WM260-15 Applied Maths - II
Introductory description
Mathematics underpins the understanding, design and development of digital and technological solutions in many areas of businesses.
This module builds on the statistics, probability and discrete maths concepts studied in the Applied Maths-I module.
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, use of statistical methods and 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 (Optimization – Stationary points, Maximum, Minimum and Saddle Points).
Linear Algebra:
- Lines, Planes, Distance.
- Vectors: Norms, Inner products, Angles and orthogonality, Linear independence, Span, Basis.
- Matrices: Matrix Algebra, Determinant, Solving system of linear equations (Cramer’s method and Inverse matrix method), Eigenvalues and Eigenvectors, Trace, Rank, Eigen-decomposition and diagonalization.
Statistics:
- Bivariate data: Linear Regression and Correlation; Scatter diagrams; Least squares linear regression; Product Moment Correlation Coefficient; Spearman’s rank correlation coefficient.
Decision Mathematics:
- Linear Programming: Graphical method of solving linear programming problems; Minimization & Maximization. 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:
- Develop conceptual understanding of relevant concepts in differential calculus and linear algebra.
- Employ linear programming techniques to formulate and solve optimization problems.
- Analyze networks and implement dynamic programming algorithms to solve shortest-path problems.
- Apply statistical models to analyze data and describe relationships in data.
Indicative reading list
- Catherine A. Gorini (no date) Master math: probability. Boston, Massachusetts: Course Technology/Cengage Learning, ISBN: 9781435456570 (e-book), 1435456572 (e-ISBN)
- Cormen, T. H. (2009) Introduction to algorithms. 3rd ed. Cambridge, Mass: MIT Press, ISBN: 0262033844
- DeCoursey, W. J. (2003) Statistics and probability for engineering applications with Microsoft Excel. Amsterdam: Newnes, PRINT ISBN: 9780750676182, EBOOK ISBN: 9780080489759
- Hu, Q. (2017) Concise Introduction to Linear Algebra. First edition. Boca Raton, FL: CRC Press, EBOOK ISBN: 9781315172309
View reading list on Talis Aspire
Subject specific skills
communicating mathematically,
quantitative reasoning,
manipulation of precise and intricate ideas,
application of analytical and critical thinking skills to technology solutions development and systematic analysis, and application of structured problem solving techniques to complex systems and situations.
Transferable skills
analytical skills,
problem solving,
flexibility ,
persistence
flexible attitude,
ability to perform under pressure,
thorough approach to work,
logical thinking and creative approach to problem solving.
Study time
| Type | Required |
|---|---|
| Lectures | 14 sessions of 1 hour (9%) |
| Seminars | 7 sessions of 1 hour (5%) |
| Online learning (scheduled sessions) | 9 sessions of 1 hour (6%) |
| 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 A
| Weighting | Study time | Eligible for self-certification | |
|---|---|---|---|
| Coursework | 40% | 25 hours | Yes (extension) |
|
One assignment with questions focusing on Differential Calculus, Linear Algebra and Statistics. |
|||
| Online Written Examination | 60% | 35 hours | No |
|
This is a 2 hour online written examination focussing on the discrete maths topics outlined in the syllabus. |
|||
Feedback on assessment
Feedback will be given as appropriate to the assessment type:
- written feedback is provided for the assignment.
- summative cohort -level feedback on exam.
Pre-requisites
To take this module, you must have passed:
Courses
This module is Core for:
- 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)