Course Information

You can find details of what is covered in the course on the course syllabus page.

All timetable information for the unit can be found on https://my.manchester.ac.uk.

Succeeding in the Course Unit

What do I need to do to succeed in this course unit?

Learning outcomes are statements that describe significant and essential learning that you will have achieved, and can reliably demonstrate, at the end of a course unit. In other words, learning outcomes identify what you will know and be able to do by the end of a course or program. The learning outcomes of the course unit are:

• calculate the hyperbolic distance between and the geodesic through points in the hyperbolic plane,
• compare different models (the upper half-plane model and the Poincaré disc model) of hyperbolic geometry,
• prove results (Gauss-Bonnet Theorem, angle formulæ for triangles, etc as listed in the syllabus) in hyperbolic trigonometry and use them to calculate angles, side lengths, hyperbolic areas, etc, of hyperbolic triangles and polygons,
• classify Möbius transformations in terms of their actions on the hyperbolic plane,
• calculate a fundamental domain and a set of side-pairing transformations for a given Fuchsian group,
• define a finitely presented group in terms of generators and relations,
• use Poincaré’s Theorem to construct examples of Fuchsian groups and calculate presentations in terms of generators and relations,
• relate the signature of a Fuchsian group to the algebraic and geometric properties of the Fuchsian group and to the geometry of the corresponding hyperbolic surface.

During this course unit you need to acquire the knowledge and develop the skills to demonstrate that you can achieve these outcomes.

How do I acquire the knowledge and develop the skills to succeed in this course unit?

Lectures and tutorials will provide guidance on what you need to study. Course materials and additional resources are available from the Course home page. To see the feedback opportunities, go to the Assessment & Feedback page.

How will I know I have the acquired the knowledge and skills to succeed in this course unit? (Self-assessment)

There are opportunities throughout the course unit to assess your own learning. For example, working through the course Exercises and checking your understanding against the Solutions. You should have a serious attempt at the exercises before referring to the solutions. In addition, within lectures and tutorials there will be opportunities for you to have your questions answered and discuss your progress on a regular basis.

How will I demonstrate that I have the acquired the knowledge and skills to succeed in this course unit? (Assessment)

You can find full details of the assessment on this course unit on the course syllabus page and coursework information and details about course unit feedback on the Assessment & Feedback page.