Commutative Algebra
Subject 620-636 (2009)
Note: This is an archived Handbook entry from 2009. Search for this in the current handbook
| Credit Points: | 12.50 | ||||||||||||
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| Level: | 9 (Graduate/Postgraduate) | ||||||||||||
| Dates & Locations: | This subject has the following teaching availabilities in 2009: Semester 1, - Taught on campus.
On-campus Timetable can be viewed here. For information about these dates, click here. | ||||||||||||
| Time Commitment: | Contact Hours: 36 hours comprising 2 one-hour lectures per week and 1 one-hour practice class per week. Total Time Commitment: 3 contact hours plus 7 hours private study per week. | ||||||||||||
| Prerequisites: | None | ||||||||||||
| Corequisites: | None | ||||||||||||
| Recommended Background Knowledge: | It is recommended that students have completed a third year subject in algebra (equivalent to 620-321 [2008] Algebra). | ||||||||||||
| 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 participation are encouraged to discuss this with the subject coordinator and the Disability Liaison Unit. |
Coordinator
Dr John Richard James Groves| Subject Overview: | Commutative algebra is the basis of modern algebraic geometry. It provides the rigorous foundation for the study of curves and surfaces and their generalisations. Students will study: basic properties of rings, basic properties of modules including Nakayama's Lemma; Hom and tensor; Localisation; Noetherian properties and the Hilbert Basis theorem; Associated primes and primary decomposition; Grobner bases; Integral extensions; extension of primes in integral extensions; the Hilbert Nullstellensatz; Extended applications taken from Algebraic Geometry and Algebraic Number Theory. |
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| Objectives: | After completing this subject, students should gain: - a deeper understanding of the theory of rings and modules; - an understanding of the basic concepts of Commutative Algebra such as localisation, Noetherian, associated primes and integral extensions; - an understanding of how these basic concepts apply in an area of mathematics other than algebra; - an understanding of proof-producing skills in an algebraic context and to assist in refining the presentation of the consequent proofs; - the ability to pursue further studies in this and related areas. |
| Assessment: | Up to 60 pages of written assignments (75%: three assignments worth 25% each, due early, mid and late in semester), a 2 hour written examination (25%, in the examination period). |
| Prescribed Texts: | TBA |
| Recommended Texts: | TBA |
| Breadth Options: | This subject is not available as a breadth subject. |
| Fees Information: | Subject EFTSL, Level, Discipline & Census Date |
| Generic Skills: | Upon completion of this subject, students should gain the following generic skills: - Problem-solving skills including the ability to engage with unfamiliar problems and identify relevant solution strategies - Analytical skills through the ability to construct and express logical arguments and to work in abstract or general terms to increase the clarity and efficiency of analysis - Through interactions with other students, the ability to work in a team - Time management skills: the ability to meet regular deadlines while balancing competing commitments |
| Related Majors/Minors/Specialisations: |
R05 RM Master of Science - Mathematics and Statistics |
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