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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 complex numbers, linear algebra and calculus 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 with respect to complex problems in the field of robotics and AI.

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. Frame problems in robotics and AI using appropriate mathematical models and solve these both by applying knowledge of the theory and by selecting and using computational tools.
4. Demonstrate increasingly developing inventive and creative problem-solving skills through participation in a real-world based project (in relation to relevant and current robotics and AI themes and synthesis of existing knowledge from the programme.)

Content:

This module provides the first part of two core 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. This course provides a practitioner’s introduction to the basics of complex numbers, linear algebra and calculus. Fundamental theory 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 throughout the programme.

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

• Complex numbers (Cartesian & polar representations, complex conjugate, functions as complex exponentials)
• Linear algebra
• Geometry (lines in 3D, scalar products, angles and perpendicularity, affine geometry, surfaces)
• Matrices (basic concepts and operations, systems of linear equations, determinant, inverse, singular and triangular matrices).
• Calculus (integration and differentiation of functions, integration by parts, multiple integration, partial differentiation, continuity).

Requisites:

To be eligible to select this module as optional or elective, a student must be registered on a programme and year of study for which it is formally available.