1 Paradoxes; 2 What Do the Paradoxes Mean?; 3 Whole Numbers;4 Functions; 5 Proofs; 6 Infinite Collections?; 7 Hilbert "On the Infinite"; 8 Computability; 9 Turing Machines; 10 The Most Amazing Fact and Church"s Thesis; 11 Primitive Recursive Functions; 12 The Grzegorczyk Hierarchy; 13 Multiple Recursion; 14 The Least Search Operator; 15 Partial Recursive Functions; 16 Numbering the Partial Recursive Functions; 17 Listability; 18 Turing Machine Computable = Partial Recursive; 19 Propositional Logic; 20 An Overview of First-Order Logic and Gödel"s Theorems; 21 First-Order Arithmetic; 22 Functions Representable in First-Order Arithmetic; 23 The Undecidability of Arithmetic; 24 The Unprovability of Consistency; 25 Church"s Thesis; 26 Constructivist Views of Mathematics; 27 Mathematics as Modeling