# MA475 - Riemann Surfaces

**Module code:**MA475**Module name:**Riemann Surfaces**Department:**Mathematics Institute**Credit:**15

Content and teaching | Assessment | Availability

## Module content and teaching

###### Principal aims

To motivate the idea of a Riemann surface along the lines of Riemann's original reasoning; to introduce the abstract concepts supported by examples; to explain the modern way of understanding Riemann surfaces and discuss their geometry and topology.

###### Principal learning outcomes

Students at the end of the module should be able to define abstract Riemann surfaces with maps between them and give examples; use hyperbolic geometry and other geometries to construct Riemann surfaces; analyse topological and numerical properties of analytic mappings between Riemann surfaces; understand the classification of complex tori; and have an overall understanding of all Riemann surfaces as quotients of their universal covers using the statement of the Uniformisation Theorem.

###### Departmental link

http://go.warwick.ac.uk/MA475/

###### Other essential notes

Prerequisites: MA3B8 Complex Analysis and MA3F1 Introduction to Topology.

## Module assessment

Assessment group | Assessment name | Percentage |
---|---|---|

15 CATS (Module code: MA475-15) | ||

B (Examination only) | 3 hour examination (Summer) | 100% |

## Module availability

This module is available on the following courses:

###### Core

N/A

###### Optional Core

N/A

###### Optional

- Undergraduate Mathematics (MMath) (G103) - Year 3
- Undergraduate Mathematics (MMath) (G103) - Year 4
- Undergraduate Master of Mathematics (with Intercalated Year) (G105) - Year 3
- Undergraduate Master of Mathematics (with Intercalated Year) (G105) - Year 4
- Undergraduate Master of Mathematics (with Intercalated Year) (G105) - Year 5
- Undergraduate Mathematics (MMath) with Study in Europe (G106) - Year 4
- Undergraduate Mathematics and Statistics (BSc MMathStat) (G1G3) - Year 3
- Undergraduate Mathematics and Statistics (BSc MMathStat) (G1G3) - Year 4
- Postgraduate Taught Mathematics (G1P0) - Year 2
- Postgraduate Taught Mathematics (Diploma plus MSc) (G1PC) - Year 2
- Postgraduate Taught Interdisciplinary Mathematics (Diploma plus MSc) (G1PD) - Year 2
- Undergraduate Master of Mathematics,Operational Research,Statistics and Economics (G300) - Year 3
- Undergraduate Master of Mathematics,Operational Research,Statistics and Economics (G300) - Year 4
- Undergraduate Master of Mathematics,Operational Research,Statistics and Economics (G30A) - Year 3
- Undergraduate Master of Mathematics,Operational Research,Statistics and Economics (G30A) - Year 4
- Undergraduate Master of Mathematics,Operational Research,Statistics and Economics (G30A) - Year 5
- Undergraduate Master of Mathematics,Operational Research,Statistics and Economics (G30B) - Year 3
- Undergraduate Master of Mathematics,Operational Research,Statistics and Economics (G30B) - Year 4
- Undergraduate Master of Mathematics,Operational Research,Statistics and Economics (G30B) - Year 5
- Undergraduate Master of Mathematics,Operational Research,Statistics and Economics (G30C) - Year 3
- Undergraduate Master of Mathematics,Operational Research,Statistics and Economics (G30C) - Year 4
- Undergraduate Master of Mathematics,Operational Research,Statistics and Economics (G30C) - Year 5
- Undergraduate Master of Mathematics,Operational Research,Statistics and Economics (G30D) - Year 3
- Undergraduate Master of Mathematics,Operational Research,Statistics and Economics (G30D) - Year 4
- Undergraduate Master of Mathematics,Operational Research,Statistics and Economics (G30D) - Year 5
- Undergraduate Master of Mathematics,Operational Research,Statistics and Economics (with Intercalated (G30E) - Year 3
- Undergraduate Master of Mathematics,Operational Research,Statistics and Economics (with Intercalated (G30E) - Year 4
- Undergraduate Master of Mathematics,Operational Research,Statistics and Economics (with Intercalated (G30E) - Year 5
- Undergraduate Master of Mathematics,Operational Research,Statistics and Economics (with Intercalated (G30F) - Year 3
- Undergraduate Master of Mathematics,Operational Research,Statistics and Economics (with Intercalated (G30F) - Year 4
- Undergraduate Master of Mathematics,Operational Research,Statistics and Economics (with Intercalated (G30F) - Year 5
- Undergraduate Master of Mathematics,Operational Research,Statistics and Economics (with Intercalated (G30G) - Year 3
- Undergraduate Master of Mathematics,Operational Research,Statistics and Economics (with Intercalated (G30G) - Year 4
- Undergraduate Master of Mathematics,Operational Research,Statistics and Economics (with Intercalated (G30G) - Year 5
- Undergraduate Master of Mathematics,Operational Research,Statistics and Economics (with Intercalated (G30H) - Year 3
- Undergraduate Master of Mathematics,Operational Research,Statistics and Economics (with Intercalated (G30H) - Year 4
- Undergraduate Master of Mathematics,Operational Research,Statistics and Economics (with Intercalated (G30H) - Year 5
- Undergraduate Discrete Mathematics (G4G3) - Year 4