Number theory

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Title: Number theory
Author: Cheqe, Paul

The number theory module consists of two units. It pre-supposes the teacher trainee is conversant with Basic mathematics. The first unit deals with properties of integers and linear diophantine equations. It progresses from properties of integers through divisibility with remainder, prime numbers and their distribution, Euclid's proof of infinitely many primes and Euclid's algorithm and its application in solving linear diophantine equations. The unit is concluded with Pythagorean triplets and Fermat's last theorem for the vitas powers and the proof of Wiles.

The second unit assumes unit one as a prerequisite for the trainees. It introduces the field of integers( mod p), squares and quadratic residues, Alar's criterion, Legendre symbol, Gauss lemma and quadratic reciprocity law, Euclid's algorithm and unique factorisation of Gaussian integers, arithmetic of quadratic fields and application of diophantine equations, and is concluded with Fermat's last theorem for cubes, Pell's equation and units in real quadratic fields.

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Date: 2010-10-11

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Files Size Format View Description
Number 901.4Kb QuickTime video View/Open Introduction (QuickTime)
Number 5.719Mb QuickTime video View/Open Overview (QuickTime)
Number theory.doc 1.224Mb Microsoft Word View/Open Whole module (doc)
Number theory.pdf 1.759Mb PDF View/Open Whole module (PDF)

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Stian Håklev (admin)

5 years ago

I found this resource very useful, and will often use it in my class.

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