Durham University
Programme and Module Handbook

Undergraduate Programme and Module Handbook 2008-2009 (archived)

Module MATH2121: CONTOURS AND HYPERBOLIC GEOMETRY II

Department: Mathematical Sciences

MATH2121: CONTOURS AND HYPERBOLIC GEOMETRY II

Type Open Level 2 Credits 20 Availability Available in 2008/09 and alternate years thereafter Module Cap None. Location Durham

Prerequisites

  • Core Mathematics A (MATH1012) and Core Mathematics B1 (MATH1051) [the latter may be a co-requisite].

Corequisites

  • Core Mathematics B1 (MATH1051) unless taken before.

Excluded Combination of Modules

  • Mathematics for Engineers and Scientists (MATH1551), Single Mathematics A (MATH1561), Single Mathematics B (MATH1571), Foundation Mathematics (MATH1641), Complex Analysis II (MATH2011), Contours and Symmetries II (MATH2111), Contours and Actuarial Mathematics II (MATH2171) and Contours and Probability II (MATH2**1).

Aims

  • To study two seperate topics in mathematics at least one of which will introduce geometrical thinking.

Content

  • Complex differentiation.
  • Power Series.
  • Contour Integrals.
  • Calculus of residues.
  • Mobius transformations.
  • Models of hyperbolic space.
  • Geodesics, length, arclength.

Learning Outcomes

Subject-specific Knowledge:
  • By the end of the module students will: be able to solve unseen problems in basic complex analysis and geometry.
  • Reproduce theoretical mathematics in the fields of basic complex analysis and geometry to a level appropriate to Level 2.
  • Have a knowledge and understanding of this subject demonstrated through one or more of the following topic areas: Complex Differentiation; Power Series; Contours integrals and calculus of residues; Mobius transformations; Models of hyperbolic space; Geodesics, Length, arclength.
Subject-specific Skills:
  • In addition students will have enhanced mathematical skills in the following area: Spatial awareness
Key Skills:
  • Have highly specialised skills in the following area: Spatial awareness and Abstract reasoning.

Modes of Teaching, Learning and Assessment and how these contribute to the learning outcomes of the module

  • Teaching is by lectures and seminars through which the main body of knowledge is made available.
  • Students do regular formative work solving problems to gain insight into the details of the relevant theories and procedures.
  • End of year examinations assess the learning.

Teaching Methods and Learning Hours

Activity Number Frequency Duration Total/Hours
Lectures 38 2 per week 1 Hour 38
Tutorials 10 Fortnightly for 20 weeks 1 Hour 10 ■
Problem Classes 10 Fortnightly for 20 weeks 1 Hour 10
Preparation and Reading 142
Total 200

Summative Assessment

Component: Examination Component Weighting: 100%
Element Length / duration Element Weighting Resit Opportunity
three-hour written examination 3 hours 100%

Formative Assessment:

Weekly written assignments; no collection.

■ 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