SveučilištegugRijecig•gUniversitygofgRijeka
TrggbraćegMažuranićag10g•g51g000gRijekag•gCroatia
T:g(051)g406-500g•gF:g(051)g216-671;g216-091
W:gwww.uniri.hrgg•gE:
I.ggDESCRIPTIONgOFgSTUDYgPROGRAMMEgFORM
BASICgINFORMATION
Titlegofgstudygprogramme Discretegmathematicsgandgitsgapplications
studygprogrammegcoordinator UniversitygofgRijeka
Studygprogrammegimplementor Departmentgofgmathematicsg–gUniversitygofgRijeka
Typegofgstudygprogramme University
Levelgofgstudygprogramme Graduateggg
Academic/professionalgdegreegawarde MastergofgSciencegingMathematicsg-
dgupongcompletiongofgstudy gcourse:gdiscretegmathematicsgandgitsgapplications
1. INTRODUCTION
1.1.gReasonsgforginitiatinggthegstudy
Reasonsgforginitiatinggthegstudygare:geconomygneeds,gimprovementggofgscientificgresearchgatgthegUniversit
ygofgRijekag(bygintroducinggcontemporarygmethodsgofgplanninggandganalysisgofgexperiments),gshownginte
restgofgpotentialgstudentsgandgpersonnelgpotentialgofgthegDepartmentgofgmathematics.
Discretegmathematicsgisgagbranchgofgmathematicsgthatghasgmanygapplicationsgingothergfieldsgofgsciencega
ndgeconomy.gIngthisgstudygprogramgstudentsgwill,gamonggothergthings,gacquiregknowledgegfromggraphgth
eory,goptimization,gcryptography,gcodinggtheorygandgdesigngofgexperiments.g
BasedgongsurveysgofggstudentsgongundergraduategcoursegofgmathematicsgatgthegUniversitygofgRijeka,gwegr
ealizedgthatgtheregisggreatginterestgingthisggraduategprogram.gWegalsogbelievegthatgmentionedgstudygprog
ramgwillgattractgstudentsgwhoglivegoutsidegourgdistrict,gsincegitgwillgbegthegonlygstudygofgthisgdirectionging
thegRepublicgofgCroatia.
Departmentgofgmathematics,gUniversitygofgRijeka,ghasgpersonnelgcapabilitiesgforgperforminggthisgstudy,gs
incegthegscientificgworkgofgthirteengemployeesgofgthegDepartmentgisgcloselygassociatedgwithgthegfundamen
talgtopicsgthatgwillgbegprocessedgingthegframeworkgofgthisgstudy.
1.2.gEstimationgofgpurposegwithgrespectgtoglaborgmarketgneedsgingpublicgandgprivategsector
Acquiredgknowledgegingthisgstudygisgverygapplicablegingthegeconomy;ggraphgtheoryghasgbroadgapplicatio
ns,gfromgtelecommunicationsgtogthegdesigngofgroadgnetworks,gcodinggtheorygandgcryptographygisgusedging
everydaygcommunication.ggSincegtheregwillgbegmoregjobsgrelatedgtogICTgtechnologiesgandgdatagprotection
,gneedsgforgthisgprofilegwillgbeglarger.gOptimizationgisgverygpurposefulgingvariousgbusinessgprocesses,gwhil
egthegdesigngandganalysisgofgexperimentsgisgnecessarygingconductinggofganygexperiment,gfromgthegmanufa
ctoringgnewgdrugsgandgtestinggmachinesgandgtheirgparts.gAlso,gknowledgegofgdesigngofgexperimentsgisgals
ogverygapplicableginganalyzinggcharacteristicsgofgthegfinishedgproducts,gsogwegexpectgthatgtheglaborgmark
etgwillgidentifygandgshowgneedgforgthisgprofile.
ggggggggg1.2.1.gRelationshipgwithgthegLocalgCommunityg(economy,gbusiness,gcivilgsociety)
Acquiredgknowledgegingthisgstudygisgapplicablegingvariousgsectorsgofgthegeconomy.gBecausegofggacquiredg
knowledgegingcodinggtheory,gcryptography,ggraphgtheory,gandgsubjectsgingcomputergscience,ggraduatesgc
angbegemployedgingthegeconomicgsubjectsgdealinggwithgtelecommunicationsgandginformationgtechnology.g
Acquiredgknowledgegfromgthegoptimizationgandgdesigngofgexperimentsgprovidesgemploymentgingseveralgb
ranchesgofgeconomy,gforgexample,gingcompaniesgthatgneedgtogtestgfinishedgproductsgorgprototypes.
