### The Great Courses No.1440: Mathematics, Philosophy, And The "Real World"

**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.

Content:

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

05.Popular Statistics—Graphs

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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