module specification

This module develops a range of mathematical techniques in set theory, logic, functions and
binary arithmetic.  The techniques are particularly relevant to students doing computing and
mathematics.

Please note: This module is superseded by MA3332
 

None

The principal graduate attributes developed in the module are (A1 and A2).
The aim of this module is to provide a firm foundation for study in further mathematics and computing.  It will also enable students to apply the methods to a range of practical problems (A2).  In addition, students will evaluate their mathematical strengths and weaknesses and implement an action plan (A1).
 

Number Representation
Decimal, binary, octal, hexadecimal representations. Simple arithmetic and conversions between for positive integers.  1 and 2s complement for negative numbers.  Fixed and floating point representations.  Accuracy.
Logic circuits and Boolean Algebra
Basic logic gates AND, OR, NOT. Construction and simplification of logic circuits.  Simplification of Boolean expressions.  Representation using Venn diagrams. Truth tables.
Set Theory
Simple introduction, and use of Union, Interection and Difference and its relation to Boolean Algebra
Functions
Definition of a function. Examples of functions used in programming and mathematics.
Special Techniques
Introduction to iteration, recursion and constructing algorithms/flowcharts.
.

This module will be delivered through a mixture of lectures (24 hours including revision) and tutorials (24 hours including a class test). 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 (48 hours) will enable students to monitor their own progress. Students will be expected to produce solutions to the problems in the lecture notes. This will form the basis for the preparation for assessments that will also include the revision of basic concepts, revisiting problem sheets and working through past test papers in a guided and structured way. Students are expected to spend further 5 hours weekly on directed reading and additional exercises (55 hours in total).
A booklet of lecture notes , exercises and answers for exercise questions will be put on the Web.
 

After successful completion of this module students should be able to,
1.  Understand the meaning of mathematical definitions of sets and perform set operations.
      [A2]
2.  Symbolise simple verbal arguments and test their validity by truth-tables. [A2]
3. Use truth-tables to test for tautologies, contradictions and for logical equivalence.
4. Work with simple predicate logic language and appreciate its uses. [A2]
5. Understand the meaning of mathematical definition of functions, to use it to construct
      functions and  to determine which functions are one-to-one. [A2]
6. Convert between different number systems, represent ones and tws complement and perform
      simple arithmetic in the binary system
 

There will be two elements of the assessment that reflect all the learning outcomes. One of them will be coursework, which consists of solutions of selected exercises together with notes on reading done outside the module sessions (L1-L6, A1). The other element is the exam, which will provide students with an opportunity to monitor their progress and to boost their confidence of success (L1-L6, A1 and A2).

In order to pass the module, a student must seriously attempt  both elements and achieve at least 40% of marks in aggregate.

Lecture Notes: “Computing Mathematics” on WebLearn. They are also available on the student’s drive.

J. Bush, Discrete Mathematics Workbook, Prentice Hall, 2003, ISBN 0-13-046327.
A. Chetwynd and P. Diggle, Discrete Mathematics, Arnold, 1994.
P. Grossman, Discrete Mathematics for Computing (2nd edition), Macmillan, 2002.
K. H. Rosen, Discrete Mathematics and Its Applications, McGraw Hill, 1994.
A. Simpson, Discrete Mathematics by Examples, McGraw Hill, 2002.
T. Feil and J. Krone, Essential Discrete Mathematics for Computer Science, Pearson Education,
2003.
R. Grimaldi, Discrete and Combinatorial Mathematics, Addison Wesley, 1994.
Crisler et al. Discrete Mathematics Through Applications, Freeman, 1994.
S. Epp, Discrete Mathematics with Applications, Thompson Learning, 1995.