gggggggg1.2.2.gCompatibilitygwithgthegrequirementsgofgprofessionalgassociationsg(recommendation)
Whilegcreatinggagstudygprogram,gthegfollowinggresourcegwasgespeciallygconsidered:
TuninggEducationalgStructuresgingEurope
(http://tuning.unideusto.org/tuningeu/),ggespeciallygthegpartgthatgrefersgtogthegstudygofgmathematics.g(http
://tuning.unideusto.org/tuningeu/index.php?option=content&task=view&id=27&Itemid=50).
, SveučilištegugRijecig•gUniversitygofgRijeka
TrggbraćegMažuranićag10g•g51g000gRijekag•gCroatia
T:g(051)g406-500g•gF:g(051)g216-671;g216-091
W:gwww.uniri.hrgg•gE:
gggggggg1.2.3.gListgofgthegpossiblegpartnersgoutsidegtheghighergeducationgsystemgwhogexpressedginterestgforgstudyg
program
Forgnow,gtheggreatestginterestgingthisgstudygshowedgcompaniesgdealinggwithginformationgtechnology,gsinc
egthesegcompaniesgaregoftengemployinggformergstudentsgofgthegDepartmentgofgmathematics,gwhoggraduat
edgongourgeducationalgcourses:gMathematicsgandgMathematicsgandgComputergScience.
1.3.gComparabilitygofgstudygprogramgwithgsimilargprogramsgofgaccreditedginstitutionsgofghighergeducationgingC
roatiagandgthegEUg(specifygandgexplaingthegcomparabilitygofgthegtwogprograms,gofgwhichgatgleastgonegofgth
egEU,gwithgagprogramgthatgisgproposed,gandgstategnetworkgsites)
StudygprogramgofgDiscretegmathematicsgandgimplementationgisgcomparablegwithgthegstudygprogramgMat
hematicsg(MSci)gatgthegQueengMarygUniversitygofgLondon
(http://www.qmul.ac.uk/courses/courses.php?course_id=127&dept_id=16&ugcourses=1&course_level=2)
andgthegstudygprogramgatgthegUniversitygofgEssex,gmodulesgMScgDiscretegmathematicsgandgitsgapplicatio
nsgandgMScgStatisticsgandgComputergScience
g(http://www.essex.ac.uk/coursefinder/pdfs/pg/MATH.pdf).
ComparabilitygwithgthegstudygofgMathematicsg(MSCI)gatgthegQueengMarygUniversitygofgLondongisgreflec
tedgingthegsubjects:gcombinatoricsgandggraphgtheoryg(Combinatorics,gEnumerativegandgAsymptoticgCom
binatorics,gExtremalgCombinatorics,gAlgorithmicgGraphgTheory),gprobabilitygtheoryg(ProbabilitygI,gPro
babilitygII,gProbabilitygIIIg),gstatisticsg(IntroductiongtogStatistics,gStatisticalgModellinggI,gStatisticalgMode
llinggII,gAdvancedgStatisticalgModelling,gStatisticalgTheory,gComputationalgStatistics,gBayesiangStatistics)
,gcodinggtheorygandgcryptographyg(CodinggTheory,gCryptography),galgebragandggroupgtheoryg(Algebraic
gStructuresgI,gAlgebraicgStructuresgII,gFieldsgandgGaloisgTheory,gGroupgTheory)gandgdesigngofgexperime
ntsg(DesigngofgExperiments).gCoursesgofgLondon'sgstudiesgaregnumerousgbecausegitgisgfour-yeargstudy.
ComparabilitygwithgstudiesgatgthegUniversitygofgEssexgisgevidentgoverggthegsubjectsgofgGraphgTheory,gCr
yptographygandgCodes,gStochasticgProcessesgandgExperimentalgDesign,gwhichgaregpartgofgthegmodulegM
ScgDiscretegMathematicsgandgitsgApplicationsgandgMScgStatisticsgandgComputergScience.
Performersgofgmentionesgprogramsgemphasizegthatgfinishinggthisgstudygrepresentsgaggoodgbasisgforgthegp
ossiblegdevelopmentgofgscientificgcareergingthegfieldgofgnaturalgsciencesgandgengineering,gbutgalsogallowsge
mploymentgingvariousgareasgwheregisgrequiredgalgorithmicgwaygofgthinkinggandgthegabilitygtoganalysegda
ta.
