The aim of this module will be to introduce mathematical concepts and techniques from probability theory and optimisation that are fundamental to many modern computing applications and are necessary for more advanced topics in computer science. The module will blend theory with examples to illustrate how mathematical methods can be applied to solve real-life computing problems.
The module will introduce fundamental mathematical tools in the areas of probability theory and optimisation that have wide applicability in all areas of modern computing. These tools will help students gain deeper understanding of more specialised topics in computer science taught in the MSc curriculum.
This is an indicative module outline only to give an indication of the sort of topics that may be covered. Actual sessions held may differ.
Probability:
Measurable Sets, Axioms of Probability, Conditional Probability, Bayes Theorem
Random Variables, common distributions, expectation, moments, generating functions, probabilistic inequalities
Jointly distributed random variables, covariance, correlation, conditional expectations, independence, laws of large numbers, central limit theorem
Markov chains, statistical estimation, hypothesis testing
Optimisation:
Introduction to mathematical optimization, linear, non-linear, and convex optimization
Convex sets, convex functions, Duality, Optimality Conditions
Gradient descent, stochastic gradient descent, Newton’s method, Simplex Method
By the end of the module, students should be able to:
Reading lists can be found in Talis
Coursework will include a research element.
Ability to apply concepts and techniques from optimization and probability theory to a broad range of computational problems including algorithm design, data analysis, and statistical modelling.
Ability to develop abstract mathematical models for real-world systems and formally analyse them using suitable mathematical techniques in a rigorous manner.
Being able to apply mathematical knowledge in computer science and understanding of specialist theoretical and methodological approaches, suggesting and incorporating interrelationships with other relevant disciplines in abstract and unpredictably complex contexts.
Students will obtain the cognitive skills to critically contribute to existing discourses and developing mathematical methodologies for developing algorithms in computer science, suggesting new ideas, and designing systematic investigations based on critical analysis and evaluation.
Students will obtain practical skills in organising and communicating information, improving Interpersonal, team
and networking skills through engaging in classes and computer laboratories. Formative assesssment will allow students to strategically enhance their own learning.
| Type | Required |
|---|---|
| Lectures | 30 sessions of 1 hour (21%) |
| Seminars | 5 sessions of 1 hour (3%) |
| Supervised practical classes | 4 sessions of 1 hour (3%) |
| Private study | 57 hours (39%) |
| Assessment | 50 hours (34%) |
| Total | 146 hours |
Private study, background reading and revision.
No further costs have been identified for this module.
You do not need to pass all assessment components to pass the module.
| Weighting | Study time | Eligible for self-certification | |
|---|---|---|---|
| Problem Set 1 | 15% | 4 hours | Yes (extension) |
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Problem set containing questions and programming assignments on probability theory. |
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| Problem Set 2 | 15% | 4 hours | Yes (extension) |
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Problem set containing questions and programming assignments on optimisation. |
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| Final Exam | 70% | 42 hours | No |
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| Weighting | Study time | Eligible for self-certification | |
|---|---|---|---|
| Resit Exam | 100% | No | |
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For problem sets 1-2 individual feedback will be provided. There will be a class test in week nine (formative assessment, not for credit). For the final exam cohort-level feedback will be provided.
This module is Core for: