Undergraduate Programme and Module Handbook 2008-2009 (archived)

Module MATH2561: CONTOURS AND PROBABILITY II

Department: Mathematical Sciences

MATH2561: CONTOURS AND PROBABILITY II

Type	Open	Level	2	Credits	20	Availability	Available in 2008/09	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 Hyperbolic Geometry II (MATH2121), Contours and Actuarial Mathematics II (MATH2171), Probability and Actuarial Mathematics II (MATH2161), Probability and Geometric Topology II (MATH2151) and Codes and Probability II (MATH2571).

Aims

To study two seperate topics in mathematics at least one of which will demonstrate how mathematics can be applied to real world situations.

Content

Topic 1: Contours: Complex differentiation, Power Series, Contour Integrals, Calculus of residues.
Topic 2: Probability: Markov chains, random walks, real and complex generating functions, convergence in function space.

Learning Outcomes

Subject-specific Knowledge:

By the end of the module students will: be able to solve unseen problems in basic complex analysis and actuarial mathematics.
Reproduce theoretical mathematics in the fields of basic complex analysis and actuarial mathematics to a level appropriate to Level 2.
Have a knowledge and understanding of these subjects demonstrated through one or more of the following topic areas: Codes: Complex Differentiation; Power Series; Contours integrals; calculus of residues; Probability; Markov Chains, random walks, real and complex generating functions, convergence in function space.

Subject-specific Skills:

In addition students will have enhanced mathematical skills in the following area: Spatial awareness.

Key Skills:

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

Lecturing demonstrates what is required to be learned and the application of the theory to practical examples.
Weekly homework problems provide formative assessment to guide students in the correct development of their knowledge and skills.
Tutorials provide active engagement and feedback to the learning process.
The end-of-year examination assesses the knowledge acquired and the ability to solve predictable and unpredictable problems.

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	■
Problems Classes	10	Fortnightly for 20 weeks	1 Hour	10
Preparation and reading				142
Total				200

Summative Assessment

Component: Examination		Component Weighting: 50%
Element	Length / duration	Element Weighting	Resit Opportunity
end of year written examination	1 hour 45 minutes	100%	yes
Component: Examination		Component Weighting: 50%
Element	Length / duration	Element Weighting	Resit Opportunity
end of year written examination	1 hour 45 minutes	100%	yes

Formative Assessment:

Weekly written assignments.

■ 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