Unit 18 Discrete Maths Assignment Brief
| Qualification | Pearson BTEC Levels 4 and 5 Higher Nationals in Computing |
| Unit Number | 18 |
| Unit Title | Discrete Maths |
| Unit code | F/618/7429 |
| Unit type | Unit level 5 |
| Unit level | 5 |
| Credit value | 15 |
Introduction
Digital computer technologies operate with distinct steps and data is stored as separate bits. This method of finite operation is known as ‘discrete’, and the division of mathematics that describes computer science concepts such as software development, programming languages and cryptography is known as ‘discrete mathematics’. This branch of mathematics is a major part of a computer science course and aids, ultimately, in the development of logical thinking and reasoning that lies at the core of all digital technology.
This unit introduces students to the discrete mathematical principles and theory that underpin software engineering. Through a series of case studies, scenarios and taskbased assessments, students will explore set theory and functions in a variety of scenarios, perform analysis using graph theory, apply Boolean algebra to applicable scenarios and, finally, explore additional concepts in abstract algebra.
Among the topics included in this unit are set theory and functions, Eulerian and Hamiltonian graphs, binary problems, Boolean equations, algebraic structures and group theory.
On successful completion of this unit, students will have gained confidence in the discrete mathematics that is needed to understand software engineering concepts. As a result, they will have developed skills such as communication literacy, critical thinking, analysis, reasoning and interpretation, which are crucial for gaining employment and developing academic competence.
Learning Outcomes
By the end of this unit students will be able to:
LO1 Examine set theory and functions applicable to software engineering
LO2 Analyse mathematical structures of objects using graph theory
LO3 Investigate solutions to problem situations using the application of Boolean algebra
LO4 Explore applicable concepts within abstract algebra.
Essential Content
LO1 Examine set theory and functions applicable to software engineering
Set theory:
Sets and set operations. Algebra within set theory.
Set identities and proof of identities. Bags manipulation functions.
Functions:
Domain, range and mappings.
Inverse relations and the inverse function. Injective and surjective functions, and transitive relations
LO2 Analyse mathematical structures of objects using graph theory
Graph theory:
Structure and characterisation of graphs. Spanning trees and rooted trees.
Eulerian and Hamiltonian graphs. Vertex and edge colourings of graphs.
Directed graphs:
Directed and undirected graphs.
Walks, trails, paths and shortest paths.
LO3 Investigate solutions to problem situations using the application of Boolean algebra
Boolean algebra:
Binary states (e.g. on/off; 1/0; open/closed; high/low).
Identification of binary problems and labelling inputs and outputs. Production of a truth table corresponding to a problem situation.
Equations:
Express a truth table as a Boolean equation.
Simplify a Boolean equation using algebraic methods. Represent a Boolean equation using logic gates.
LO4 Explore applicable concepts within abstract algebra
Algebraic structures:
Binary operations and associated properties. Commutative and associative operations.
Algebraic structures and substructures.
Groups:
Introduction to groups, semigroups and monoids. Families of groups and group codes.
Substructures and morphisms.
Learning Outcomes and Assessment Criteria
| Pass | Merit | Distinction |
| LO1 Examine set theory and functions applicable to software engineering | ||
| P1 Perform algebraic set operations in a formulated mathematical problem.
P2 Determine the cardinality of a given bag (multiset). |
M1 Determine the inverse of a function using appropriate mathematical techniques. | D1 Formulate corresponding proof principles to prove properties about defined sets. |
| LO2 Analyse mathematical structures of objects using graph theory | ||
| P3 Model contextualised problems using trees, both quantitatively and qualitatively.
P4 Use Dijkstra’s algorithm to find a shortest path spanning tree in a graph. |
M2 Assess whether a Eulerian and Hamiltonian circuit exists in an undirected graph.
|
D2 Construct a proof of the Five Color Theorem. |
| Pass | Merit | Distinction |
| LO3 Investigate solutions to problem situations using the application of Boolean algebra | ||
| P5 Diagram a binary problem in the application of Boolean algebra.
P6 Produce a truth table and its corresponding Boolean equation from an applicable scenario. |
M3 Simplify a Boolean equation using algebraic methods.
|
D3 Design a complex system using logic gates. |
| LO4 Explore applicable concepts within abstract algebra | ||
| P7 Describe the distinguishing characteristics of different binary operations that are performed on the same set.
P8 Determine the order of a group and the order of a subgroup in given examples. |
M4 Validate whether a given set with a binary operation is indeed a group.
|
D4 Explore, with the aid of a prepared presentation, the application of group theory relevant to your given example. |
Recommended Resources
Textbooks
Attenborough, M. (2003) Mathematics for Electrical Engineering and Computing. Oxford: Newnes.
Piff, M. (2008) Discrete Maths Software Engineers: An Introduction for Software Engineers. Cambridge: Cambridge University Press.
Journals
Journal of Graph Theory. Wiley.
Journal of Mathematical Modelling and Algorithms in Operations Research. Springer.
Links
This unit links to the following related units:
Unit 33: Applied Analytical Models.
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