MA4005  Logic and Mathematical Techniques (2017/18)
Module specification  Module approved to run in 2017/18  
Module title  Logic and Mathematical Techniques  
Module level  Certificate (04)  
Credit rating for module  30  
School  School of Computing and Digital Media  
Total study hours  300  


Assessment components 


Running in 2017/18 

Module summary
This module develops a range of mathematical techniques including set theory, logic, relations and functions,algebra, differentiation and integration. The techniques provide the foundation for further study of mathematics, computer science and computer games.
Module aims
The aim of this module is to provide a firm foundation for study in further mathematics computer games and computer science. It will also enable students to apply the methods to a range of practical problems.
Syllabus
 Propositional Logic: representation of simple verbal arguments; truthtables; logical equivalence, validity and consequence, logic circuits. Predicate logic.
 Propositional Logic: representation of simple verbal arguments; truthtables; logical equivalence, validity and consequence, logic circuits. Predicate logic.
 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 & Functions: Relations: representations of relations (matrix and digraph); equivalence relations; partitions; partial orderings. Functions: ways of defining functions; composition; inverse functions.
 Algebra: Basic numbers, indices, brackets; Manipulation of algebraic expressions; Linear and quadratic equations.
 Matrices Representation of the coordinate plane. Use of matrices to represent the vertices of a plane figure. Simple transformations. Vector algebra. Matrix algebra. Application to computer graphics.
 Calculus. Functions. Graphs; Exponential function and natural logarithm; Trignometric functions. Differentiation of basic functions x^n, ln x, e^x, sin x, cos x ; Stationary points. Indefinite and definite integrals; Area under a curve. Application to kinematics.
Learning and teaching
This module will be delivered through a mixture of lectures and tutorials. The lectures will develop theory, explain the methods and techniques and demonstrate them by going through examples. The tutorials will provide students with the opportunity of reviewing their lecture notes and working through the problems designed for their practice, which will underpin the skills and techniques demonstrated in the lectures. Students will be encouraged to construct valid and precise mathematical arguments and will be expected to produce solutions using appropriate notational and stylistic conventions. Selfstudy exercises will enable students to monitor their own progress.
A set of lecture notes will be provided to students and answers for exercise questions will be put on the VLE.
Blended learning is incorporated by using on line resources as a medium for communication (both peer and tutorled) and will also provide additional materials to stimulate the student interest and broaden their horizons.
Learning outcomes
After successful completion of this module students should be able to:
LO1 Demonstrate skill in formulating, manipulating and solving algebraic equations.
LO2 Use functions appropriately and identify their graphical equivalents.
LO3 Understand the meaning of mathematical definition of relations and to determine which relations are equivalence relations.
LO4 Understand the meaning of mathematical definitions of sets/propositions and perform set/logic operations.
LO5 Demonstrate skill in, and application of, the techniques of vector algebra, differentiation and integration.
Assessment strategy
This module is assessed through four tests (LO1LO5) . These tests will provide students with an opportunity to monitor their progress and adapt their study plan.
In the Test 1 and 2, the students are assessed on learning outcomes LO2 ,LO3 and LO4.
In the Test 3 and 4, the focus will on learning outcomes LO1 and LO5.
Bibliography
1. Rod Haggarty, Discrete Mathematics for Computing , Addison Wesley, 2002.
2. Anthony Croft and Robert Davison, Foundation Maths, third edition, Prentice Hall.