Undergraduate Programme and Module Handbook 2012-2013 (archived)

Module MATH2151: PROBABILITY AND GEOMETRIC TOPOLOGY II

Department: Mathematical Sciences

MATH2151: PROBABILITY AND GEOMETRIC TOPOLOGY II

Type	Open	Level	2	Credits	20	Availability	Available in 2012/13	Module Cap	None.	Location	Durham

Prerequisites

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

Corequisites

Core B1 (MATH 1051) unless taken before.

Excluded Combination of Modules

Probability and Actuarial Mathematics II (MATH2161) and Codes and Geometric Topology II (MATH2141).

Aims

To provide basic notions of two separate topics in mathematics with a view to study them in more depth in subsequent years.

Content

Topic 1: Probability: Markov chains, random walks, real and complex generating functions, convergence in function space.
Topic 2: Geometric topology: knots, surfaces, knot invariants.

Learning Outcomes

Subject-specific Knowledge:

By the end of the module students will: be able to solve a range of predictable and unpredictable problems in the given topics.
Have an awareness of the abstract concepts of theoretical mathematics in the field of the given topics.
Have a knowledge and understanding of the major theories of these subjects demonstrated through one or more of the following topic areas: Probability: Markov Chains, random walks, real and complex generating functions, convergence in function space; Geometric topology: knots, surfaces, knot invariants.

Subject-specific Skills:

In addition students will have the ability to undertake and defend the use of alternative mathematical skills in the following areas with minimal guidance: Modelling.

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	42	2 per week for 21 weeks	1 Hour	42
Tutorials	10	Fortnightly for 20 weeks	1 Hour	10	■
Problems Classes	10	Fortnightly for 20 weeks	1 Hour	10
Preparation and Reading				138
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