module specification

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.

• 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
• Propositional Logic: representation of simple verbal arguments; truth-tables; logical equivalence, validity and consequence, logic circuits. Predicate logic.
• 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.
• Algorithms: understanding how problems can be solved systematically, plan their solutions and write them in form of  algorithms (e.g. Euclid's Algorithm)
• Combinatorics: combinations, permutation and probability
• Relations: representations of relations (matrix and digraph); equivalence relations; partitions; partial orderings.
• Functions: ways of defining functions; composition; inverse functions. LO2,LO3,LO4

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.

LO1   Create algorithmic methods of real-world problems and to develop and present the solutions.
LO2   Understand the meaning of mathematical definitions of sets/propositions and perform set/logic operations.
LO3   Understand the meaning of mathematical definition of relations and to determine which relations are equivalence relations.
LO4   Understand the meaning of mathematical definition of functions, to use it to construct functions and to determine which functions are one-to-one.

This module is assessed through tests and coursework.
The first component will be take-away coursework and it will assess LO1.
In the first test the students are assessed on sets and logic (LO2).
The first test and feedback is designed so that students can identify any deficiencies in their learning strategies and put corrective strategies in place at an early point in studying Logic. The second test will assess the learning outcomes LO3 to LO4.

Reassessment Strategy for the group coursework:
Students who have reassessment opportunity in the Group Coursework will be required to work on the first sit coursework and submit it as an individual coursework on Weblearn.

Core Text:
Rod Haggarty (2006), Discrete Mathematics for Computing, Addison Wesley.
Recommended Reading:
Quantitative Techniques by Terry Lucey (Author) Publisher: Cengage Learning EMEA; 6 edition  2002.