# fundamental theorem of algebra

Published articles for fundamental theorem of algebra.

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## Fundamental Theorem of Algebra (With Picard's Little Theorem)

DevFeed: [Fundamental Theorem of Algebra (With Picard's Little Theorem)](<https://devfeed.tech/articles/fundamental-theorem-of-algebra-with-picard-s-little-theorem-40261.md>)

Original publisher: [Read original article](<https://www.jeremykun.com/2012/02/07/fundamental-theorem-of-algebra-with-picards-little-theorem/>)

Published: 2012-02-07T21:30:12Z

Content type: tutorial

Language: en

Sources: [Jeremy Kun](<https://devfeed.tech/sources/jeremy-kun.md>)

Topics: [Math and Logic](<https://devfeed.tech/topics/math-and-logic.md>), [Mathematics](<https://devfeed.tech/topics/mathematics.md>)

Tags: [complex-analysis](<https://devfeed.tech/tags/complex-analysis.md>), [fundamental-theorem-of-algebra](<https://devfeed.tech/tags/fundamental-theorem-of-algebra.md>), [mathematics](<https://devfeed.tech/tags/mathematics.md>), [polynomials](<https://devfeed.tech/tags/polynomials.md>)

### AI overview

This post proves the Fundamental Theorem of Algebra using Picard's Little Theorem. Assuming basic complex analysis, it argues that a nonconstant polynomial cannot omit both zero and a suitable reciprocal value, because continuity and boundedness would force a zero.

### Source excerpt

This post assumes familiarity with some basic concepts in complex analysis, including continuity and entire (everywhere complex-differentiable) functions. This is likely the simplest proof of the theorem (at least, among those that this author has seen), although it stands on the shoulders of a highly nontrivial theorem. The fundamental theorem of algebra has quite a few number of proofs (enough to fill a book!). In fact, it seems a new tool in mathematics can prove its worth by being able to prove the fundamental theorem in a different way.

## The Fundamental Theorem of Algebra (with Galois Theory)

DevFeed: [The Fundamental Theorem of Algebra (with Galois Theory)](<https://devfeed.tech/articles/the-fundamental-theorem-of-algebra-with-galois-theory-40259.md>)

Original publisher: [Read original article](<https://www.jeremykun.com/2012/02/02/the-fundamental-theorem-of-algebra-galois-theory/>)

Published: 2012-02-02T22:42:11Z

Content type: article

Language: en

Sources: [Jeremy Kun](<https://devfeed.tech/sources/jeremy-kun.md>)

Topics: [Mathematics](<https://devfeed.tech/topics/mathematics.md>), [Math and Logic](<https://devfeed.tech/topics/math-and-logic.md>)

Tags: [field](<https://devfeed.tech/tags/field.md>), [fundamental-theorem-of-algebra](<https://devfeed.tech/tags/fundamental-theorem-of-algebra.md>), [galois-theory](<https://devfeed.tech/tags/galois-theory.md>), [group-theory](<https://devfeed.tech/tags/group-theory.md>), [mathematics](<https://devfeed.tech/tags/mathematics.md>), [polynomials](<https://devfeed.tech/tags/polynomials.md>), [roots](<https://devfeed.tech/tags/roots.md>)

### AI overview

This mathematics post presents a Galois-theoretic proof strategy for the fundamental theorem of algebra. It assumes familiarity with field extensions, Galois theory, and group theory, and develops the argument using splitting fields, an intermediate extension of degree 2, Sylow subgroups, and the Galois correspondence.

### Source excerpt

This post assumes familiarity with some basic concepts in abstract algebra, specifically the terminology of field extensions, and the classical results in Galois theory and group theory. The fundamental theorem of algebra has quite a few number of proofs (enough to fill a book!). In fact, it seems a new tool in mathematics can prove its worth by being able to prove the fundamental theorem in a different way. This series of proofs of the fundamental theorem also highlights how in mathematics there are many many ways to prove a single theorem, and in re-proving an established theorem we introduce new concepts and strategies.