Module Catalogue 2024/25

Pre Requisite Comment

A level Maths or equivalent

Co Requisite Comment

N/A

Aims

The module aims to provide students of differing mathematical backgrounds with a common algebraic foundation for more advanced mathematical study. The first part of the module is devoted to complex numbers and polynomial equations in one variable. The second part treats elementary concepts of linear algebra, in particular systems of linear equations and matrix methods for their solution and applications to geometry.

Outline Of Syllabus

Complex numbers, arithmetic, Argand diagram, polar form, de Moivre's theorem, powers and roots of unity.

Vectors: sums, products (scalar, dot, cross), equations of lines and planes, orthogonality, norm.

Linear algebra: row operations, solution of linear equations, Gaussian elimination, matrix operations, determinants, inverting matrices, eigenvectors, quadratic forms.

Intended Knowledge Outcomes

Students will gain an understanding of complex numbers and of vector and matrix methods in algebra and geometry.

Intended Skill Outcomes

Perform arithmetic manipulations with complex numbers.

Solve polynomial equations of small degree.

Use De Moivre’s Theorem to compute powers, determine n-th roots, and to obtain trigonometric identities.

Solve general systems of linear equations by Gauss eliminations. Use the dot product and the cross product to describe equations of lines and planes in three dimensional space.

Describe rotations and reflections in matrix form. Perform algebraic operations with matrices and apply them to solve linear equations.

Evaluate determinants and invert matrices. Determine eigenvalues and eigenvectors of matrices. Manipulate quadratic forms.

Students will develop skills across the cognitive domain (Bloom’s taxonomy, 2001 revised edition): remember, understand, apply, analyse, evaluate and create.

Teaching Rationale And Relationship

The teaching methods are appropriate to allow students to develop a wide range of skills, from understanding basic concepts and facts to higher-order thinking. Lectures are used for the delivery of theory and explanation of methods, illustrated with examples, and for giving general feedback on marked work. Problem Classes are used to help develop the students’ abilities at applying the theory to solving problems.

Assessment Rationale And Relationship

A substantial formal unseen examination is appropriate for the assessment of the material in this module. The format of the examination will enable students to reliably demonstrate their own knowledge, understanding and application of learning outcomes. The assurance of academic integrity forms a necessary part of the programme accreditation.

Examination problems may require a synthesis of concepts and strategies from different sections, while they may have more than one ways for solution. The examination time allows the students to test different strategies, work out examples and gather evidence for deciding on an effective strategy, while carefully articulating their ideas and explicitly citing the theory they are using.

The coursework assignments allow the students to develop their problem solving techniques, to practise the methods learnt in the module, to assess their progress and to receive feedback; these assessments have a secondary formative purpose as well as their primary summative purpose.

General Notes

N/A