MA4005 - Logic and Mathematical Techniques (2018/19)
|Module specification||Module approved to run in 2018/19|
|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|
|Running in 2018/19||
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 Programming and Computer Systems Engineering.
• 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. LO1
• Relations & Functions: Relations: representations of relations (matrix and digraph); equivalence relations; partitions; partial orderings. Functions: ways of defining functions; composition; inverse functions. LO2
• Algebra: Basic numbers, indices, brackets; Manipulation of algebraic expressions; Linear and quadratic equations.LO3
• Functions. Graphs; Exponential function and natural logarithm; Trigonometric functions. Differentiation of basic Polynomial, exponential, Logarithms and Trigonometrical functions; Stationary points. Indefinite and definite integrals; Area under a curve. Application to kinematics.LO4
• 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. LO5
Balance of independent study and scheduled teaching activity
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.
After successful completion of this module students should be able to:
LO1 Understand the meaning of mathematical definition of relations and to determine
which relations are equivalence relations.
LO2 Understand the meaning of mathematical definitions of sets/propositions and
perform set/logic operations.
LO3 Demonstrate skill in formulating, manipulating and solving algebraic equations.
LO4 Use functions appropriately and identify their graphical equivalents.
LO5 Demonstrate skill in, and application of, the techniques of vector algebra,
Differentiation and integration.
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 LO1- LO3 and LO4.
In the Test 3 and 4, the focus will on learning outcomes LO3 - LO5.The volume, timing and nature of assessment enable students to demonstrate the extent to which they have achieved the intended learning outcomes.
Discrete Mathematics for Computing, Rod Haggarty, 2002, Addison Wesley.
Mathematics for Engineers Fourth edition Tony Croft, Robert Davison r Pearson Education Limited 2015.