Introductory description

This module makes use of modelling and algorithms to solve problems involving networks, linear programming and critical path analysis. Simulation is introduced as a modelling technique. A wide variety of problems is considered, and a flexible approach is modelled in this course with due consideration given to the success of models used and the limitations of solutions. This module will provide the foundation for mathematical concepts in problem-solving within information systems.

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.

Statistics & Probability (I)

• Introduction to Data: Numerical & categorical data; discrete & continuous data; Statistical perspectives: (simplification, abstraction, and modelling); Population and samples: Sampling Techniques (Simple random, stratified, cluster, systematic, self-selecting, opportunity, quota); Graphical representation of data:, frequency distribution, cumulative frequency, stem & leaf diagrams, histogram, boxplots, shapes of distribution of data.
• Data Summary: Measure of Central Tendency (mean, median, mode, mid-range); Measure of Dispersion (variance, standard deviation, range, quartiles, inter-quartile range); Outliers; Estimating quartiles using cumulative frequency curve.
• Probability: Probabilities of single events; complement of events; probabilities of more than one event; expected frequency of an event; venn diagrams; conditional probability; mutually exclusive and independent events: addition rule of probabilities; tree diagrams; probabilities based on selecting or arranging objects; Discrete Random Variables and Discrete Probability Distributions: Expectation (mean) and variance of a discrete random variable. Uniform distribution; Binomial distribution; probabilities involving binomial distributions.
• Hypothesis Testing: Hypothesis testing based on Binomial distribution: (p-values, critical values, critical regions, one-tailed test, two-tailed test).

Discrete Mathematics (I)
-Discrete modelling: abstracting from a problem, and comparing to the real world.
-Algorithms: understanding and implementing a variety of algorithms expressed as lists of instructions, flow charts or in pseudo code.
-Critical path analysis: activity or precedence networks, performing forward and backward passes, drawing cascade charts and resource levelling.
-Introduction to graph theory: definition of a graph and the associated vocabulary, mathematical modelling with graphs.
-Graphical linear programming: formulating a problem as a linear programming problem, solving a linear programming problem (maximisation and minimisation) and integer programming.
-Introduction to networks: applying Kruskal’s and Prim’s algorithms to find the minimum spanning tree of a network, applying Dijkstra’s algorithm to find the shortest (or least value) path from one vertex to any other vertex in the network.
Simulation: using random devices, especially random number generators to simulate events that are affected by chance, simulating queues.

Learning outcomes

By the end of the module, students should be able to:

• Know and use the mathematical language necessary for communicating ideas in digital and information systems.
• Know probability and distributions to present data.
• Use algorithms, graphs and networks to analyze data.
• Apply appropriate mathematical methods to solve substantial statistical and discrete problems.

Indicative reading list

R. J. Barlow, Statistics, A Guide to the Use of Statistical Methods in the Physical Sciences, Wiley (1989), ISBN: 978-0471922957.
C. A. Gorini, Master Math Probability, Course Technology Cengage Learning (2012), ISBN: 1435456564, 9781435456563.
S. S. Epp, Discrete Mathematics with Applications, Cengage Learning (2011), ISBN: 0495391328, 0495826162, 9780495391326, 9780495826163.
R. P. Grimaldi, Discrete and Combinatorial Mathematics, an applied introduction, Addison-Wesley-Longmann (2014), ISBN: 1292022795, 9781292022796.

View reading list on Talis Aspire

Subject specific skills

communicating mathematically
quantitative reasoning
manipulation of precise and intricate ideas

Transferable skills

analytical skills
problem solving
flexibility
persistence