Algebraic Geometry (MAST90097)
Graduate courseworkPoints: 12.5Not available in 2017
About this subject
Overview
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This course is an introduction to algebraic geometry. Algebraic geometry is the study of zero sets of polynomials. It exploits the interplay between rings of functions and the underlying geometric objects on which they are defined. It is a fundamental tool in may areas of mathematics, including number theory, physics and differential geometry. The syllabus includes affine and projective varieties, coordinate ring of functions, the Nullstellensatz, Zariski topology, regular morphisms, dimension, smoothness and singularities, sheaves, schemes.
Intended learning outcomes
After completing this subject, students should gain:
- an understanding of the concepts of affine and projective varieties;
- an understanding of schemes;
- the ability to calculate invariants of varieties;
- the ability to solve problems involving varieties by converting them into problems in algebra;
- the ability to pursue further studies in this and related areas.
Generic skills
In addition to learning specific skills that will assist students in their future careers in science, they will have the opportunity to develop generic skills that will assist them in any future career path. These include:
- problem-solving skills: the ability to engage with unfamiliar problems and identify relevant solution strategies;
- analytical skills: the ability to construct and express logical arguments and to work in abstract or general terms to increase the clarity and efficiency of analysis;
- collaborative skills: the ability to work in a team;
- time-management skills: the ability to meet regular deadlines while balancing competing commitments.
Last updated: 3 November 2022
Eligibility and requirements
Prerequisites
| Code | Name | Teaching period | Credit Points |
|---|---|---|---|
| MAST30005 | Algebra | Semester 1 (On Campus - Parkville) |
12.5 |
| MAST90025 | Commutative and Multilinear Algebra | Not available in 2017 |
12.5 |
Corequisites
None
Non-allowed subjects
None
Inherent requirements (core participation requirements)
The University of Melbourne is committed to providing students with reasonable adjustments to assessment and participation under the Disability Standards for Education (2005), and the Assessment and Results Policy (MPF1326). Students are expected to meet the core participation requirements for their course. These can be viewed under Entry and Participation Requirements for the course outlines in the Handbook.
Further details on how to seek academic adjustments can be found on the Student Equity and Disability Support website: http://services.unimelb.edu.au/student-equity/home
Last updated: 3 November 2022
Assessment
Additional details
Up to 60 pages of assignments (60%: three assignments worth 20% each, due early, mid and late in semester), a 2-hour written examination (40%, in the examination period)
Last updated: 3 November 2022
Dates & times
Not available in 2017
Time commitment details
170 hours
Last updated: 3 November 2022
Further information
- Texts
Prescribed texts
Recommended texts and other resources
Robin Hartshorne, Algebraic Geometry, Graduate Texts in Mathematics Volume 52 (1977).
Igor R. Shafarevich, Basic Algebraic Geometry 1: Varieties in Projective Space, Springer-Verlag (1994).
David Eisenbud and Joe Harris, The geometry of Schemes, Springer (2000).
- Related Handbook entries
This subject contributes to the following:
Type Name Course Master of Science (Mathematics and Statistics) - Available through the Community Access Program
About the Community Access Program (CAP)
This subject is available through the Community Access Program (also called Single Subject Studies) which allows you to enrol in single subjects offered by the University of Melbourne, without the commitment required to complete a whole degree.
Please note Single Subject Studies via Community Access Program is not available to student visa holders or applicants
Entry requirements including prerequisites may apply. Please refer to the CAP applications page for further information.
Last updated: 3 November 2022