Mathematics and the Real World (75 page)
Read Mathematics and the Real World Online
Authors: Zvi Artstein
32. The Strings Return
33. Another Look at Platonism
34. The Scientific Method: Is there an Alternative?
Chapter V. The Mathematics of Randomness
35. Evolution and Randomness in the Animal World
36. Probability and Gambling in Ancient Times
37. Pascal and Fermat
38. Rapid Development
39. The Mathematics of Predictions and Errors
40. The Mathematics of Learning from Experience
41. The Formalism of Probability
42. Intuition versus the Mathematics of Randomness
43. Intuition versus the Statistics of Randomness
Chapter VI. The Mathematics of Human Behavior
44. Macro-considerations
45. Stable Marriages
46. The Aggregation of Preferences and Voting Systems
47. The Mathematics of Confrontation
48. Expected Utility
49. Decisions in a State of Uncertainty
50. Evolutionary Rationality
Chapter VII. Computations and Computers
51. Mathematics for Computations
52. From Tables to Computers
53. The Mathematics of Computations
54. Proofs with High Probability
55. Encoding
56. What Next?
Chapter VIII. Is there Really no Doubt?
57. Mathematics without Axioms
58. Rigorous Development without Geometry
59. Numbers as Sets, Logic as Sets
60. A Major Crisis
61. Another Major Crisis
Chapter IX. The Nature of Research in Mathematics
62. How Does a Mathematician Think?
63. On Research in Mathematics
64. Pure Mathematics vis-à-vis Applied Mathematics
65. The Beauty, Efficiency, and Universality of Mathematics
Chapter X. Why is Teaching and Learning Mathematics so Hard?
66. Why Learn Mathematics?
67. Mathematical Thinking: There is no Such Thing
68. A Teacher-Parent Meeting
69. A Logical Structure vis-à-vis a Structure for Teaching
70. What is Hard in Teaching Mathematics?
71. The Many Facets of Mathematics
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