1.4.gggOpennessgtogtheghorizontalgandgverticalgstudentgmobilitygingnationalgandginternationalghighergeducation
Thisggraduategprogramgcangenrollgbachelorsgwhoghavegcompletedgundergraduategcoursegingmathematicsg
inganygCroatiangorgforeignguniversity.gAftergfinishinggthisgstudy,gmastersgofgmathematicsgwillgbegablegtog
enrollgthegCommongdoctoralgprogramgingmathematicsgatgthegUniversitygJ.J.gStrossmayergingOsijek,gUniv
ersitygofgRijeka,gUniversitygofgSplitgandgthegUniversitygofgZagreb,gasgwellgasgappropriategdoctoralgstudie
sgabroad.
1.5.gCompatibilitygwithgmissiongandgstrategygofgthegUniversitygofgRijeka
AccordinggtogthegStrategyggofgUniversitygofgRijekaggforg2007-
2013,gguniversitygwillgdevotegspecialgattentiongtogthegdevelopmentgofgnaturalgscience.gSincegthisgisgthegfirs
tgnoneducationalggraduategcoursegingmathematicsgatgourguniversity,ggimplementationgofgthisgstudygcertai
nlygcontributesgingachievinggthegstrategicgaimgofgdevelopmentgofgthegnaturalgsciences.gWegalsogexpectgtha
tgthisgstudygwillgcontributegtogthegdevelopmentgofgothergnaturalgsciencesgatgthegUniversitygbygcreatinggpe
rsonnelgwhogcangapplygappropriategmathematicalgmethodsgforgimprovinggthegprocessgofgplanninggandgi
mplementinggexperiments.gOnegofgthegstrategicgaimsgofgthegUniversitygisgdevelopmentgofgresearchgingtheg
fieldgofginformationgandgcommunicationgtechnologies.gSincegcodinggtheorygandgcryptographygaregonegofg
thegmaingcontentgofgthisgprogram,ggstudygalsogcontributesgingachievingggoalgofgdevelopmentgofgICTgresea
rch.
ThegprogrammegisgalsogadjustedgwithgthegStrategygofgUniversitygofgRijekag2014.-2020.
• Increasegthegnumbergofgstudentsgingengineering,gbiomedicine,gbiotechnologygandgnaturalgsciences,
ginginformationgandgcommunicationgtechnologygandginginterdisciplinarygstudiesgrelatedgtogthesegfi
elds
Theregisgnotgmanygcandidatesgwithgthisgprofilegingtheglaborgmarket.gAccordinggtogthegStrategygofgUniver
, SveučilištegugRijecig•gUniversitygofgRijeka
TrggbraćegMažuranićag10g•g51g000gRijekag•gCroatia
T:g(051)g406-500g•gF:g(051)g216-671;g216-091
W:gwww.uniri.hrgg•gE:
sitygofgRijekag(2014.-
2020.),gstrategicggoalgofgUniversitygisgtogincreasegentrygquotasgandgthegnumbergofggraduatesgongstudygpro
grammesgrelatedgtognaturalgsciences.
• Achievegfavorablegratiogofgstudentsgperglecturer
Entrygquotagofg15genablesgagfavorablegratiogofgstudentsgperglecturergongthegDepartmentgstudies.
• Increasegeligibilitygingthegregimegofginternalgmobility
Thegprogrammegensuresgeligibilitygingthegregimegofginternalgmobilitygwithgtheglargegnumbergofgelectivegc
oursesgingthisgstudygprogrammegbeinggcompulsorygongothergstudygprogrammesg(studiesgongDepartmentg
ofgMathematics,gDepartmentgofgInformaticsgorgDepartmentgofgPhysics).
• Increasegthegportiongofge-learninggingstudygprogrammes
Almostgallgcoursesgusegadvancedgtoolsgforge-
learning,gwhichgcausesgqualitygchangesgingeducation.gForgthegmajoritygofgcourses,gtheregisgagversiongofgag
coursegongMudRi,ge-
learninggsystemgofgUniversitygofgRijeka,gatgthegsamegtimegkeepingghighgstandardsgofgeducationgquality,ge
speciallygcommunicationgbetweengprofessorsgandgstudents.gThegneededgICTginfrastructuregisgsecured,gie.
gcomputergandgsoftwaregsupportgforgeducationalgactivitiesgandge-learning.
