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Study-Unit Description
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CODE CPS2007

 
TITLE Further Discrete Mathematics

 
LEVEL 02 - Years 2, 3 in Modular Undergraduate Course

 
ECTS CREDITS 5

 
DEPARTMENT Computer Science

 
DESCRIPTION The study-unit 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 study-unit, concentrating on syntax, and formal proofs. The study-unit builds upon the basic mathematical tools presented in CPS1001, and similarly 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.

- Natural Numbers and cardinality, including reasoning about infinite sets
- Further sequences, multisets, graph theory
- Principles of Induction and structured types

Study-unit Aims

The main aims of the study-unit 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 study-unit 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 study-units;
- 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 study-unit 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,
- Springer-Verlag. ISBN 978-3-642-29839-4, 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, McGraw-Hill, ISBN 0-07-709840-4, 2002.
- John O'Donnell, Cordelia Hall, Rex Page, Discrete Mathematics Using a Computer, Springer-Verlag, 2006.

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

 
STUDY-UNIT 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 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 study-unit description above applies to the academic year 2017/8, if study-unit is available during this academic year, and may be subject to change in subsequent years.
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