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Study-Unit Description
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CODE CPS1001

 
TITLE Mathematics of Discrete Structures

 
LEVEL 01 - Year 1 in Modular Undergraduate Course

 
ECTS CREDITS 10

 
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 course, concentrating on syntax, and formal proofs. The unit also explains various mathematical notions and structures that will be used in later courses.

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.
- 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

Study-unit Aims

The main aims of the study-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:

- 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 study-unit 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, Springer-Verlag. ISBN 978-3-642-29839-4, 2012.

Supplementary reading:

- Andrew Simpson, Discrete Mathematics by Example, McGraw-Hill, ISBN0-07-709840-4, 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 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 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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