An Outline of Set Theory

This book is an innovative problem-oriented introduction to undergraduate set theory. It is intended to be used in a course in which the students work in groups on projects and present their solutions to the class. Students completing such a course come away with a deeper understanding of the material, as well as a clearer view of what it means to do mathematics. The topics covered include standard undergraduate set theory, as well as some material on nonstandard analysis, large cardinals, and Goodstein's Theorem.

Contenu
One Projects.- 1. Logic and Set Theory.- 2. The Natural Numbers.- 3. The Integers.- 4. The Rationals.- 5. The Real Numbers.- 6. The Ordinals.- 7. The Cardinals.- 8. The Universe.- 9. Choice and Infinitesimals.- 10. Goodstein's Theorem.- Two Suggestions.- 1. Logic and Set Theory.- 2. The Natural Numbers.- 3. The Integers.- 4. The Rationals.- 5. The Real Numbers.- 6. The Ordinals.- 7. The Cardinals.- 8. The Universe.- 9. Choice and Infinitesimals.- 10. Goodstein's Theorem.- Three Solutions.- 1. Logic and Set Theory.- 2. The Natural Numbers.- 3. The Integers.- 4. The Rationals.- 5. The Real Numbers.- 6. The Ordinals.- 7. The Cardinals.- 8. The Universe.- 9. Choice and Infinitesimals.- 10. Goodstein's Theorem.