Table of Contents Introduction ix Acknowledgements xiii Chapter 1. Sets, Functions, and Other Basic Ideas 1 §1. Sets and Elements 2 §2. Equality, Inclusion, and Notation 2 §3. The Algebra of Sets 4 §4. Cartesian Products, Counting, and Power Sets 8 §5. Some Sets of Numbers 10 §6. Equivalence Relations and the Construction of Q 15 §7. Functions 22 §8. Countability and Other Basic Ideas 30 §9. Axiom of Choice 38 §10. Independent Projects 41 Chapter 2. Linear Algebra 47 §1. Fundamentals of Linear Algebra 48 §2. Linear Transformations 54 §3. Linear Transformations and Matrices 56 §4. Determinants 59 §5. Geometric Linear Algebra 67 §6. Independent Projects 76 Chapter 3. The Construction of the Real and Complex Numbers 89 vii
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