Durham University
Programme and Module Handbook

Undergraduate Programme and Module Handbook 2018-2019 (archived)

Module MATH2647: PROBABILITY II

Department: Mathematical Sciences

MATH2647: PROBABILITY II

Type Open Level 2 Credits 10 Availability Available in 2018/19 Module Cap Location Durham

Prerequisites

  • Calculus and Probability I (MATH1061) and Linear Algebra I (MATH1071) and Analysis I (MATH1051) [the latter may be a co-requisite].

Corequisites

  • Analysis I (MATH1051) unless taken before.

Excluded Combination of Modules

  • None

Aims

  • To reinforce the knowledge of Probability gained at Level 1 and provide a firm foundation for modules in this area in higher years.

Content

  • Infinite collections of events.
  • Sequences of random variables and their convergence.
  • Generating functions.
  • Markov chains.

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: Markov Chains, random walks, real and complex generating functions, convergence in function space.
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 22 2 per week in Michaelmas and in first week of Easter 1 Hour 22
    Tutorials 5 Fortnightly in Michaelmas and one in Easter 1 Hour 5 ■
    Problems Classes 4 Fortnightly in Michaelmas 1 Hour 4
    Preparation and Reading 69
    Total 100

    Summative Assessment

    Component: Examination Component Weighting: 100%
    Element Length / duration Element Weighting Resit Opportunity
    End of year written examination 2 hours 100% Yes

    Formative Assessment:

    Fortnightly or 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