This page is for the academic year 2021-22. The current handbook year is 2022-23
Department: Mathematical Sciences
||Available in 2021/22
- Complex Analysis II (MATH2011) AND Analysis in Many
Variables II (MATH2031) AND Algebra II (MATH2581).
Excluded Combination of Modules
- To give students a basic grounding in various aspects of plane
- In particular, to elucidate different types of plane geometries and
to show how these may be handled from a group theoretic viewpoint.
- Euclidean geometry: isometry group, its generators, conjugacy classes.
- Discrete group actions: fundamental domains, orbit space.
- Spherical geometry.
- Affine geometry.
- Projective line and projective plane. Projective duality.
- Hyperbolic geometry: Klein disc model (distance, isometries, perpendicular lines).
- Moebius transformations, inversion, cross-ratios.
- Inversion in space and stereographic projection.
- Conformal models of hyperbolic geometry (Poincare disc and upper half-plane models).
- Elementary hyperbolic geometry: sine and cosine rules, area of a triangle.
- Projective models of hyperbolic geometry: Klein model and hyperboloid model.
- Types of isometries of the hyperbolic plane. Horocycles and equidistant curves.
- Additional topics: hyperbolic surfaces, 3D hyperbolic geometry.
- By the end of the module students will: be able to solve
novel and/or complex problems in Geometry.
- have a systematic and coherent understanding of theoretical
mathematics in the field of Geometry.
- have acquired a coherent body of knowledge of these subjects
demonstrated through one or more of the following topic areas: Isometries and affine transformations of the plane.
- Spherical geometry.
- Mobius transformations.
- Projective geometry.
- Hyperbolic geometry.
- In addition students will have specialised mathematical
skills in the following areas which can be used with minimal guidance:
Modes of Teaching, Learning and Assessment and how these contribute to
the learning outcomes of the module
- Lectures demonstrate what is required to be learned and the
application of the theory to practical examples.
- Assignments for self-study develop problem-solving skills and
enable students to test and develop their knowledge and
- Formatively assessed assignments provide practice in the
application of logic and high level of rigour as well as feedback for the students and the lecturer on students' progress.
- The end-of-year examination assesses the knowledge acquired
and the ability to solve unpredictable problems of some
Teaching Methods and Learning Hours
||2 per week in Michaelmas and Epiphany; 2 in Easter
||Fortnightly in Michaelmas and Epiphany
|Preparation and Reading
||Component Weighting: 100%
||Length / duration
Eight written or electronic assignments to be assessed and returned. Other assignments are set for self-study and complete solutions are made available to students.
■ Attendance at all activities marked with this symbol will be monitored. Students who fail to attend these activities, or to complete the summative or formative assessment specified above, will be subject to the procedures defined in the University's General Regulation V, and may be required to leave the University