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MATH4277: Discrete and Continuous Probability IV

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Type Open
Level 4
Credits 10
Availability Available in 2023/24
Module Cap None.
Location Durham
Department Mathematical Sciences

Prerequisites

  • Analysis in Many Variables II (MATH2031) AND Complex Analysis II (MATH2011) AND EITHER [Probability II (MATH2647)] OR [Stochastic Processes III (MATH3251)] OR [Markov Chains II (MATH22707) and Analysis III (MATH3011)]

Corequisites

  • None

Excluded Combinations of Modules

  • None

Aims

  • To explore in depth fundamental probabilistic systems in both discrete and continuous settings, building on earlier probability courses.

Content

  • Coin tossing and trajectories of random walks
  • Classical limit theorems
  • Order statistics
  • Some non-classical limits
  • Brownian motion

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 analyse the behaviour of the probabilistic systems explored in the course.
  • Reproduce theoretical mathematics concerning probabilistic systems at a level appropriate to Level 4, including key definitions and theorems.

Subject-specific Skills:

  • In addition students will have enhanced mathematical skills in the following areas: probabilistic intuition.

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 the development of mathematical ideas into a coherent body of material, and how the theory is applied to practical examples.
  • Four homework assignments provide formative assessment and 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 Michaelmas term; 1 in Easter term1 hour21 
Problem Classes4Fortnightly in Michaelmas term1 hour4 
Preparation and reading75 
Total100 

Summative Assessment

Component: ExaminationComponent Weighting: 100%
ElementLength / DurationElement WeightingResit Opportunity
Written examination2 hours100 

Formative Assessment

Four assignments.

More information

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