Group theory | Wikipedia audio article
Channel: wikipedia tts
Date: 2018-12-25

This is an audio version of the Wikipedia Article:
https://en.wikipedia.org/wiki/Group_theory


00:01:10 1 Main classes of groups
00:01:34 1.1 Permutation groups
00:02:42 1.2 Matrix groups
00:03:20 1.3 Transformation groups
00:04:13 1.4 Abstract groups
00:06:05 1.5 Groups with additional structure
00:08:21 2 Branches of group theory
00:08:30 2.1 Finite group theory
00:09:52 2.2 Representation of groups
00:11:55 2.3 Lie theory
00:13:00 2.4 Combinatorial and geometric group theory
00:16:37 3 Connection of groups and symmetry
00:19:10 4 Applications of group theory
00:19:42 4.1 Galois theory
00:20:35 4.2 Algebraic topology
00:21:42 4.3 Algebraic geometry and cryptography
00:22:58 4.4 Algebraic number theory
00:23:40 4.5 Harmonic analysis
00:24:04 4.6 Combinatorics
00:24:24 4.7 Music
00:24:41 4.8 Physics
00:25:21 4.9 Chemistry and materials science
00:27:30 4.10 Statistical mechanics
00:27:43 5 History
00:27:53 6 See also
00:28:08 7 Notes
00:30:20 8 References



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SUMMARY
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In mathematics and abstract algebra, group theory studies the algebraic structures known as groups.  
The concept of a group is central to abstract algebra: other well-known algebraic structures, such as rings, fields, and vector spaces, can all be seen as groups endowed with additional operations and axioms. Groups recur throughout mathematics, and the methods of group theory have influenced many parts of algebra. Linear algebraic groups and Lie groups are two branches of group theory that have experienced advances and have become subject areas in their own right.
Various physical systems, such as crystals and the hydrogen atom, may be modelled by symmetry groups. Thus group theory and the closely related representation theory have many important applications in physics, chemistry, and materials science. Group theory is also central to public key cryptography.
One of the most important mathematical achievements of the 20th century was the collaborative effort, taking up more than 10,000 journal pages and mostly published between 1960 and 1980, that culminated in a complete classification of finite simple groups.