Computer Science

ECM1415 - Discrete Mathematics for Computer Science (2019)

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MODULE TITLEDiscrete Mathematics for Computer Science CREDIT VALUE15
MODULE CODEECM1415 MODULE CONVENERDr Leon Danon (Coordinator)
DURATION: TERM 1 2 3
DURATION: WEEKS 11 0 0
Number of Students Taking Module (anticipated) 63
DESCRIPTION - summary of the module content

Discrete mathematics is concerned with quantities which vary discretely, and because of that has an important role in Computer Science, in which discrete structures such as sets, graphs, lists, and trees play a fundamental role, and the underlying forms of reasoning are based on propositional and predicate logic rather than on calculus and mathematical analysis, with an emphasis on counting rather than measuring, e.g. enumerating permutations and combinations of objects satisfying specified conditions. This module will provide a thorough grounding in the fundamental structures and methods of discrete mathematics that are required for computer science.

AIMS - intentions of the module

The aim of this module is to provide you with the basic concepts and tools developed in discrete mathematics disciplines but needed for the study of computer science. As such, it forms an essential part of a rounded education of a computer scientist or computer expert whose work includes computer-based data manipulations.

INTENDED LEARNING OUTCOMES (ILOs) (see assessment section below for how ILOs will be assessed)

On successful completion of this module, you should be able to:
 

Module Specific Skills and Knowledge:
1 demonstrate a sound understanding of selected essential topics in discrete mathematics and their importance in computer science disciplines.
Discipline Specific Skills and Knowledge:
2 reveal sufficient knowledge of fundamental discrete mathematics concepts.
Personal and Key Transferable / Employment Skills and Knowledge:
3 show independent learning skills;
4 reason using abstract ideas, formulate and solve problems and communicate reasoning and solutions effectively in writing;
5 use learning resources appropriately.

 

SYLLABUS PLAN - summary of the structure and academic content of the module

number systems: natural numbers, integers, rationals, reals, complex numbers;

number representation: positional notation (decimal, binary, hexadecimal), twos complement, fixed-point, floating point;

computer arithmetic: addition and subtraction, multiplication and division

set theory and standard notation: Intersection, union, complement, power set, Cartesian product;

functions and relations;

methods of proof;

propositional and first-order logic;

sums of standard finite and infinite series;

counting principles: the addition principle, the multiplication principle, permutations, combinations; some counting problems;

graph theory: basic concepts, definitions and results. Trees, balanced trees.

LEARNING AND TEACHING
LEARNING ACTIVITIES AND TEACHING METHODS (given in hours of study time)
Scheduled Learning & Teaching Activities 32.00 Guided Independent Study 118.00 Placement / Study Abroad 0.00
DETAILS OF LEARNING ACTIVITIES AND TEACHING METHODS
Category Hours of study time Description
Scheduled learning and teaching 22 Lectures
Scheduled learning and teaching 10 Problem classes
Guided independent study 20 Coursework
Guided independent study 98 Independent study

 

ASSESSMENT
FORMATIVE ASSESSMENT - for feedback and development purposes; does not count towards module grade
Form of Assessment Size of Assessment (e.g. duration/length) ILOs Assessed Feedback Method
Problem sets   All Verbal and written
       
       
       
       

 

SUMMATIVE ASSESSMENT (% of credit)
Coursework 20 Written Exams 80 Practical Exams 0
DETAILS OF SUMMATIVE ASSESSMENT
Form of Assessment % of Credit Size of Assessment (e.g. duration/length) ILOs Assessed Feedback Method
Written exam – Closed  book 80% 2 hours - January Exam  All Model answers supplied on request
Coursework 20% 20 hours All Written feedback
         
         
         

 

DETAILS OF RE-ASSESSMENT (where required by referral or deferral)
Original Form of Assessment Form of Re-assessment ILOs Re-assessed Time Scale for Re-assessment
All above Written exam (100%) All August Ref/Def period
       
       

 

RE-ASSESSMENT NOTES

Referred and deferred assessment will normally be by examination. For referrals, only the examination will count, a mark of 40% being awarded if the examination is passed. For deferrals, candidates will be awarded the higher of the deferred examination mark or the deferred examination mark combined with the original coursework mark.

RESOURCES
INDICATIVE LEARNING RESOURCES - The following list is offered as an indication of the type & level of
information that you are expected to consult. Further guidance will be provided by the Module Convener

Reading list for this module:

Type Author Title Edition Publisher Year ISBN Search
Set McColl, J Probability Arnold 1995 0000340614269 [Library]
Set McGregor C., Nimmo J. & Stothers W. Fundamentals of University Mathematics 2nd Horwood, Chichester 2000 000-1-898-56310-1 [Library]
Set Biggs N.L. Discrete Mathematics Oxford University Press 1989 000-0-198-53427-2 [Library]
Extended James, G Modern Engineering Mathematics 4th with MyMathLab Addison Wesley 2010 027373413x [Library]
CREDIT VALUE 15 ECTS VALUE 7.5
PRE-REQUISITE MODULES None
CO-REQUISITE MODULES None
NQF LEVEL (FHEQ) L4 AVAILABLE AS DISTANCE LEARNING No
ORIGIN DATE Tuesday 10 July 2018 LAST REVISION DATE Tuesday 10 July 2018
KEY WORDS SEARCH Discrete mathematics; computer science; set theory; functions and relations; graph theory.