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 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:
Derivative of functions; Techniques of Differentiation (Product, Quotient, Chain, Power, Exponential and Logarithmic rules); Applications of Differentiation (Optimization – Stationary points, Maxima, Minima).
Linear Algebra:
- Lines, Planes, Distance.
- Vectors: Norms, Inner products, Angles and orthogonality, Linear independence, Span, Basis, Orthogonal basis.
- Matrices: Matrix Algebra, Determinant, Solving system of linear equations (Cramer’s method and Inverse matrix method), Eigen values and Eigenvectors, Trace, Rank, Eigen-decomposition and diagonalization.
Statistics and Probability (II):
- Bivariate data: Linear Regression and Correlation; Scatter diagrams; Least squares linear regression; Product Moment Correlation Coefficient; Spearman’s rank correlation coefficient.
- Continuous Probability distribution: Continuous Random Variables; Probability density function; Mean (Expectation) and variance of continuous probability distribution. Normal (Gaussian) distribution; Normal distribution as an approximation to the Binomial distribution.
Decision Mathematics (II)
- Linear programming: The Simplex method: The initial simplex tableau, Manipulating systems of equations, The simplex method; Problems involving ≥ constraints, Terminology, Post-optimal analysis, Two-stage simplex, The big M method; Problem Solving: Equalities and practicalities.
- Analyzing networks:
o Route inspection problem: Euler Cycles; Solving route inspection problems; Complexity of the route inspection algorithm.
o Travelling Salesperson problem, Practical and classical problem, Upper and Lower bounds, Tour building. - Dynamic Programming: Floyd’s Algorithm.
- Decision Analysis: Organising data using decision trees to clarify and facilitate complex decision-making; EMV; Utility function
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 | 20 sessions of 1 hour (13%) |
| Seminars | 12 sessions of 1 hour (8%) |
| Private study | 78 hours (52%) |
| Assessment | 40 hours (27%) |
| Total | 150 hours |
Private study description
78 hours guided self-study including:
- Pre-block exercises given on Moodle.
- 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.
Costs
No further costs have been identified for this module.
You must pass all assessment components to pass the module.
Assessment group D
| Weighting | Study time | Eligible for self-certification | |
|---|---|---|---|
| Mid-Module Assessment | 40% | 15 hours | Yes (extension) |
|
One assignment with questions focusing on the Linear Algebra and Statistics & Probability. |
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| Written Examination | 60% | 25 hours | No |
|
This is a 2 hour written exam. |
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Feedback on assessment
Feedback will be given as appropriate to the assessment type:
- written feedback is provided for the assignment.
- further verbal feedback is made available.
- 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)