Module overview
This module provides students with fundamental mathematical concepts relevant to applications in AI and CE. The focus will be on probability, statistical inference, combinatorics, optimization techniques, calculus – partial derivatives and ordinary differential equations, and symbolic maths. There will be laboratory applications using Python and Jupyter to visualise, manipulate and explore these topics.
Aims and Objectives
Learning Outcomes
Subject Specific Intellectual and Research Skills
Having successfully completed this module you will be able to:
- Critical analysis of counting problems on finite, discrete structures
- Definition and properties of discrete and continuous probability distributions
- Nonlinear optimization via gradient methods
- Unconstrained and constrained optimization including the use of Lagrange multipliers
- Elements of statistical inference, including hypothesis testing
- Analytical and numerical solution of ordinary differential equations
Knowledge and Understanding
Having successfully completed this module, you will be able to demonstrate knowledge and understanding of:
- Understanding of the use of the Jacobian matrix for stability analysis of a system of ordinary differential equations.
- Concepts of probability and statistical inference
- Appreciate applications of the above concepts in AI and CE.
- Concepts of partial differentiation and its applications
- Advantages and disadvantages of numerical vs symbolic computation.
Subject Specific Practical Skills
Having successfully completed this module you will be able to:
- Be able to solve systems of ordinary differential equations derived from real-world problems using numeric and symbolic approaches.
- Simple computation using tools of symbolic mathematics
Syllabus
Combinatorics
- Basic principles of counting: product and sum rules, inclusion-exclusion principle, pigeonhole principle.
- Combinations, permutations and arrangements, binomial theorem.
Probability and statistical inference
- Probability and statistics
- Introduction to probability: elementary probability formulae, discrete and continuous probability distributions.
- Introduction to statistics: sampling, confidence intervals, hypothesis testing, regression.
Calculus
- Partial differentiation; Ordinary differential equations; Jacobian matrix and stability analysis; Numerical integration introduction.
Optimization
- Gradient methods
- Lagrange multipliers
Symbolic maths
- Numeric vs symbolic processing for solving ordinary differential equations
Example application of symbolic maths
- Lane centering in an autonomous driving application
Learning and Teaching
Teaching and learning methods
The module consists of:
- Lectures
- Tutorials
- Guided self-study
- Labs as part of the AICE Lab Programme which will cover practical aspects
Type | Hours |
---|---|
Independent Study | 108 |
Lecture | 32 |
Specialist Laboratory | 10 |
Total study time | 150 |
Assessment
Summative
This is how we’ll formally assess what you have learned in this module.
Method | Percentage contribution |
---|---|
Exam | 60% |
Coursework | 35% |
Lab work | 5% |
Referral
This is how we’ll assess you if you don’t meet the criteria to pass this module.
Method | Percentage contribution |
---|---|
Exam | 95% |
Lab Marks carried forward | 5% |
Repeat
An internal repeat is where you take all of your modules again, including any you passed. An external repeat is where you only re-take the modules you failed.
Method | Percentage contribution |
---|---|
Lab work | 5% |
Exam | 95% |