The Great Courses No.1440: Mathematics, Philosophy, And The "Real World"
36 lectures | 30 minutes each | Year Released: 2009
MPEG-3 | 128 Kbps, 44.1 KHz, 2 channels | English | 0.98 GB
Mathematics has spread its influence far beyond the realm of numbers. The concepts and methods of mathematics are crucially important to all of culture and affect the way countless people in all spheres of life look at the world.
Consider these cases:
- When Leonardo da Vinci planned his mural The Last Supper in the 1490s, he employed geometric perspective to create a uniquely striking composition, centered on the head of Jesus.
- When Thomas Jefferson sat down to write the Declaration of Independence in 1776, he composed it on the model of a geometric proof, which is what gives it much of its power as a defense of liberty.
- When Albert Einstein developed his theory of general relativity in the early 20th century, he used non-Euclidean geometry to prove that the path of a ray of light, in the presence of a gravitational field, is not straight but curved.
Intriguing examples like these reflect the important dialogue between mathematics and philosophy that has flourished throughout history. Indeed, mathematics has consistently helped determine the course of Western philosophical thought. Views about human nature, religion, truth, space and time, and much more have been shaped and honed by the ideas and practices of this vital scientific field.
01.What's It All About?
02.You Bet Your Life—Statistics and Medicine
03.You Bet Your Life—Cost-Benefit Analysis
04.Popular Statistics—Averages and Base Rates
06.Popular Statistics—Polling and Sampling
07.The Birth of Social Statistics
08.Probability, Multiplication, and Permutations
09.Combinations and Probability Graphs
10.Probability, Determinism, and Free Will
11.Probability Problems for Fun and Profit
12.Probability and Modern Science
13.From Probability to Certainty
14.Appearance and Reality—Plato's Divided Line
15.Plato's Cave—The Nature of Learning
16.Euclid's Elements—Background and Structure
17.Euclid's Elements—A Model of Reasoning
18.Logic and Logical Fallacies—Why They Matter
19.Plato's Meno—How Learning Is Possible
20.Plato's Meno—Reasoning and Knowledge
21.More Euclidean Proofs, Direct and Indirect
22.Descartes—Method and Mathematics
23.Spinoza and Jefferson
24.Consensus and Optimism in the 18th Century
25.Euclid—Parallels, Without Postulate 5
26.Euclid—Parallels, Needing Postulate 5
27.Kant, Causality, and Metaphysics
28.Kant's Theory of Space and Time
29.Euclidean Space, Perspective, and Art
30.Non-Euclidean Geometry—History and Examples
31.Non-Euclidean Geometries and Relativity
32.Non-Euclidean Geometry and Philosophy
33.Art, Philosophy, and Non-Euclidean Geometry
34.Culture and Mathematics in Classical China
35.The Voice of the Critics
36.Mathematics and the Modern World
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