Algebraic Geometry
Subject 620-630 (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 2, - 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 computer lab/practical 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 subject equivalent to 620636 Commutative 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 Paul Timothy Norbury| Subject Overview: | Algebraic geometry is the study of the zero sets of polynomials. As the name suggests, it combines algebra and geometry. It is a fundamental tool in many areas of mathematics, including differential geometry, number theory, integrable systems and in physics, such as string theory. Syllabus: Plane conics, cubics and the group law, genus of a curve, commutative algebra Noetherian rings, Zariski topology, the Nullstellensatz, coordinate ring of functions on a variety, projective varieties, singularities, divisors, Riemann Roch theorem. |
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| Objectives: | After completing this subject, students should gain: - an appreciation of the geometry underlying commutative algebra, e.g. the geometry of the zero set of a polynomial; - an understanding of the Nullstellensatz; - a fundamental understanding of projective varieties; - experience with the Zariski topology; - applications of algebraic geometry to related areas such as differential geometry, number theory and physics. - the ability to pursue further studies in this and related areas. |
| Assessment: | Up to 60 pages of written assignments (60%: three assignments worth 20% each, due early, mid and late in semester), a 2 hour written examination (40%, 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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