From the Preface: "This book is addressed to all who are curious about the nature of mathematics and its role in society. It is neither a text book nor a specialists' book. It consists of a number of loosely linked essays that may be read independently and for which I have tried to provide a leitmotif by throwing light on the relationship between mathematics and common sense. In these essays I hope to foster a critical attitude towards both the existence of common sense in mathematics and the ambiguous role that it can play."
1. What Is Mathematics?
2. Mathematics and Common Sense: Relations and
Contrasts.
3. How Common Sense Impacts Mathematical Reasoning: Some Very
Simple Problems.
4. Where Is Mathematical Knowledge Lodged, and Where Does It
Come From?
5. What Is Mathematical Intuition?
6. Are People Hard Wired to Do
Mathematics?
7. Why Counting Is Impossible.
8. Quantification in Todays
World.
9. When Should One Add Two Numbers?
10. Category Dilemma.
11.
Deductive Mathematics
12. Mathematics Brings Forth Entities Whose Existence
Is Counterintuitive.
13. "In Principle We Can". Mathematical Existentialism.
14. Mathematical Proof and Its Discontents.
15. The Logic of Mathematics Can
Spawn Monsters .
16. Rules and Their Exceptions.
17. If Mathematics Says "No"
Does It Really Mean It?.18. Inconsistencies and Their Virtues.
19. On
Ambiguity in Mathematics.
20. Mathematical Evidence: Why Do I Believe a
Theorem?.21. Simplicity, Complexity, Beauty.
22. The Decline and Resurgence
of the Visual in Mathematics.
23. When Is a Problem Solved?.24. What Is Meant
by the Word "Random"?
25. The Paradox of "Hitting It Big".
26. Probability
and Common Sense: A Second Look.
27. Astrology as Early Applied Mathematics.
28. Mumbo Math.
29. Math Mixes It Up with Baseball.
30. Mickey Flies the
Stealth: Mathematics, War, and Entertainment.
31. The Media and Mathematics
Look at Each Other.
32. Platonism vs. Social Constructivism.
33. Mathematics
at the Razors Edge
Davis\, Philip J.
Rohkem infot Taylor & Francis e-raamatute kohta