Unit name | Topics in Modern Geometry 34 |
---|---|
Unit code | MATHM0008 |
Credit points | 10 |
Level of study | M/7 |
Teaching block(s) |
Teaching Block 1A (weeks 1 - 6) |
Unit director | Dr. Jordan |
Open unit status | Not open |
Pre-requisites |
Math 20200 (Metric spaces) and Math 21800 (Algebra 2). Students may not take this unit if they have taken the corresponding Level H/6 unit Topics in Modern Geometry 3. |
Co-requisites |
Math 33300 (Group Theory) is helpful but not essential. |
School/department | School of Mathematics |
Faculty | Faculty of Science |
Geometry is a very significant part of several areas of mathematics and also has important applications to physics. The unit will start by giving the key definitions of topological groups, discrete groups and manifolds, with several examples given to illustrate the definitions. The course will then look at spherical geometry and hyperbolic geometry, as illustrations of non-Euclidean geometries. Finally the unit will give an introduction to algebraic curves and introduce the concept of a Lie group, both of these will be illustrated with several examples.
The aims of this new unit are to give students an introduction to selected areas of modern geometry and in particular to make students familiar with several examples of discrete groups and actions of discrete groups. A recurring theme in the unit will be gaining an understanding of abstract definitions via concrete examples.
Note that although there there may be a slight overlap in topics between this unit and the proposed new unit 'Introduction to Lie Groups, Lie Algebras and their Representations', the treatments will will be given from very different points of view and will be complementary rather than overlapping.
Students who successfully complete the unit should:
By pursuing an individual project on a more advanced topic students should have:
Lectures, including examples and revision classes, supported by lecture notes with problem sets and model solutions. Self-study with directed reading based on recommended material.
The final assessment mark will be based on:
Lecture notes and handouts will be provided covering all the main material.
The following supplementary texts provide additional background reading: