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Analysis of Kneser's Root Finding Algorithm for Polynomials in a Constructive Setting

Gamboa Quintero, Guillermo (2018) Analysis of Kneser's Root Finding Algorithm for Polynomials in a Constructive Setting. Bachelor's Thesis, Mathematics.

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Abstract

This Bachelor thesis reproduces the proof of the Kneser Algorithm which is used to find roots of nonconstant polynomials as well as providing an analysis of the algorithm in a constructive setting. At first, the motivation for Mathematical Constructivism is presented. Second, the real numbers are constructed through Cauchy sequences and equivalence classes. This leads to an axiomatization of the real numbers in the proof assistant Coq through the construction of a real number structure that is composed of Cauchy sequences of rationals. This will be proven in the first part of the thesis. The second part contains a detailed proof of the Kneser Algorithm. Finally, it contains a brief section that treats an alternative method of proving the algorithm.

Item Type: Thesis (Bachelor's Thesis)
Supervisor:
Supervisor nameSupervisor E mail
Renardel de Lavalette, G.R.G.R.Renardel.de.Lavalette@rug.nl
Top, J.J.Top@rug.nl
Degree programme: Mathematics
Thesis type: Bachelor's Thesis
Language: English
Date Deposited: 12 Jul 2018
Last Modified: 24 Jul 2018 14:04
URI: http://fse.studenttheses.ub.rug.nl/id/eprint/17828

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