CODE 
CPS2007 

TITLE 
Further Discrete Mathematics 

LEVEL 
02  Years 2, 3 in Modular Undergraduate Course 

ECTS CREDITS 
5 

DEPARTMENT 
Computer Science 

DESCRIPTION 
The studyunit is primarily aimed to introduce fundamental 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 studyunit, concentrating on syntax, and formal proofs. The studyunit builds upon the basic mathematical tools presented in CPS1001, and similarly explains various mathematical notions and structures that will be used in later studyunits.
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.
 Natural Numbers and cardinality, including reasoning about infinite sets  Further sequences, multisets, graph theory  Principles of Induction and structured types
Studyunit Aims The main aims of the studyunit are to continue to: 1. 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; 2. 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 have:
 an understanding of the mathematical process and familiarity with the tools of proof and reasoning which will be applied in other studyunits;  gained knowledge of various topics (logic, set theory, etc.) and fundamental results which are used in later on in the programme of study;  the tools to reason mathematically about programs and systems.
2. Skills: By the end of the studyunit the student will be able to:
 understand further the underlying notions underneath many computing concepts, such as programming, complex data structures and databases;  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. (The main text will be published in June 2012, and is thus not yet available at the University Library)
Supplementary reading:  Andrew Simpson, Discrete Mathematics by Example, McGrawHill, ISBN 0077098404, 2002.  John O'Donnell, Cordelia Hall, Rex Page, Discrete Mathematics Using a Computer, SpringerVerlag, 2006.


ADDITIONAL NOTES 
Students taking this studyunit are assumed to have knowledge of the material covered in CPS1002. 

STUDYUNIT TYPE 
Lecture, Independent Study & Practicum 

METHOD OF ASSESSMENT 
Assessment Component/s 
Resit Availability 
Weighting 
Examination (2 Hours)

Yes 
100% 


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.

18 October 2017
http://www.um.edu.mt/ict/studyunit