Unit information: Topics in Modern Geometry 34 in 2018/19

Description including Unit Aims

Relation to Other Units

The course expands ideas introduced in MATH21800 Algebra 2, and has relations to MATH20200 Metric Spaces, MATH33300 Group Theory and MATHM1200 Algebraic Topology.

Additional unit information can be found at http://www.maths.bristol.ac.uk/study/undergrad/current_units/index.html

Intended Learning Outcomes

Students who successfully complete the unit should:

• be able to clearly define topological groups, discrete groups and manifolds
• be familiar with examples of all three;
• be able to use techniques from abstract algebra and mathematical analysis to solve problems in geometry;
• be familiar with aspects of one of differentiable manifolds, projective space and algebraic curves or hyperbolic geometry.
• have developed an awareness of a broader literature,
• have gained an appreciation of how the basic ideas may be further developed,
• be able to assimilate material from several sources into a coherent document.

Teaching Information

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.

Assessment Information

80% Examination and 20% Coursework.

Coursework will be 4 homework sheets during the lectures weeks 1-6 each worth 2.5% and then a sheet with questions from the whole unit set in weeks 7-10 worth 10%

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.

Reading and References

Recommended:

Harris, Algebraic Geometry: A First Course

Smith et al., An Invitation to Algebraic Geometry

Reid, Undergraduate Algebraic Geometry

Gathmann, Algebraic Geometry class notes