• Ensuregregulargmonitoringgofgstudents'gsatisfaction
Studygprogrammegpredictsgefficientgadministrationgofgmeasuresgforgmonitoringgandgimprovementgofgstu
dents'gsuccessgwhichgisgconductedgbygthegdepartment'sgBoardgforgqualitygassurance.
• Determinegtheglistgofgpracticalgcompetenciesgwhichgaregguaranteedgaftergfinishinggthegstudiesgand
gadjustgthegstudygprogrammesgingtheg(re)accreditationalgprocedure.
1.6.gInstitutionalgdevelopmentgstrategygofgstudygprogramsg(compatibilitygwithgthegmissiongandgstrategicgaimsgof
gtheginstitution)
Thisgstudy,gasggfirstgnoneducationalgcoursegingmathematicsgatgthegUniversitygofgRijeka,gisgextremelygimp
ortantgforgimplementinggthegstrategygofgdevelopmentgprogramsgatgthegDepartmentgofgmathematics.gWega
lsogexpectgconnectinggwithgothergprogramsgofgcomponentsgofgthegUniversityg(mainlyguniversitygdepartme
nts)gthatgshouldgrecognizegthegprograms'gpotentialgingthegdevelopmentgofgcompetenciesgforgfuturegresear
chers.
Ongtheg65.gmeeting,gongOctoberg20th,g2014.,gThegCouncilgofgthegDepartmentgofgMathematicsghasgaccepte
dgthegStrategygofgUniversitygofgRijekag2014.-
2020.gasgagstrategicgdocumentgofgthegDepartmentgofgMathematics,gUniversitygofgRijeka,gandgdefinedgprio
ritizedgstrategicggoalsgofgthegDepartment.gSomegofgthegstrategicggoalsgrelatedgtogeducationgare:
• Increasegthegnumbergofgstudentsgwhogenrolledginggraduategstudies
• Increasegthegnumbergofgstudentsgwhoggraduated
• Determinegtheglistgofgpracticalgcompetenciesgwhichgaregguaranteedgaftergfinishinggthegstudiesgand
gadjustgthegstudygprogrammesgingtheg(re)accreditationalgprocedure
• Increasegthegportiongofge-learninggingstudygprogrammes
ThegimplementationgofgGraduateguniversitygstudiesgDiscretegMathematicsgandgApplicationsgisgingaccorda
ncegwithgthegafore-
mentionedgmissiongandgitgcontributesgtogrealisationgofgstrategicggoalsgofgDepartmentgofgMathematics,gUn
iversitygofgRijeka.
1.7. gOthergimportantginformationg-gingthegopiniongofgthegproposer
AlthoughgthegproposedgstudygisgfirstgnoneducationalggraduategcoursegstudygimplementedgbygthegDepart
mentgofgmathematics,gUniversitygofgRijeka,gandgdifferentgbygitsgcontentgandglearninggoutcomesgfromgexis
tinggcoursesgofgmathematicsgingRepublicgofgCroatia,gwegwantgtogemphasizegthatghegwillgnotgrepresentgagsi
gnificantgadditionalgburdengingtermsgofgteachergload.gIngfact,gsomegcompulsorygandgallgofgelectivegcourse
sgaregalreadygimplementedg(asgcompulsorygorgelective)gwithingthegframeworkgofgexistinggstudiesgperform
edgbygthegDepartmentgofgmathematics,gDepartmentgofgphysicsgandgDepartmentgofginformatics,gUniversit
ygofgRijekag(seegsectiong3.4).gAlso,g6gnewgcoursesg(36gECTS)gwillgbegofferedgasgangelectivegcoursesgtogstud
entsgofgexistinggprogramsgingthegDepartmentgofgmathematics,gasgwellgasgothergcomponentsgofgthegUnivers
itygofgRijeka.
