547304044 by Unknown

Author:Unknown
Language: eng
Format: epub

1832 France

Galois Theory

Evariste Galois (1811–1832)

Galois theory is a branch of mathematics derived from the theory of equations.

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Galois theory analyses the solutions of an equation in terms of permutations. It led to group theory, one of the major topics of mathematics.

Many of the topics in this book have been concerned with solving equations such as the quadratic, the cubic, the quartic, and the quintic. The first three can be solved by formulae, the last cannot. Galois theory puts it all together, considering the possible solutions of an equation, and showing how they can be interchanged. These interchanges are called “permutations” and the properties of these permutations decide how the equation can be solved.

The permutations form what Galois called a group. The groups of permutations corresponding to the quadratic, cubic, and quartic have a property that the quintic doesn’t, and that is why there is no general formula for the quintic. Group theory is now one of the major areas of mathematics. It has been extended to many other structures besides permutations and is used in physics, as well as in pure mathematics.

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