Module Catalogue 2024/25

Pre Requisite Comment

N/A

Co Requisite Comment

N/A

Aims

This module introduces the essential concepts of algebra relevant for the physical sciences, including complex numbers, vectors and matrices.

Outline Of Syllabus

Complex numbers: arithmetic, the complex plane, polar form, Euler's formula, de Moivre's theorem, roots of unity.

Vectors: sums, products (scalar, vector, triple), orthogonality, equations of lines and planes.

Linear algebra: matrix addition, multiplication and inversion, eigenvalues and eigenvectors, diagonalisation, determinants, Cramer's rule, Gaussian elimination.

Intended Knowledge Outcomes

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

Intended Skill Outcomes

Students will:

Perform arithmetic manipulations with complex numbers in real-imaginary, modulus-argument and exponential form. Apply Euler's formula and de Moivre's theorem to determine powers, roots, and derive trigonometric identities.

Compute scalar, vector and triple products of vectors, and formulate equations for lines and planes.

Study basic matrix operations including addition, multiplication, inversion, finding eigenvalues and eigenvectors, diagonalization, and the computation of determinants. Use matrices to solve systems of linear equations and describe geometrical transformations.

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.

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 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