Group Theory Transforms Math

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mathematical history

Wired

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A group is a set, or collection of objects, together with an operation that takes in two objects and outputs a third

Summary

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77% Informative

The term "group" in a mathematical context was coined in 1830 by Évariste Galois , a French prodigy.

Groups generalize essential properties of the whole numbers.

They have transformed geometry, algebra, and analysis, the mathematical study of smoothly changing functions.

Physicists rely on them to unify the fundamental forces of nature.

Zn is a group with n elements obtained from the numbers { 0 , 1 , 2 , 3 , ,n 1 } together with addition modulo n.

Unlike D6 , Z6 is commutative, because 3 + 5 = 5 + 3, and so forth. In D6 you can generate any element of Z6 using just one of its elements, the number 1 .

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