Note: This is an archived Handbook entry from 2009. Search for this in the current handbook
|Dates & Locations:|| |
This subject has the following teaching availabilities in 2009:Semester 1, - Taught 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.
|Recommended Background Knowledge:||It is recommended that students have completed a third year subject in algebra (equivalent to 620-321  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.|
CoordinatorDr 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.|
|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).|
|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
R05 RM Master of Science - Mathematics and Statistics |
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