, SveučilištegugRijecig•gUniversitygofgRijeka
TrggbraćegMažuranićag10g•g51g000gRijekag•gCroatia
T:g(051)g406-500g•gF:g(051)g216-671;g216-091
W:gwww.uniri.hrgg•gE:
2. GENERALgPART
2.1. Titlegofgstudygprogrammeg
Discretegmathematicsgandgitsgapplications
2.1.1. Typegofgstudygprogrammeg
Universityggg
2.1.2. Levelgofgstudygprogrammeg
gGraduate
2.1.3. Areagofgstudygprogrammeg(scientific/artistic)g–gindicategthegtitleg
Mathematics
2.2. Studygprogrammegcoordinator
UniversitygofgRijeka
2.3. Implementor/sgofgstudygprogrammeg
Departmentgofgmathematicsg–gUniversitygofgRijeka
2.4. Durationgofgstudygprogrammeg(indicateggpossibilitiesgofgpart-timegstudy,glonggdistancegstudy)g
Studyglastsg4gsemesters,gtheregisgnogpossibilitygofgattendinggclassesgingworkinggtime,gneithergthroughgdist
anceglearning.
2.4.1. ECTSgcreditsg–gminimalgnumbergofgcreditsgrequiredgforgcompletiongofgstudygprogrammeg
120gECTS
2.5. Enrolmentgrequirementsgandgselectiongprocedureg
Candidatesgwhogachievedgmathematicalgcompetenciesgdescribedgbygthegfollowingglearninggoutcomesgcang
enrollgthegstudygprogramme:
1. axiomaticallygandginductivelygconstructgthegfieldsgofgrealgandgcomplexgnumbers
2. describegangalgebraic,gmetricalgandgtopologicalgstructuregofgEuclideangspacegRn
3. determineglimitsgofgagfunction,gcontinuitygandguniformgcontinuity,gandgothergpropertiesgofgagfunc
tiongfromgRngtogRmg
4. analysegalgebraicgstructuresgandgdifferentiategbasicgpropertiesgofggroups,grings,gfieldsgandgvectorg
spaces
5. differentiategpropertiesgofgaglineargoperatorg
6. axiomaticallygconstructgEuclideanggeometrygwithgthegoverviewgofgitsghistoricalgdevelopmentg
7. formulategpropertiesgandgexistencegconditionsgofgregulargpolygonsgandgpolyhedra
8. formulategandganalyseggraphgproperties
9. formulategbasicgnotionsgofgdescriptivegstatistics
10. usegbasicgnotionsgrelatedgtogbinarygquadraticgforms
11. describegsetgoperationsgongfinitegandginfinitegsets
12. applygandgunderstandgpropertiesgofgrealgelementarygfunctionsgandgfundamentalgcomplexgfunctio
nsgofgagcomplexgvariableg
13. applygandgunderstandgusegofgdifferentialgcalculusginggeometrygandgingtheganalysisgofgpropertiesgo
fgfunctionsgthatgareggivengingangexplicit,gimplicitgandgparametricgform
TrggbraćegMažuranićag10g•g51g000gRijekag•gCroatia
T:g(051)g406-500g•gF:g(051)g216-671;g216-091
W:gwww.uniri.hrgg•gE:
I.ggDESCRIPTIONgOFgSTUDYgPROGRAMMEgFORM
BASICgINFORMATION
Titlegofgstudygprogramme Discretegmathematicsgandgitsgapplications
studygprogrammegcoordinator UniversitygofgRijeka
Studygprogrammegimplementor Departmentgofgmathematicsg–gUniversitygofgRijeka
Typegofgstudygprogramme University
Levelgofgstudygprogramme Graduateggg
Academic/professionalgdegreegawarde MastergofgSciencegingMathematicsg-
dgupongcompletiongofgstudy gcourse:gdiscretegmathematicsgandgitsgapplications
1. INTRODUCTION
1.1.gReasonsgforginitiatinggthegstudy
Reasonsgforginitiatinggthegstudygare:geconomygneeds,gimprovementggofgscientificgresearchgatgthegUniversit
ygofgRijekag(bygintroducinggcontemporarygmethodsgofgplanninggandganalysisgofgexperiments),gshownginte
restgofgpotentialgstudentsgandgpersonnelgpotentialgofgthegDepartmentgofgmathematics.
Discretegmathematicsgisgagbranchgofgmathematicsgthatghasgmanygapplicationsgingothergfieldsgofgsciencega
ndgeconomy.gIngthisgstudygprogramgstudentsgwill,gamonggothergthings,gacquiregknowledgegfromggraphgth
eory,goptimization,gcryptography,gcodinggtheorygandgdesigngofgexperiments.g
BasedgongsurveysgofggstudentsgongundergraduategcoursegofgmathematicsgatgthegUniversitygofgRijeka,gwegr
ealizedgthatgtheregisggreatginterestgingthisggraduategprogram.gWegalsogbelievegthatgmentionedgstudygprog
ramgwillgattractgstudentsgwhoglivegoutsidegourgdistrict,gsincegitgwillgbegthegonlygstudygofgthisgdirectionging
thegRepublicgofgCroatia.
