Unit 34 Analytical Methods (J/618/7450) Assignment Brief 2026

Unit 34 Analytical Methods Assignment Brief 2026

Introduction

John von Neumann, a Hungarian mathematician, outlined the architecture for a stored-program computer in a paper he wrote in 1945. In order to fully develop new software and hardware technologies within this architecture, analytical skills and techniques needed to be applied to any proposed design. In the modern era, analytical methods still underpin theoretical computer science fundamentals and developing this mathematical knowledge will support development in many aspects of computing.

This unit introduces students to advanced analytical techniques that will be relevant to them as they progress with their studies in computing. The unit also advances their knowledge of mathematical modelling and application of theory.

Among the topics included in this unit are complex numbers, numerical methods, matrices, formal logic and Z specification.

On successful completion of this unit, students will be able to use applications of complex number theory, approximate solutions of contextualised examples with numerical methods, apply matrix theory to a variety of different scenarios and use formal methods of logic. They will develop skills such as communication literacy, critical thinking, analysis, reasoning and interpretation, which are crucial for gaining employment and developing academic competence.

Learning Outcomes

By the end of this unit students will be able to:

LO1 Examine complex number theory in practical situations

LO2 Approximate solutions using numerical methods

LO3 Employ matrix methods to contextualised examples relevant to computing

LO4 Investigate the concepts of formal methods in computer science.

Essential Content

LO1 Examine complex number theory within practical situations

Complex number theory:

Introduction to imaginary numbers and complex numbers. The modulus, argument and conjugate of complex numbers. The polar form of complex numbers.

The use of de Moivre’s Theorem.

Using quaternions for spatial rotation in computer graphics.

LO2 Approximate solutions using numerical methods

Numerical methods:

Using sketches to approximate solutions of equations.

Numerical analysis using the bisection method and the Newton–Raphson method.

Numerical integration, the trapezium rule and Simpson’s rule.

Analysis:

Error analysis to determine the accuracy of approximations.

Explanation of numerical method failure and comparison of methodology.

LO3 Employ matrix methods to contextualised examples relevant to computing

Matrix methods:

Introduction to matrices and matrix notation.

Using matrices to represent ordered data and the relationship with program variable arrays.

The process for addition, subtraction and multiplication of matrices. Calculating the determinant and inverse of a matrix.

Application of matrices to vector transformations and rotation, maps and graphs.

LO4 Investigate the concepts of formal methods within computer science

Formal reasoning:

Logic and proof. Introduction to Hoare logic.

Hoare logic to assess the correctness of computer programs. Automated proof checking.

Z specification language:

Model-based specification.

The modelling of software systems using Z specification. Proving properties using Z specification.

Learning Outcomes and Assessment Criteria

Recommended Resources

Textbooks

Garnier, R. and Taylor, J. (1992) Discrete Mathematics: For New Technology. Oxfordshire: Taylor & Francis.

Stroud, K. A. (2009) Foundation Mathematics. Basingstoke: Palgrave Macmillan.

Journal

Communications on Pure and Applied Mathematics. Wiley.

Links

This unit links to the following related unit:

Unit 14: Maths for Computing.

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