Introductory description

This module extends students’ skills in applying advanced mathematical and statistical methods to scientific and engineering problems. It emphasises building, applying, and reviewing models, with a focus on real-world applications that require both further mathematics and statistical reasoning. Students will gain confidence in using advanced processes and techniques, equipping them for degree-level study in mathematics-based subjects. By the end of the module, students will be able to use advanced mathematics and statistics to model, analyse, and interpret complex problems in science and engineering.

Module web page

Module aims

Outline syllabus

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.

Algebra: Modulus and Quadratic Inequalities, Polynomial factorisation, Trigonometry, Binomial Theorem, Sequence & Series, Matrices, Vector Geometry, Euler’s Theorem & DeMoivre’s Theorem, Complex roots.

Calculus: Applications of derivatives, Taylor’s series, Applications of integration in area, volume, arc-length, Numerical Integration, First and Second order Ordinary Differential Equations, Partial differentiation.

Statistics & Probability: Data representation, Correlation and regression, probability, probability distribution, Data analysis, Hypothesis testing.

Learning outcomes

By the end of the module, students should be able to:

• Analyse problems and use mathematical and statistical knowledge to plan strategies for solving them.
• Select and apply a range of mathematical and statistical tools and techniques that are appropriate to solve a given problem.
• Create and use appropriate mathematical and statistical models to solve and understand practical real-life problems, in appropriate contexts.
• Construct and present arguments through appropriate use of logical deduction and precise statements involving correct use of symbols and appropriate statistical and further mathematical language.
• Communicate effectively solution to the given real world problem by employing mathematical terminology and notations.
• Evaluate the outcomes and predictions of a mathematical model by considering any assumptions made, and its validity and limitations.

Indicative reading list

Reading lists can be found in Talis

Interdisciplinary

Students will have opportunities to draw on knowledge and skills acquired within the different modules on their pathway.

International

All students are international, representing a wide range of cultural, linguistic, and educational backgrounds. They bring diverse experiences and perspectives, enriching discussion and supporting the development of intercultural awareness. Examples for analysis and evaluation are drawn from a variety of countries, ensuring that teaching and learning are embedded in an international context.

Subject specific skills

Students will have opportunities to:
construct and present mathematical and logical arguments,
convert real-world problems taken from financial and economical contexts into mathematical problems,
solve mathematical problems using appropriate advanced techniques including using suitable technology when
appropriate,
clearly present solutions to mathematical and statistical problems using appropriate symbols and terms.

Transferable skills

Transferable skills will include: problem solving skills, analytical and logical thought processes and appropriate use of suitable technology