# Study-Unit Description

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CODE CPS1002

TITLE Mathematics of Discrete Structures

LEVEL 01 - Year 1 in Modular Undergraduate Course

ECTS CREDITS 5

DEPARTMENT Computer Science

DESCRIPTION The study-unit is primarily aimed to introduce the basic mathematical tools that are required for the formal and rigorous treatment of the various aspects of computing. The importance of formal reasoning is emphasised in the unit, concentrating on syntax, and formal proofs. The unit also explains various mathematical notions and structures that will be used in later study-units.

The study-unit introduces fundamental mathematical concepts - the use of axioms, rules of inference and syntactic definitions to express concepts in a precise mathematical notation, thus making them amenable to formal reasoning and proof.

Propositional Calculus: The use of truth tables, axiomatic and algebraic approaches, including the concept of soundness and completeness of formal models.

Predicate Calculus: Axiomatic approach to typed predicate calculus.

Typed Set Theory: A definitional approach based on predicate calculus allowing reasoning about sets.

Relations and Functions: Reasoning about relations and functions in terms of sets.

Basic notions of graphs and sequences.

Study-unit Aims:

The main aims of this unit are to:

- Provide the students with an understanding of mathematical tools pertaining to discrete structures which will be required to reason and understand scientific and engineering notions later on in the degree programme;
- Build and strengthen the students' skills in decomposing and tackling abstract problems - indirectly applicable to many computing domains, from programming, to information management.

Learning Outcomes:

1. Knowledge & Understanding:
By the end of the study-unit the student will be able to:

- Demonstrate an understanding of the mathematical process and familiarity with the tools of proof and reasoning which will be applied in other study-units;
- Demonstrate knowledge of various topics (logic, set theory, etc.) and fundamental results which are used later on in the programme of study.

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

- Comprehend the underlying notions underneath many computing concepts, such as programming and databases;
- Reason formally about such concepts.

Main Text/s

- Gordon J. Pace, Mathematics of Discrete Structures for Computer Science, Springer-Verlag. ISBN 978-3-642-29839-4, 2012

- Andrew Simpson, Discrete Mathematics by Example, McGraw-Hill, ISBN 0-07-709840-4, 2002
- John O'Donnell, Cordelia Hall, Rex Page, Discrete Mathematics Using a Computer, Springer-Verlag, 2006

STUDY-UNIT TYPE Lecture, Independent Study & Tutorial

METHOD OF ASSESSMENT
 Assessment Component/s Assessment Due Resit Availability Weighting Online Examination (2 Hours) SEM1 Yes 100%

LECTURER/S Christian Colombo
Neville Grech

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 2020/1. It may be subject to change in subsequent years.

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