module specification

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
 
81 hours Scheduled learning & teaching activities
219 hours Guided independent study
Assessment components
Type Weighting Qualifying mark Description
In-Course Test 25%   Test 1 (1 hour)
In-Course Test 25%   Test 2 (1 hour)
In-Course Test 25%   Test 3 (1 hour)
In-Course Test 25%   Test 4 (1 hour)
Running in 2017/18
Period Campus Day Time Module Leader
Year North Thursday Morning

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; truth-tables; logical equivalence, validity and consequence, logic circuits. Predicate logic.
  • Propositional Logic: representation of simple verbal arguments; truth-tables; 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 co-ordinate 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. Self-study 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 tutor-led) 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 (LO1-LO5) . 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.