Classification theorems | Wikipedia audio article
Channel: Subhajit Sahu
Date: 29/12/2018

This is an audio version of the Wikipedia Article:
https://en.wikipedia.org/wiki/Classification_theorem


00:01:22 1 Geometry
00:02:11 2 Algebra
00:02:32 3 Linear algebra
00:03:06 4 Complex analysis



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SUMMARY
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In mathematics, a classification theorem answers the classification problem "What are the objects of a given type, up to some equivalence?". It gives a non-redundant enumeration: each object is equivalent to exactly one class.
A few related issues to classification are the following.

The equivalence problem is "given two objects, determine if they are equivalent".
A complete set of invariants, together with which invariants are realizable, solves the classification problem, and is often a step in solving it.
A computable complete set of invariants (together with which invariants are realizable) solves both the classification problem and the equivalence problem.
A canonical form solves the classification problem, and is more data: it not only classifies every class, but provides a distinguished (canonical) element of each class.There exist many classification theorems in mathematics, as described below.