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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