Handbook 1996 : Faculty of Science (Volume 4 page 210)
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618-222 Algebra (Advanced)

Note: Students with a high level of achievement in 618-102 (1995 Handbook) or 618-122 may approach the Head of the Department of Mathematics to seek permission to enrol in this subject.

Credit points: 12.0

Coordinator: Dr J R J Groves

Prerequisite: Mathematics 618-112 or 618-211 or by invitation (See Note below).

Contact: 39 lectures (three a week)

Timetable: Second semester

Objectives:

On completion of this subject, students should:

Comprehend:

• the basic algebraic structure of abstract rings, fields and groups;
• the concepts of isomorphism, homomorphism and quotient algebraic structures; Euclidean algorithm, irreducibility and unique factorization in polynomial rings;
• basic isomorphism theorems.

Have developed:

• the ability to understand and write proofs of basic theorems;
• the ability to use the Euclidean algorithm in integers and polynomial rings;
• a knowledge of basic examples of the abstract algebraic structures;
• the ability to construct quotient objects.

Appreciate:

• the clarity and economy of abstract algebra, and the pleasure of proofs involving concepts rather than calculations.

Content:

Rings: congruences, modular arithmetic and the division algorithm in the integers; abstract rings and isomorphisms; examples including matrix rings; polynomial rings, the division algorithm, irreducible polynomials and unique factorisation; ideals and quotient rings in polynomial rings. Groups: introduction to the symmetry groups of two and three dimensional Euclidean geometry; abstract groups, examples including matrix groups; homomorphism, normal subgroups, quotients and the first homomorphism theorem; group actions and permutation groups; conjugacy classes and their interpretation in symmetry groups, permutation groups and matrix groups.

Assessment:

Up to 26 pages of written assignments and up to three hours of end-of-semester written examination.

Mathematics subject : Next:618-231 | Prev:618-212 | Search | Help
Handbook 1996 : Faculty of Science (Volume 4 page 210)

Status:          Official 1996
Date created:    Oct  9 1995
Last modified:   Oct  9 1995
Authorised by:   Academic Registrar
Email enquiries: Course_Information@registrar.unimelb.edu.au

Copyright © University of Melbourne 1995,1996.