers
Decimals and the Rational Numbers
Summary So Far
Definition and Properties
Infinite Series
Cauchy Sequences
Definition and Properties
Cardinality of the Real Numbers
Foreshadowing: Topology
Foreshadowing – Calculus and Analysis
Summary So Far
Definition and Properties
Definition and Properties
Foreshadowing – Trigonometry
Foreshadowing – Matrix Theory
Summary So Far
What Do Mathematicians Do?
A Simple Example
Index