# Study-Unit Description

﻿
CODE MAT1804

TITLE Mathematics for Computing

UM LEVEL 01 - Year 1 in Modular Undergraduate Course

MQF LEVEL 5

ECTS CREDITS 5

DEPARTMENT Mathematics

DESCRIPTION - Sets, union and intersection, complements, de Morgan's laws, power sets, relations, equivalence relations, partitions, order relations, properties of reflexivity, symmetry, transitivity;
- Functions as mappings, injectivity, surjectivity, bijectivity, inverse, composition, recurrence; operators (unary, binary, etc) and their properties – associativity, commutativity, and distributivity;
- Graphs, trees, paths, cycles, connectivity, adjacency matrix, spanning trees; directed graphs, acyclic directed graphs, strong components;
- Matrices, matrices as linear transformations, bases, determinants, inverses, Gaussian elimination, eigenvalues and eigenvectors.

Study-Unit Aims:

The aim of this study-unit is to introduce the students to basic notions of sets and functions, as well as graphs and matrices. Students will be introduced to techniques for working with matrices, and will be given ample opportunity to practice these skills. This study-unit lays the mathematical foundation for the rest of the undergraduate Software Development programme.

Learning Outcomes:

1. Knowledge & Understanding:

By the end of the study-unit the student will be able to:

- Describe the basic properties of sets and functions, including functions whose domain and co-domain are different sets, e.g., Strings and Boolean;
- Work with examples of functions, operators and relations on numbers, strings, sets, trees, etc;
- Work with matrices, determinants and vectors to solve problems in computing;
- Apply transformations to points and coordinate systems;
- Find the inverse of a matrix by Gaussian elimination;
- Determine the eigenvalues and eigenvectors of a given matrix.

2. Skills:

By the end of the study-unit the student will be able to:

- Formulate solutions to problems by using appropriate mathematical techniques;
- Evaluate the applicability of different theorems and results to computing problems;
- Address computing problems by applying appropriate mathematical tools.

Main Text/s and any supplementary readings:

- Mathematics for Computer Science, by Eric Lehman, F Thomson Leighton, Albert R Meyer, ISBN 978-9888407064
- Essential Discrete Mathematics for Computer Science, by Harry Lewis, Rachel Zax, ISBN 978-0691179292
- Concrete Mathematics: A Foundation for Computer Science (2nd Edition), by Ronald Graham, Donald Knuth, Oren Patashnik, ISBN 978-0201558029.

ADDITIONAL NOTES Pre-Requisite qualifications: MATSEC Intermediate Level Pure Mathematics

STUDY-UNIT TYPE Lecture and Independent Study

METHOD OF ASSESSMENT
 Assessment Component/s Assessment Due Sept. Asst Session Weighting Assignment SEM1 Yes 15% Examination (2 Hours) SEM1 Yes 85%

LECTURER/S Luke Collins

The University makes every effort to ensure that the published Courses Plans, Programmes of Study and Study-Unit information are complete and up-to-date at the time of publication. The University reserves the right to make changes in case errors are detected after publication.
The availability of optional units may be subject to timetabling constraints.
Units not attracting a sufficient number of registrations may be withdrawn without notice.
It should be noted that all the information in the description above applies to study-units available during the academic year 2024/5. It may be subject to change in subsequent years.

https://www.um.edu.mt/course/studyunit