Skip to main content
Module Search
A street in Durham, with old buildings and people walking down the street
 

MATH2647: PROBABILITY II

Please ensure you check the module availability box for each module outline, as not all modules will run in each academic year. Each module description relates to the year indicated in the module availability box, and this may change from year to year, due to, for example: changing staff expertise, disciplinary developments, the requirements of external bodies and partners, and student feedback. Current modules are subject to change in light of the ongoing disruption caused by Covid-19.

Type Open
Level 2
Credits 10
Availability Available in 2023/24
Module Cap
Location Durham
Department Mathematical Sciences

Prerequisites

  • (Calculus I (Maths Hons) (MATH1081) or Calculus I (MATH1061) and Probability I (MATH1597)) and Linear Algebra I (Maths Hons) (MATH1091) or Linear Algebra I (MATH1071) and Analysis I (MATH1051) [the latter may be a co-requisite].

Corequisites

  • Analysis I (MATH1051) unless taken before.

Excluded Combinations of Modules

  • None

Aims

  • To reinforce the knowledge of Probability gained at Level 1, develop probabilistic ideas and techniques in more sophisticated settings and to provide a firmfoundation for modules in this area in higher years.

Content

  • Probability spaces and probability measures.
  • Infinite collections of events.
  • Random variables and expectation.
  • Infinite sequences of random variables.
  • Modes of convergence.
  • Limit theorems
  • Generating functions.
  • Further topics to be chosen from: random graphs, branching processes, probability and algorithms.

Learning Outcomes

Subject-specific Knowledge:

  • By the end of the module students will: be able to solve seen and unseen problems on the given topics.
  • Have a knowledge and understanding of this subject demonstrated through an ability to establish probabilistic results for sequences of events and sequences of random variables and a workig knowledge of generating functions and their computational and theoretical power.
  • Reproduce theoretical mathematics concerning sequences of events and sequences of random variables to a level appropriate to Level 2, including key definitions and theorems..

Subject-specific Skills:

  • In addition students will have emhanced mathematical skills in the followingareas: intuition for probabilistic reasoning.

Key Skills:

  • Students will have basic mathematical skills in the following areas: problem solving, modelling, computation.

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 theapplication of the theory to practical examples.
  • Problem classes show how to solve example problems in an ideal way, revealling also the thought processes behind such solutions.
  • Tutorials provide active problem-solving engagement and immediate feedback to the learning processes.
  • Formative assessments provide feedback to guide students in the correct development of their knowledge and skills in preparation for the summative assessment.
  • The end-of-year examination assesses the knowledge acquired and the ability to solve predictable and unpredictable problems.

Teaching Methods and Learning Hours

ActivityNumberFrequencyDurationTotalMonitored
Lectures212 per week in Epiphany; 1 in Easter1 Hour21 
Tutorials5Fortnightly in Epiphany; 1 in Easter1 Hour5Yes
Problems Classes4Fortnightly in Epiphany1 Hour4 
Preparation and Reading70 
Total100 

Summative Assessment

Component: ExaminationComponent Weighting: 100%
ElementLength / DurationElement WeightingResit Opportunity
End of year written examination2 hours100Yes

Formative Assessment

Weekly written or electronic assignments to be assessed and returned.

More information

If you have a question about Durham's modular degree programmes, please visit our FAQ webpages, Help page or our glossary of terms. If you have a question about modular programmes that is not covered by the FAQ, or a query about the on-line Undergraduate Module Handbook, please contact us.

Prospective Students: If you have a query about a specific module or degree programme, please Ask Us.

Current Students: Please contact your department.