STOCHASTIC PROCESSES  2024/5
Module code: MAT2003
Module Overview
Stochastic processes are a series of random variables. Students will be introduced to both Markov Chains and continuous Markov stochastic processes, where the distributions of future random variables are determined by the value of the most recent random variable. These models are important for modelling things which change over time, such as voting intention or population size.
Module provider
Mathematics & Physics
Module Leader
KUEH Audrey (Maths & Phys)
Number of Credits: 15
ECTS Credits: 7.5
Framework: FHEQ Level 5
Module cap (Maximum number of students): N/A
Overall student workload
Independent Learning Hours: 58
Lecture Hours: 33
Tutorial Hours: 11
Guided Learning: 15
Captured Content: 33
Module Availability
Semester 2
Prerequisites / Corequisites
None
Module content
Indicative content includes:
Probabilities and expectations of a Markov Chain;
Onestep and tstep transition probabilities of a Markov Chain;
Gambler’s Ruin and other random walks;
Properties of Markov Chains: recurrence/transience, periodicity and irreducibility;
Basic Limit Theorem and stationary distributions;
Poisson processes, pure birth processes and birth and death processes.
Assessment pattern
Assessment type  Unit of assessment  Weighting 

Schooltimetabled exam/test  Insemester test (50 minutes)  20 
Examination  Exam (2 hours)  80 
Alternative Assessment
N/A
Assessment Strategy
The assessment strategy is designed to provide students with the opportunity to demonstrate:¿
Interpretation and manipulation of mathematical statements.
Subject knowledge through implicit recall of key definitions, theorems and their proofs.
Analytical ability to calculate probabilities, expectations and longterm distributions.
Thus, the summative assessment for this module consists of:
One insemester test taken during the semester, worth 20% of the module mark, corresponds to Learning Outcome 1.
A synoptic examination (2 hours), worth 80% of the module mark, corresponds to Learning Outcomes 1, 2, 3, 4.
Formative assessment
There are two formative unassessed courseworks over an 11 week period, designed to consolidate student learning.
Feedback
Individual written feedback is provided to students for formative unassessed courseworks. The feedback is timed such that feedback from the first coursework will assist students with preparation for the insemester test. The feedback from both courseworks and the insemester test will assist students with preparation for the synoptic examination. Students also receive verbal feedback during lectures and tutorials.
Module aims
 Introduce students to Markov Chains and enable them to calculate simple probabilities and expectations.
 Facilitate students' understanding of the longterm behaviours of Markov Chains by studying their properties in a formal way.
 Enable students to determine longterm behaviour of a given Markov Chain.
 Introduce students to continuous Markov processes and relate them to differential equations.
Learning outcomes
Attributes Developed  
001  Students will understand discrete and continuous Markov processes and calculate simple probabilities and expectations.  KC 
002  Students will be able to state and prove definitions and theorems about the longterm behaviour of discrete Markov processes.  KC 
003  Students will be able to find the longterm behaviour of a given discrete Markov process, occurring for example in politics.  KCT 
004  Students will be able to find the related differential equation of a given continuous Markov process, occurring for example in biology.  KCT 
Attributes Developed
C  Cognitive/analytical
K  Subject knowledge
T  Transferable skills
P  Professional/Practical skills
Methods of Teaching / Learning
The learning and teaching strategy is designed to:
Give a detailed introduction to Markov Chains and continuous Markov processes and ensure experience in the methods used to interpret, understand, prove theorems and solve problems related to probabilities and expectations of stochastic processes.
The learning and teaching methods include:
Three onehour lectures per week for eleven weeks, with typeset notes to complement the lectures. The lectures provide a structured learning environment with opportunities for students to ask questions and to practice methods taught.
Eleven tutorials for guided discussion of solutions to problem sheets (provided to students in advance for completion to reinforce their understanding and guide their learning).
Two unassessed courseworks to provide students with further opportunity to consolidate learning. Students receive individual written feedback on these as guidance on their progress and understanding.
Lectures may be recorded or equivalent recordings of lecture material provided. These recordings are intended to give students the opportunity to review parts of lectures that they may not fully have understood and should not be seen as an alternative to attending lectures.
Indicated Lecture Hours (which may also include seminars, tutorials, workshops and other contact time) are approximate and may include inclass tests where one or more of these are an assessment on the module. Inclass tests are scheduled/organised separately to taught content and will be published on to student personal timetables, where they apply to taken modules, as soon as they are finalised by central administration. This will usually be after the initial publication of the teaching timetable for the relevant semester.
Reading list
https://readinglists.surrey.ac.uk
Upon accessing the reading list, please search for the module using the module code: MAT2003
Other information
The School of Mathematics and Physics is committed to developing graduates with strengths in Digital Capabilities, Employability, Global and Cultural Capabilities, Resourcefulness and Resilience, and Sustainability. This module is designed to allow students to develop knowledge, skills, and capabilities in the following areas:

Digital Capabilities: The SurreyLearn page for MAT2003 features a dynamic discussion forum where students can pose questions and engage with others using e.g. LaTeX and MathML tools. This enhances their digital competencies and facilitates collaborative learning and information sharing.

Employability: The module MAT2003 equips students with skills which significantly enhance their employability. Students gain mathematical proficiency, which hones critical thinking and problemsolving abilities. Students learn to evaluate complex problems, break them into manageable components, and apply logical reasoning to arrive at solutions — these are highly sought after skills in any profession.

Global and Cultural Capabilities: Students enrolled in MAT2003 originate from a variety of countries and have a wide range of cultural backgrounds. Students are encouraged to work together during problemsolving teaching activities in tutorials and lectures, which naturally facilitates the sharing of different cultures.

Resourcefulness and Resilience: MAT2003 is a module which demands a rigorous approach to Stochastic Processes, to which students will learn to adapt. They will gain skills in analysing problems and lateral thinking. Students will complete assessments which challenge them and build resilience.
Programmes this module appears in
Programme  Semester  Classification  Qualifying conditions 

Mathematics with Statistics BSc (Hons)  2  Compulsory  A weighted aggregate mark of 40% is required to pass the module 
Mathematics with Statistics MMath  2  Compulsory  A weighted aggregate mark of 40% is required to pass the module 
Mathematics with Music BSc (Hons)  2  Optional  A weighted aggregate mark of 40% is required to pass the module 
Mathematics BSc (Hons)  2  Optional  A weighted aggregate mark of 40% is required to pass the module 
Financial Mathematics BSc (Hons)  2  Compulsory  A weighted aggregate mark of 40% is required to pass the module 
Mathematics MMath  2  Optional  A weighted aggregate mark of 40% is required to pass the module 
Economics and Mathematics BSc (Hons)  2  Compulsory  A weighted aggregate mark of 40% is required to pass the module 
Please note that the information detailed within this record is accurate at the time of publishing and may be subject to change. This record contains information for the most up to date version of the programme / module for the 2024/5 academic year.