Foundations of Mathematics|Foundations of Logic|Proofs and Refutations|Functions|Relations|Perm

Aims:

To equip first year computer science students with knowledge of foundational mathematics and logic that will be needed for future computer science...

Discrete Mathematics for Computer Scientists (COMP0147)

Aims:

To equip first year computer science students with knowledge of foundational mathematics and logic that will be needed for future computer science modules. To provide students with basic tools and skills for mathematical problem solving, proof and refutation.Learning outcomes:

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

Analyse and solve typical problems in discrete mathematics and logic.
	Identify and reason with the logical content of arguments.
	Carry out standard mathematical proofs and refutations.
Content:

The first part of the course will focus on foundational discrete mathematics, including but not necessarily limited to: functions and relations, permutations, group theory, set theory, cardinalities, diagonalisation, linear algebra and combinatorics. The module continues with mathematical reasoning, logical notation and proof by mathematical induction.Requisites:

To be eligible to select this module as an 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 passed A-level Mathematics (or an appropriate equivalent).

Advanced Mathematical Modelling &amp; Analysis will deepen your understanding of the core mathematical concepts, and modelling and analysis skills, that...

Advanced Mathematical Modelling and Analysis (BARC0130)

Advanced Mathematical Modelling & Analysis will deepen your understanding of the core mathematical concepts, and modelling and analysis skills, that underpin the practise of engineering and architectural design. You will learn mathematical tools and approaches that you will call upon throughout your career, regardless of specialism. You will do this by developing mathematical models of the engineering and design problems, and then simulating and analysing these models using software tools like MATLAB and Excel.

By the end of this module, you will be expected to:

Recognise the connections between mathematics and engineering and how mathematical ideas are embedded in engineering and architectural contexts;
	Represent real-world systems from Engineering and Architectural Design in a mathematical framework;
	Identify and draw upon a range of advanced mathematical concepts in Real and Complex Analysis (Series and Approximations), Linear Algebra (Matrices, Frame Transformations, Least Squares Analysis in matrix form), Probability & Statistics (Statistical Inference, Time Series Analysis), and Estimation Theory to analyse specific problems and identify the appropriate mathematics required to create a solution;
	Employ appropriate computer programming and modelling software such as MATLAB and Excel and statistical analysis to efficiently solve and evaluate the performance of engineering systems;
	Relate the behaviour of the output of mathematical models to the underlying physical or conceptual models of interest;
	Carry out engineering problem solving collaboratively and independently;
	Present and interpret mathematical results in effective and appropriate ways to varied audiences, including non-mathematical audiences.