Download lagu Group theory Math History NJ Wildberger Mp3

Deskripsi:

Title:	Group theory Math History NJ Wildberger
Contributing Artist:	Insights into Mathematics
Album:	Group theory Math History NJ Wildberger - Single
Date:	08 May 2014
Duration:	58 Menit 54.00 detik
Type of file:	Audio MP3 (.mp3)
Audio Summary:	mp3, 44100 Hz, stereo, s16p, 128 kb/s

Here we give an introduction to the historical development of group theory, hopefully accessible even to those who have not studied group theory before, showing how in the 19th century the subject evolved from its origins in number theory and algebra to embracing a good part of geometry.
Actually the historical approach is a very fine way of learning about the subject for the first time.
We discuss how group theory enters perhaps first with Euler's work on Fermat's little theorem and his generalization of it, involving arithmetic mod n. We mention Gauss' composition of quadratic forms, and then look at permutations, which played an important role in Lagrange's approach to the problem of solving polynomial equations, and was then taken up by Abel and Galois.
The example of the symmetric group is at the heart of the subject, and so we examine S_3. In the 19th century groups of transformations became to be intimately tied to symmetries of geometries, with the work of Klein and Lie. A nice example that ties together the algebraic and geometric sides of the subject is the symmetry groups of the Platonic solids.
Video Contents:
00:00 Group theory Introduction
01:13 Origins in Algebra - theory of equations
03:55 Euler 1758: Theorem
07:25 The numbers less than n relatively prime to n
09:50 Group properties
16:34 Theory of polynomial equations
23:38 Permutations - Levi Ben Gershon (1321)
32:38 Multiplication table of S_3
41:44 Lagrange theorem's
44:34 Polyhedral groups
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