Mathematical Reasoning : Patterns, Problems, Conjectures, and Proofs (Hardcover)

1. What Is Mathematics? 2. Counting. 3. Numbers. 4. Deduction and Abstraction. 5. Proofs. 6. Informal Reasoning. 7. Representations. 8. Infinity. 9. Infinitesimals. 10. Predilections. 11. Esthetics in Mathematics. 12. The Usefulness of Mathematics. 13. Foundations. 14. Preschool Development. 15. Math in Schools. 16. Math Problem Solving. 17. Final Thoughts.