Undergraduate Programme and Module Handbook 2020-2021 (archived)
Module MATH2667: MONTE CARLO II
Department: Mathematical Sciences
MATH2667: MONTE CARLO II
| Type | Open | Level | 2 | Credits | 10 | Availability | Available in 2020/21 | Module Cap | Location | Durham |
|---|
Prerequisites
- (Calculus 1 (MATH1061) and Probability 1 (MATH1597)) and Linear Algebra 1 (MATH1071) and (Programming 1 (MATH1587) and Dynamics 1 (MATH1607)) OR (Calculus 1 (MATH1061) and Probability 1 (MATH1597) and Linear Algebra 1 (MATH1071) and Discovery Skills in Physics (PHYS1101)) OR (Calculus 1 (MATH1061) and Probability 1 (MATH1597) and Linear Algebra 1 (MATH1071) and Computational Thinking (COMP1051))
Corequisites
- None.
Excluded Combination of Modules
- None
Aims
- To provide a working knowledge of the theory, computation and practice of Monte Carlo (stochastic) simulation and an introduction to stochastic modelling.
Content
- Foundations of the Monte Carlo method
- Random number generation
- Generating random variables
- Stochastic modelling
- Advanced topics from: Markov chain Monte Carlo, variance reduction, continuous time models
Learning Outcomes
Subject-specific Knowledge:
- By the end of the module students will:
- be able to solve novel and/or complex random number generation and distribution sampling problems,
- be able to build and/or extend simple stochastic models,
- have acquired programming skills in python related to stochastic modelling.
Subject-specific Skills:
- In addition students will have specialised mathematical skills in the following areas which can be used with minimal guidance: Modelling, Computation.
Key Skills:
- Synthesis of data, critical and analytical thinking, computer skills
Modes of Teaching, Learning and Assessment and how these contribute to the learning outcomes of the module
- Lectures demonstrate the theory to be learned and the application of the theory to practical examples.
- Computer practical sessions develop and practice programming and modelling skills, and provide active engagement and feedback to the learning process.
- Tutorials develop theoretical knowledge and provide active engagement and feedback to the learning process.
- Fortnightly theoretical provide formative assessment to guide students in the correct development of their knowledge and skills.
- The computer-based practical examination assesses the ability to use programming skills to solve predictable and unpredictable problems.
- The end-of-year written examination assesses the acquired knowledge from a more conceptual viewpoint, including mastery of theoretical aspects underpinning practical applications.
Teaching Methods and Learning Hours
| Activity | Number | Frequency | Duration | Total/Hours | |
|---|---|---|---|---|---|
| Lectures | 22 | 2 per week in Epiphany and in first week of Easter | 1 Hour | 22 | |
| Tutorials | 5 | Fortnightly in Epiphany and one in Easter | 1 Hour | 5 | ■ |
| Computer Practicals | 10 | Weekly in Epiphany | 1 Hour | 10 | ■ |
| Preparation and Reading | 63 | ||||
| Total | 100 |
Summative Assessment
| Component: Computer Practical Examination | Component Weighting: 25% | ||
|---|---|---|---|
| Element | Length / duration | Element Weighting | Resit Opportunity |
| Practical examination | 2 hours | 100% | Yes |
| Component: Written Examination | Component Weighting: 75% | ||
| Element | Length / duration | Element Weighting | Resit Opportunity |
| End of year written examination | 90 minutes | 100% | Yes |
Formative Assessment:
One written assignment to be handed in every fortnight in Epiphany. Weekly quizzes in Computer Practical Sessions.
■ 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