Undergraduate Programme and Module Handbook 2019-2020 (archived)
Module MATH4091: STOCHASTIC PROCESSES IV
Department: Mathematical Sciences
MATH4091:
STOCHASTIC PROCESSES IV
Type |
Open |
Level |
4 |
Credits |
20 |
Availability |
Available in 2019/20 |
Module Cap |
|
Location |
Durham
|
Prerequisites
- Analysis in Many Variables II (MATH2031) AND
Probability II (MATH2647)
Corequisites
Excluded Combination of Modules
- Stochastic Processes III (MATH3251).
Aims
- This module continues on from the treatment of probability in
Probability II (MATH2647).
- It is designed to introduce mathematics students to the wide
variety of models of systems in which sequences of events are governed
by probabilistic laws.
- Students completing this course should be equipped to read for
themselves much of the vast literature on applications to problems in
physics, engineering, chemistry, biology, medicine, psychology and many
other fields.
Content
- Probability revision.
- Branching processes.
- Coupling.
- Martingales and applications.
- Poisson processes.
- Continuous-time Markov chains.
- Brownian motion.
- Additional topics in stochastic processes.
Learning Outcomes
- By the end of the module students will: be able to solve
novel and/or complex problems in Stochastic Processes.
- have a systematic and coherent understanding of theoretical
mathematics in the field of Stochastic Processes.
- have acquired coherent body of knowledge of these subjects
demonstrated through one or more of the following topic areas:
- Probability.
- Discrete Parameter Martingales.
- Brownian motion.
- Poisson processes.
- Continuous-time Markov processes.
- Coupling.
- In addition students will have highly specialised and
advanced mathematical skills in the following areas: Modelling,
Computation.
- Students will be able to study independently to further their
knowledge of an advanced topic.
Modes of Teaching, Learning and Assessment and how these contribute to
the learning outcomes of the module
- Lectures demonstrate what is required to be learned and the
application of the theory to practical examples.
- Subject material assigned for independent study develops the
ability to acquire knowledge and understanding without dependence on
lectures.
- Assignments for self-study develop problem-solving skills and
enable students to test and develop their knowledge and
understanding.
- Formatively assessed assignments provide practice in the
application of logic and high level of rigour as well as feedback for
the students and the lecturer on students' progress.
- The end-of-year examination assesses the knowledge acquired
and the ability to solve complex and specialised problems. The Subject
material assigned for independent study will form part of the examined
material.
Teaching Methods and Learning Hours
Activity |
Number |
Frequency |
Duration |
Total/Hours |
|
Lectures |
42 |
2 per week for 20 weeks and 2 in term 3 |
1 Hour |
42 |
|
Problems Classes |
8 |
Four in each of terms 1 and 2 |
1 Hour |
8 |
|
Preparation and Reading |
|
|
|
150 |
|
Total |
|
|
|
200 |
|
Summative Assessment
Component: Examination |
Component Weighting: 100% |
Element |
Length / duration |
Element Weighting |
Resit Opportunity |
Written examination |
3 Hours |
100% |
|
Eight written assignments to be assessed and
returned. Other assignments are set for self-study and complete solutions
are made available to students.
■ 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