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− | = | + | =Applications: Other= |

+ | =====Eisenstein's Criterion===== | ||

+ | Eisenstein's criterion provides a useful way to figure out the Galois group of a polynomial. If one knows the factors of a polynomial f, then using the Galois groups of those factors, one can determine the Galois group of f, as the Galois group of f also contains all the Galois groups of its factors. | ||

+ | =====In other fields outside mathematics===== | ||

+ | Galois theory is rarely applicable outside of mathematics. Therefore it is often difficult to find applications of Galois groups outside of the realm of graduate level mathematics. Galois theory and Galois groups have provided a nice way to solve problems within the realm of mathematics, but like some concepts within modern pure math, it just has not found many direct applications in other fields yet. | ||

+ | =====Further Reading===== | ||

− | + | [[ Walther MA271 Fall2020 topic1|Back to Walther MA271 Fall2020 topic1]] | |

− | + | [[Category:MA271Fall2020Walther]] | |

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## Revision as of 21:30, 6 December 2020

## Contents

# Applications: Other

##### Eisenstein's Criterion

Eisenstein's criterion provides a useful way to figure out the Galois group of a polynomial. If one knows the factors of a polynomial f, then using the Galois groups of those factors, one can determine the Galois group of f, as the Galois group of f also contains all the Galois groups of its factors.

##### In other fields outside mathematics

Galois theory is rarely applicable outside of mathematics. Therefore it is often difficult to find applications of Galois groups outside of the realm of graduate level mathematics. Galois theory and Galois groups have provided a nice way to solve problems within the realm of mathematics, but like some concepts within modern pure math, it just has not found many direct applications in other fields yet.