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Unit information: Topics in Modern Geometry 34 in 2021/22

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

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

Lecturers: Heilbronn Fellows (to be confirmed)

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 of notion from abstract algebra and analysis in geometry.

Unit Description

The unit will look at two topics in modern geometry. This topic will be two out of topological groups, hyperbolic groups, Lie groups, geometry of group actions and fractal geometry. It will also develop the topology and algebra needed to study 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. Students may not take this unit if they have taken the corresponding Level H/6 unit MATH30001 Topics in Modern Geometry 3.

Intended learning outcomes

Intended Learning Outcomes:

  • To know and be able to apply key definitions from the two topics covered.
  • To develop problem solving skills, writing skills and gained an appreciation of connections between areas.

Teaching details

The unit will be taught through a combination of

  • synchronous online and, if subsequently possible, face-to-face lectures
  • asynchronous online materials, including narrated presentations and worked examples
  • guided asynchronous independent activities such as problem sheets and/or other exercises
  • synchronous weekly group problem/example classes, workshops and/or tutorials
  • synchronous weekly group tutorials
  • synchronous weekly office hours

Assessment Details

80% Timed, open-book examination 20% Coursework

Raw scores on the examinations will be determined according to the marking scheme written on the examination paper. The marking scheme, indicating the maximum score per question, is a guide to the relative weighting of the questions. Raw scores are moderated as described in the Undergraduate Handbook.

If you fail this unit and are required to resit, reassessment is by a written examination in the August/September Resit and Supplementary exam period.

Resources

If this unit has a Resource List, you will normally find a link to it in the Blackboard area for the unit. Sometimes there will be a separate link for each weekly topic.

If you are unable to access a list through Blackboard, you can also find it via the Resource Lists homepage. Search for the list by the unit name or code (e.g. MATHM0008).

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