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Algebraic Geometry (MAST90097)

Graduate courseworkPoints: 12.5On Campus (Parkville)

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Overview

Year of offer2018
Subject levelGraduate coursework
Subject codeMAST90097
Campus
Parkville
Availability
Semester 2
FeesSubject EFTSL, Level, Discipline & Census Date

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: 20 October 2018