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 web page

Module aims

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