Grabiner, Judith V. 1938- creator Teaching Company text bibliography vau Chantilly, Va Teaching Co. 2009 monographic eng

print

3 volumes ; 21 cm. These lectures reveal how mathematics has changed the way people look at the world. We study how the model of certainty in Euclid's revolutionary Elements influenced philosophers for centuries, and how the invention of non-Euclidiean geometry further influenced philosophy and changed modern views of the world. As well. we consider how the newer disciplines of probability and statistics gave scientists ways of dealing--with precision--with events that did not seem to follow laws but were due to chance. We look at some elementary probability theory and its applications to the study of society, and we examine such issues as free will, determinism, and chance in the context of the philosophical views of thinkers from Pascal to Gould. v. 1: Lecture 1. What's it all about? -- Lecture 2. You bet your life -- statistics and medicine -- Lecture 3. You bet your life -- cost-benefit analysis -- Lecture 4. Popular statistics -- averages and base rates -- Lecture 5. Popular statistics -- graphs -- Lecture 6. Popular statistics -- polling and sampling. Disc 2: Lecture 7. The birth of social statistics -- Lecture 8. Probability, multiplication, and permutations -- Lecture 9. Combinations and probability graphs -- Lecture 10. Probability, determinism, and free will -- Lecture 11. Probability problems for fun and profit -- Lecture 12. Probability and modern science. v.3: Lecture 13. From probability to certainty -- Lecture 14. Appearance and reality -- Plato's divided line -- Lecture 15. Plato's cave -- the nature of learning -- Lecture 16. Euclid's Elements -- background and structure -- Lecture 17. Euclid's Elements -- a model of reasoning -- Lecture 18. Logic and logical fallacies -- why they matter. Lecture 19. Plato's Meno -- how learning is possible -- Lecture 20. Plato's Meno -- reasoning and knowledge -- Lecture 21. More Euclidean proofs, direct and indirect -- Lecture 22. Descartes -- method and mathematics -- Lecture 23. Spinoza and Jefferson -- Lecture 24. Consensus and optimism in the 18th century. v.3: Lecture 25. Euclid -- parallels, without Postulate 5 -- Lecture 26. Euclid -- parallels, needing Postulate 5 -- Lecture 27. Kant, causality, and metaphysics -- Lecture 28. Kant's Theory of Space and Time -- Lecture 29. Euclidean space, perspective, and art -- Lecture 30. Non-Euclidean geometry -- history and examples. Lecture 31. Non-Euclidean geometries and relativity -- Lecture 32. Non-Euclidean geometry and philosophy -- Lecture 33. Art, philosophy, and non-Euclidean geometry -- Lecture 34. Culture and mathematics in classical China -- Lecture 35. The voice of the critics -- Lecture 36. Mathematics and the modern world. Judith V. Grabiner. Course no. 1440. "Lecture transcript and course guidebook"--Cover. Educación Enseñanza Matemáticas Filosofía Matemáticas Historia Matemáticas LB 14.6 G728m 2009 1598035541 9781598035544 2011377509 DLC 120409 20230411090132.0 17247672