An Invitation to Abstract Mathematics

Preface to Instructors.- Preface to Students.- Acknowledgments.- I What''s Mathematics.- 1 Let''s Play a Game!.- 2 What''s the Name of the Game?.- 3 How to Make a Statement.- 4 What''s True in Mathematics?.- A Ten Famous Conjectures.-B Ten Famous Theorems.- II The Foundations of Mathematics.- 5 Let''s Be Logical!.- 6 Setting Examples.- 7 Quantifier Mechanics.- 8 Let''s Be Functional!.- C The Foundations of Set Theory.- III How to Prove It.- 9 Universal Proofs.- 10 The Domino Theory.- 11 More Domino Games.- 12 Existential Proofs.- D Ten Famous Problems.- IV Advanced Math for Beginners.- 13 Mathematical Structures.- 14 Working in the Fields (and Other Structures).- 15 Group Work.- 16 Good Relations.- 17 Order, Please!.- 18 Now That''s the Limit!.- 19 Sizing It Up.- 20 Infinite Delights.- 21 Number Systems Systematically.- 22 Games Are Valuable!.- E Graphic Content.- F All Games Considered.- G A Top Forty List of Math Theorems.