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Aims:

The aims of this module are to:

• Provide students with a solid grounding in recognising and using the basic mathematical techniques in the solution of problems in the domain of robotics and AI.
• Support students in the development of a breadth of knowledge and understanding in the fundamentals of Mathematics 2 with the goal of applying this to complex problems in the field of robotics and AI.
• Provide students with the confidence and skills to apply mathematical concepts and methods in later modules in Year 1 on complex problems in the field of robotics and AI.
• Support students to develop a holistic understanding of the practical application of theory and foundational knowledge of AI–based robotic systems (project).
• Build students’ confidence when liaising with and presenting in future industrial contexts, working with peers and participating in AI–based robotics projects.

Intended learning outcomes:

On successful completion of the module, a student will be able to:

1. Select and then apply basic mathematical techniques in the solution of problems in the domain of robotics and AI.
2. Formulate concise, correct and complete mathematical proofs.
3. Employ statistical techniques in the analysis of experimental datasets.
4. Explain the advantages and limitations of using computational tools in quantitative analysis; be able to select and employ numerical techniques that are appropriate to specific problems.
5. Select and apply appropriate optimisation techniques in both synthetic and real-world examples of robotic systems.
6. Identify and demonstrate a critical understanding of the role that mathematical knowledge plays in the development and build of AI-based robotic systems.
7. Demonstrate engagement with reflective and learning as key academic and professional skills.

Indicative content:

This module provides the second part of two foundational mathematical knowledge and skills modules which form the basis of its subsequent application of this to complex problems in the field of robotics and AI. The module focusses on an introduction to three things: probability and statistics, finding optimal solutions to problems, and the issues associated with performing mathematical calculations on computer systems. Like Mathematics 1, in this second part foundational knowledge will form a key part of the maths content delivered in this module and students will be expected to apply the mathematical techniques covered in a range of graduated problems.

The following are indicative of the topics the module will typically cover:

• Numerical analysis (floating point representation, numerical stability, Taylor series).
• Optimisation (convexity, conditions for optimality, the simplex algorithm, linear/quadratic programming, constrained optimisation, least squares)
• Probability and statistics (random variables, distributions, joint and conditional probability, Bayes, Gaussians, covariance).

Requisites:

To be eligible to select this module as optional or elective, a student must: (1) be registered on a programme and year of study for which it is a formally available; and (2) have completed Mathematics for Robotics and Artificial Intelligence 1 (COMP0202) in Term 1.