# module specification

## MA4001 - Logic and Problem Solving (2024/25)

Module specification Module approved to run in 2024/25
Module title Logic and Problem Solving
Module level Certificate (04)
Credit rating for module 30
School School of Computing and Digital Media
Total study hours 300

 90 hours Scheduled learning & teaching activities 210 hours Guided independent study
Assessment components
Type Weighting Qualifying mark Description
In-Course Test 25%   Test 1 (1 hour, unseen)
In-Course Test 25%   Test 2 (1 hour, unseen)
Group Coursework 50%   Group coursework (2500 words)
Running in 2024/25

(Please note that module timeslots are subject to change)
Period Campus Day Time Module Leader
Year North Friday Morning

## Module summary

The module aims are to give the students an understanding of how problems can be solved systematically, plan their solutions and write them in the form of algorithms. This module also develops a range of mathematical techniques including set theory, logic, relations, functions and operational research techniques. In addition, it gives a grounding in standard software packages, to give students an understanding of their use in problem solving as well as to make students able to apply these packages appropriately in subsequent modules.

None.

## Syllabus

Puzzles: developing logical reasoning, introducing systematic approach to solving puzzles, developing appropriate strategies to solve puzzles (LO1).

Linear Programming, Sensitivity analysis, simulation modelling, Maths of Finance and Break-even analysis (LO1).

Propositional Logic: representation of simple verbal arguments; truth-tables; logical equivalence, validity and consequence, logic circuits. Predicate logic (LO2).

Sets: introduction to notation; set operations; Venn diagrams; universal, empty set and subsets; set identities (De Morgan etc.); duality; power sets, ordered pairs and Cartesian products (LO2).

Algorithms: understanding how problems can be solved systematically, plan their solutions and write them in form of algorithms (e.g., Euclid's Algorithm) (LO3)

Relations: representations of relations (matrix and digraph); equivalence relations; partitions; partial orderings.

Functions: ways of defining functions; composition; inverse functions (LO4).

## Balance of independent study and scheduled teaching activity

Learning technologies will be used for providing the teaching materials (e.g. WebLearn). The module will be taught by a mixture of lectures, supervised computer laboratory sessions and self-study practical exercises. In particular, the lectures will be used to introduce the various concepts and principles of the module's topics or demonstrate worked examples. Each lecture will be followed by a practical supervised session where the students will be able to apply/experiment with the various notions introduced in the lectures, using examples and following detailed instructions. The materials that will be used in the practical sessions will allow each student to work at his/her own speed. Furthermore, students will be pointed to self-study exercises which they will attempt in their own time. The students will also be expected to spend time on private study and on preparation for the assessments.

## Learning outcomes

On successful completion of this module, students should be able to:

- Create algorithmic methods of real-world problems and to develop and present the solutions (LO1).

- Understand the meaning of mathematical definitions of sets/propositions and perform set/logic operations (LO2).

- Understand the meaning of mathematical definition of relations and to determine which relations are equivalence relations (LO3).

- Understand the meaning of mathematical definition of functions, to use it to construct functions and to determine which functions are one-to-one (LO4).

## Bibliography

Core Text:

Rod Haggarty (2006), Discrete Mathematics for Computing, Addison Wesley.

Other Texts:

Quantitative Techniques by Terry Lucey (Author) Publisher: Cengage Learning EMEA; 6 edition 2002.

Journals:

Mathematical problems in engineering

Journal of applied mathematics

Websites:

University Library website

Subject guides and research support

Electronic Databases:

IEEE Xplore / IET Digital Library (IEL)

Wiley Online Library

Social Media Sources: