Osnovni teorem algebre

Kišić, Nika (2014) Osnovni teorem algebre. Diploma thesis, Faculty of Science > Department of Mathematics.

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Abstract

In this graduate thesis we prove the fundamental theorem of algebra in several ways. In the first chapter we give a historical overview of this theorem. In the second chapter we outline the first proof using properties of complex polynomials. In the next chapter, we interpret complex polynomials as algebraic objects. In this way we are able to present the second proof by applying field and extension field properties. The final chapter is dedicated to complex analysis. We demonstrate that the fundamental theorem of algebra can be proved by using Liouville’s theorem. At the end of the work, we give two additional proofs rooted in complex analysis. The first one uses the mean value inequality and the second one is based on the maximum modulus principle.

Item Type: Thesis (Diploma thesis)
Supervisor: Krčadinac, Vedran
Date: 2014
Number of Pages: 37
Subjects: NATURAL SCIENCES > Mathematics
Divisions: Faculty of Science > Department of Mathematics
Depositing User: Iva Prah
Date Deposited: 03 Jun 2015 11:32
Last Modified: 03 Jun 2015 11:32
URI: http://digre.pmf.unizg.hr/id/eprint/3984

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