CONTENTS vii Appendix A. Sets, Functions, and Other Basic Ideas 271 A.1. Sets and Elements 271 A.2. Equality, Inclusion, and Notation 272 A.3. The Algebra of Sets 273 A.4. Cartesian Products, Counting, and Power Sets 277 A.5. Some Sets of Numbers 279 A.6. Equivalence Relations and the Construction of Q 284 A.7. Functions 290 A.8. Countability and Other Basic Ideas 297 A.9. The Axiom of Choice 305 A.10. Independent Projects 308 Appendix B. Linear Algebra 313 B.1. Fundamentals of Linear Algebra 313 B.2. Linear Transformations 319 B.3. Linear Transformations and Matrices 321 B.4. Determinants 324 B.5. Geometric Linear Algebra 332 B.6. Independent Projects 340 Bibliography 351 Index of Terminology 353 Index of Notation Definitions 361

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