CODE 
CPS1001 

TITLE 
Mathematics of Discrete Structures 

LEVEL 
01  Year 1 in Modular Undergraduate Course 

ECTS CREDITS 
10 

DEPARTMENT 
Computer Science 

DESCRIPTION 
The studyunit 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 course, concentrating on syntax, and formal proofs. The unit also explains various mathematical notions and structures that will be used in later courses.
The studyunit 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.  Natural Numbers and cardinality, including reasoning about infinite sets  Sequences, multisets, graph theory: These concepts are formalised in terms of the notions formalised earlier in the course
Studyunit Aims
The main aims of the studyunit 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 studyunit the student will be able to:
 Prove results and reason formally about mathematical and computer science related domains.  Demonstrate results about various computer science notions which will be required for advanced courses.
2. Skills: By the end of the studyunit the student will be able to:
1. Understand the underlying notions underneath many computing concepts, such as programming and databases. 2. Reason formally about such concepts.
Main Text/s and any supplementary readings
Main Text:
 Gordon J. Pace, Mathematics of Discrete Structures for Computer Science, SpringerVerlag. ISBN 9783642298394, 2012.
Supplementary reading:
 Andrew Simpson, Discrete Mathematics by Example, McGrawHill, ISBN0077098404, 2002.  John O'Donnell, Cordelia Hall, Rex Page, Discrete Mathematics Using a Computer, SpringerVerlag, 2006.


STUDYUNIT TYPE 
Lecture, Independent Study & Tutorial 

METHOD OF ASSESSMENT 
Assessment Component/s 
Resit Availability 
Weighting 
Examination
(1 Hour and 30 Minutes)

Yes 
30% 
Examination
(2 Hours and 30 Minutes)

Yes 
70% 


LECTURER/S 
Gordon J. Pace


The University makes every effort to ensure that the published Courses Plans, Programmes of Study and StudyUnit information are complete and uptodate 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 studyunit description above applies to the academic year 2017/8, if studyunit is available during this academic year, and may be subject to change in subsequent years.

9 November 2017
https://www.um.edu.mt/ict/studyunit