WM260-15 Applied Maths - II
Introductory description
Mathematics underpins the understanding, design and development of digital and technological solutions in many areas of business. Students will study maths concepts and methods to develop a broad and solid foundation for more advanced topics taught in later years.
Module aims
Students will gain an appreciation of the applications of differential calculus and linear algebra concepts in digital and technological systems. The module also equips students with mathematical skills to formulate and solve real-world problems using linear programming and dynamic programming. Students will also develop problem-solving techniques through the analysis of networks and the use of algorithms to model and solve problems in digital technologies and information systems.
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.
Differential Calculus:
- Partial differentiation of functions of two or more variables;
- Differentiation Techniques;
- Applications of Differentiation (Optimisation – Stationary points, Maximum, Minimum and Saddle Points).
Linear Algebra:
- Lines, Planes, Distance.
- Vectors: Norms, Inner products, Angles and orthogonality, Linear independence, Span, Basis.
- Matrices: Linear Transformation, Matrix Algebra, Determinant, Solving system of linear equations (Cramer’s method and Inverse matrix method), Eigenvalues and Eigenvectors, Trace, Rank, Eigen-decomposition and Diagonalisation.
Decision Mathematics:
- Linear Programming: Graphical method of solving linear programming problems; Minimisation & Maximisation. Simplex Method.
- Analysing Networks: Route inspection problem. Travelling Salesperson problem.
- Dynamic Programming: Floyd’s Algorithm.
Learning outcomes
By the end of the module, students should be able to:
- Select and apply techniques in differential calculus to solve applied problems involving partial derivatives of multivariable functions. [AHEP:4 – C1, C2, C3 ][CITP: 2.1.9, 2.1.10]
- Apply concepts and methods of linear algebra to illustrate key principles of data analysis. [AHEP:4 – C1, C2, C3 ][CITP: 2.1.9, 2.1.10]
- Employ linear programming techniques to formulate and solve optimisation problems. [AHEP:4 – C1, C2, C3 ][CITP: 2.1.9, 2.1.10]
- Analyse networks and implement dynamic programming algorithms to solve shortest-path problems. [AHEP:4 – C1, C2, C3 ][CITP: 2.1.9, 2.1.10]
Indicative reading list
- Kuldeep, S. (2011) Engineering Mathematics Through Applications. Second edition. Bloomsbury Publishing Plc, ISBN: 9780230345980, 9780230274792.
- Hu, Q. (2017) Concise Introduction to Linear Algebra. First edition. Boca Raton, FL: CRC Press, EBOOK ISBN: 9781315172309.
- Rosen, K. (2019) Discrete Mathematics and its applications. Eighth edition. McGraw-Hill, ISBN:
1260091996, 9781260091991 - Cormen, T. H. (2009) Introduction to algorithms. 3rd ed. Cambridge, Mass: MIT Press, ISBN: 0262033844.
View reading list on Talis Aspire
Subject specific skills
Determine and use appropriate data analysis techniques (S11);
Principles of data analysis for digital and technology solutions (K13);
Has a strong work ethic and commitment in order to meet the standards required (B1).
Transferable skills
Problem solving;
Critical thinking;
Communicating mathematically.
Study time
| Type | Required |
|---|---|
| Lectures | 20 sessions of 1 hour (13%) |
| Seminars | 10 sessions of 1 hour (7%) |
| Online learning (scheduled sessions) | (0%) |
| Online learning (independent) | 8 sessions of 1 hour (5%) |
| Other activity | 2 hours (1%) |
| Private study | 50 hours (33%) |
| Assessment | 60 hours (40%) |
| Total | 150 hours |
Private study description
Inclusive of:
- Pre-block and Post-block problem sets released on Moodle.
- Online Quiz for revision.
- Online forum for discussing queries with course peers and tutor.
- Online tutor-recorded videos.
Recapping of prior learning is expected where necessary. Reading around the topics covered will provide the depth of understanding required to complete the course to a good standard. This may be both prior to and/or after the teaching and learning sessions. Support from teaching staff is available but students will be expected to increasingly develop their independent learning skills.
Other activity description
Support Sessions
Costs
No further costs have been identified for this module.
You must pass all assessment components to pass the module.
Assessment group D2
| Weighting | Study time | Eligible for self-certification | |
|---|---|---|---|
| Coursework | 40% | 24 hours | Yes (extension) |
|
A collection of several problems based on the differential calculus and linear algebra topics outlined in the syllabus. Students are expected to solve with a full written solution. |
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| Exam | 60% | 36 hours | No |
|
This is an online examination focussing on the decision maths topics outlined in the syllabus. |
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Feedback on assessment
Feedback will be given as appropriate to the assessment type:
- summative cohort-level feedback on exam.
- individual feedback is provided for the coursework.
Pre-requisites
To take this module, you must have passed:
Courses
This module is Core for:
- Year 2 of DWMS-H655 Undergraduate Digital and Technology Solutions (Cyber) (Degree Apprenticeship)
- Year 2 of DWMS-H652 Undergraduate Digital and Technology Solutions (Data Analytics) (Degree Apprenticeship)
- Year 2 of DWMS-H653 Undergraduate Digital and Technology Solutions (Network Engineering) (Degree Apprenticeship)
- Year 2 of DWMS-H654 Undergraduate Digital and Technology Solutions (Software Engineering) (Degree Apprenticeship)