Contents Preface Xi 1 The How,wnen. and Why of Mathematics Spotlight: George P61ya Tips on Doing Homework 2 Logically Speaking 3 Introducing the contrapositivc and Converse 4 Set Notation and opantificrs Tips on Quantification 5 Proof Techniques Tips on Definitions 6 Sets Spotlight:Paradoxs 7 Operations on Sets 8 More on Operations on Sets 9 The Power Set and the Cartesian Product Tips on Writing Mathematics 10 Relations Tips on Reading Mathematics 11 Partitions Tips on Putting It All Together 12 Order in the Reals Tips:You Solved It Now What? 13 Functions, Domain, and Range Spotlight:The Definition of Function 14 Functions, One-to-One, and Onto 15 Inverses 16 Images and Inverse Images Spotlight. Minimum or Infimum 17 Mathematical Induction …… 18 Sequences 19 Convergence of Sequences of Real Numbers 20 Equivalent Sets 21 Finite Sets and an Infinite Set 22 Countable and Uncountable Sets 23 Metric Spaces 24 Getting to Know Open and Closed Sets 25 Modular Arithmetic 26 Fermat's Little Theorem 27 Projects 28 Appendix References Index
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