MTH2121 - Algebra and number theory

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Overview

Groups in geometry, linear algebra, and number theory; cyclic and abelian groups; permutation groups; subgroups, cosets and normal subgroups; homomorphisms, isomorphisms and the first isomorphism theorem. The Euclidean algorithm, prime factorisation, congruences, the Euler totient function; the theorems of Fermat, Euler and Wilson, and the RSA public key cryptosystem; Chinese … For more content click the Read More button below.

Groups in geometry, linear algebra, and number theory; cyclic and abelian groups; permutation groups; subgroups, cosets and normal subgroups; homomorphisms, isomorphisms and the first isomorphism theorem. The Euclidean algorithm, prime factorisation, congruences, the Euler totient function; the theorems of Fermat, Euler and Wilson, and the RSA public key cryptosystem; Chinese remainder theorem; quadratic reciprocity; factorisation and primality testing algorithms.

Offerings

S1-01-CLAYTON-ON-CAMPUS

S1-FF-CLAYTON-FLEXIBLE

Rules

Enrolment Rule

Contacts

Chief Examiner(s)

Professor Ian Wanless

Unit Coordinator(s)

Professor Ian Wanless

Learning outcomes

On successful completion of this unit, you should be able to:

Appreciate the beauty and the power of pure mathematics;

Recognise the fundamental concepts of algebra and number theory;

Explain the notion of proof in mathematics and be able to carry out basic proofs;

Illustrate how thousands of years of pure mathematical developments have enabled secure electronic communication;

Apply important number theoretic algorithms;

Describe the power of the generality of the concepts in group theory.

Assessment summary

Examination (3 hours and 10 minutes): 60% (Hurdle)

Continuous assessment: 40% (Hurdle)

Hurdle requirement: If you would otherwise have passed the unit but you do not achieve at least 45% in the end of semester written examination and continuous assessment you will receive a Hurdle Fail (NH) grade and a mark of 45 on your transcript.

Workload requirements

Workload

Other unit costs

Costs are indicative and subject to change.
Miscellaneous Items Required (Unit Course Reader,Printing, Stationery)- $120.

Availability in areas of study

Applied mathematics
Mathematical statistics
Mathematics
Pure mathematics