Unit information: Topics in Modern Geometry 3 in 2019/20

Unit name	Topics in Modern Geometry 3
Unit code	MATH30001
Credit points	10
Level of study	H/6
Teaching block(s)	Teaching Block 1A (weeks 1 - 6)
Unit director	Dr. Jordan
Open unit status	Not open
Pre-requisites	MATH20006 Metric Spaces and MATH21800 Algebra 2. MATH20004 Introduction to Geometry and MATH33300 Group Theory are helpful but not essential.
Co-requisites	None
School/department	School of Mathematics
Faculty	Faculty of Science

Description including Unit Aims

Unit Aims

The aim of the unit is to introduce students to types of geometry which are instrumental in current research. In particular the unit will look at the use fo notion from abstract algebra and analysis in geometry.

Unit Description

The unit will look at two topics in modern geometry. This topic will be one of topological groups, hyperbolic geometry, Lie groups or the geometry of group actions. It will also develop the topology and algebra needed to studey these topics.

Relation to Other Units

The course expands ideas introduced in MATH21800 Algebra 2, and has relations to MATH20200 Metric Spaces, MATH33300 Group Theory, MATHM1200 Algebraic Topology and the proposed new level M unit Algebraic Geometry.

Intended Learning Outcomes

Learning Objectives

Students who successfully complete the unit should:

• be able to clearly define topological groups, discrete groups and manifolds and *be familiar with examples of all three;

use techniques from abstract algebra and mathematical analysis to solve problems in geometry;

• be familiar with aspects of Lie groups;
• be familiar with aspects of algebraic curves.

Teaching Information

Lectures, including examples and revision classes, supported by lecture notes with problem sets and model solutions.

Assessment Information

80% Examination and 20% Coursework.

Reading and References

Recommended

• Joseph Harris, Algebraic Geometry: A First Course, Springer, 1992
• Frances Clare Kirwan, Complex Algebraic Curves, Cambridge University Press, 1992
• Miles Reid, Undergraduate Algebraic Geometry, Cambridge University Press, 1988
• Karen E. Smith et al., An Invitation to Algebraic Geometry, Springer, 2000