Algebra
Subject 620-321 (2008)
Note: This is an archived Handbook entry from 2008.Search for this in the current handbookSearch for this in the current handbook
| Credit Points: | 12.500 | ||||||||||||
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| Level: | Undergraduate | ||||||||||||
| Dates & Locations: | This subject has the following teaching availabilities in 2008: Semester 1, - Taught on campus.
Timetable can be viewed here. For information about these dates, click here. | ||||||||||||
| Time Commitment: | Contact Hours: 36 lectures (three per week) and up to 12 practice classes (one per week) Total Time Commitment: 120 hours. | ||||||||||||
| Prerequisites: | 620-222 with a grade of H3 or better. | ||||||||||||
| Corequisites: | None | ||||||||||||
| Recommended Background Knowledge: | None | ||||||||||||
| Non Allowed Subjects: | None | ||||||||||||
| Core Participation Requirements: | It is University policy to take all reasonable steps to minimise the impact of disability upon academic study and reasonable steps will be made to enhance a student's participation in the University's programs. Students who feel their disability may impact upon their active and safe participation in a subject are encouraged to discuss this with the relevant subject coordinator and the Disability Liaison Unit. |
Coordinator
Dr L Reeves| Subject Overview: | This subject provides further experience with abstract algebraic concepts and methods. General structural results are proved and algorithms developed to determine the invariants they describe. The material covered is widely used in algebraic topology and in number theory. Rings topics include: abstract rings and isomorphisms; matrix rings and polynomial rings; homomorphisms, ideals and quotient rings; integral domains and the field of quotients; units, irreducibles and primes; prime and maximal ideals; Euclidean domains; principal ideal domains; and unique factorisation domains. Modules topics include: submodules; homomorphisms of modules and quotient modules; free modules and bases; the structure of a finitely generated module over a principal ideal domain; and applications to abelian groups and to Jordan normal form of matrices. Field theory topics include: field extensions and their construction; the degree of a field extension; Galois extensions, splitting fields and the Galois correspondence. Applications topics may include tensor and exterior algebras, applications to number theory, the classical impossibility theorems, and structure theory for simple rings. |
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| Assessment: | Up to 24 pages of written assignments due during semester (20%); a 3-hour written examination in the examination period (80%). |
| Prescribed Texts: | None |
| Breadth Options: | This subject is a level 2 or level 3 subject and is not available to new generation degree students as a breadth option in 2008. This subject or an equivalent will be available as breadth in the future. Breadth subjects are currently being developed and these existing subject details can be used as guide to the type of options that might be available. 2009 subjects to be offered as breadth will be finalised before re-enrolment for 2009 starts in early October. |
| Fees Information: | Subject EFTSL, Level, Discipline & Census Date |
| Notes: | This subject is available for science credit to students enrolled in the BSc (pre-2008 degree only), BASc or a combined BSc course. |
| Related Course(s): |
Bachelor of Arts Bachelor of Arts and Bachelor of Science Bachelor of Arts and Sciences Bachelor of Science |
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