Preface  1    The How, When, and Why of Mathematics    Spotlight: George Polya    Tips on Doing Homework  2    Logically Speaking  3    Introducing the Contrapositive and Converse  4    Set Notation and Quantifiers    Tips on Quantification  5    Proof Techniques    Tips on Definitions  6    Sets    Spotlight: Paradoxes  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    Spotlight: Public and Secret Research  27    Projects    Tips on Talking about Mathematics    27.1    Picture Proofs    27.2    The Best Number of All    27.3    Set Constructions    27.4    Rational and Irrational Numbers    27.5    Irrationality of $e$ and $\pi $    27.6    When does $f^{-1} = 1/f$?    27.

7    Pascal's Triangle    27.8    The Cantor Set    27.9    The Cauchy-Bunyakovsky-Schwarz  Inequality    27.10    Algebraic Numbers    27.11    The RSA Code    Spotlight: Hilbert's Seventh Problem  28    Appendix    28.1    Algebraic Properties of $\@mathbb {R}$    28.2    Order Properties of $\@mathbb {R}$    28.3    Polya's List      References      Index.