Departmentgofgmathematics,gUniversitygofgRijeka,ghasgpersonnelgcapabilitiesgforgperforminggthisgstudy,gs
incegthegscientificgworkgofgthirteengemployeesgofgthegDepartmentgisgcloselygassociatedgwithgthegfundamen
talgtopicsgthatgwillgbegprocessedgingthegframeworkgofgthisgstudy.
1.2.gEstimationgofgpurposegwithgrespectgtoglaborgmarketgneedsgingpublicgandgprivategsector
Acquiredgknowledgegingthisgstudygisgverygapplicablegingthegeconomy;ggraphgtheoryghasgbroadgapplicatio
ns,gfromgtelecommunicationsgtogthegdesigngofgroadgnetworks,gcodinggtheorygandgcryptographygisgusedging
everydaygcommunication.ggSincegtheregwillgbegmoregjobsgrelatedgtogICTgtechnologiesgandgdatagprotection
,gneedsgforgthisgprofilegwillgbeglarger.gOptimizationgisgverygpurposefulgingvariousgbusinessgprocesses,gwhil
egthegdesigngandganalysisgofgexperimentsgisgnecessarygingconductinggofganygexperiment,gfromgthegmanufa
ctoringgnewgdrugsgandgtestinggmachinesgandgtheirgparts.gAlso,gknowledgegofgdesigngofgexperimentsgisgals
ogverygapplicableginganalyzinggcharacteristicsgofgthegfinishedgproducts,gsogwegexpectgthatgtheglaborgmark
etgwillgidentifygandgshowgneedgforgthisgprofile.
ggggggggg1.2.1.gRelationshipgwithgthegLocalgCommunityg(economy,gbusiness,gcivilgsociety)
Acquiredgknowledgegingthisgstudygisgapplicablegingvariousgsectorsgofgthegeconomy.gBecausegofggacquiredg
knowledgegingcodinggtheory,gcryptography,ggraphgtheory,gandgsubjectsgingcomputergscience,ggraduatesgc
angbegemployedgingthegeconomicgsubjectsgdealinggwithgtelecommunicationsgandginformationgtechnology.g
Acquiredgknowledgegfromgthegoptimizationgandgdesigngofgexperimentsgprovidesgemploymentgingseveralgb
ranchesgofgeconomy,gforgexample,gingcompaniesgthatgneedgtogtestgfinishedgproductsgorgprototypes.
gggggggg1.2.2.gCompatibilitygwithgthegrequirementsgofgprofessionalgassociationsg(recommendation)
Whilegcreatinggagstudygprogram,gthegfollowinggresourcegwasgespeciallygconsidered:
TuninggEducationalgStructuresgingEurope
(http://tuning.unideusto.org/tuningeu/),ggespeciallygthegpartgthatgrefersgtogthegstudygofgmathematics.g(http
://tuning.unideusto.org/tuningeu/index.php?option=content&task=view&id=27&Itemid=50).
, SveučilištegugRijecig•gUniversitygofgRijeka
TrggbraćegMažuranićag10g•g51g000gRijekag•gCroatia
T:g(051)g406-500g•gF:g(051)g216-671;g216-091
W:gwww.uniri.hrgg•gE:
gggggggg1.2.3.gListgofgthegpossiblegpartnersgoutsidegtheghighergeducationgsystemgwhogexpressedginterestgforgstudyg
program
Forgnow,gtheggreatestginterestgingthisgstudygshowedgcompaniesgdealinggwithginformationgtechnology,gsinc
egthesegcompaniesgaregoftengemployinggformergstudentsgofgthegDepartmentgofgmathematics,gwhoggraduat
edgongourgeducationalgcourses:gMathematicsgandgMathematicsgandgComputergScience.
1.3.gComparabilitygofgstudygprogramgwithgsimilargprogramsgofgaccreditedginstitutionsgofghighergeducationgingC
roatiagandgthegEUg(specifygandgexplaingthegcomparabilitygofgthegtwogprograms,gofgwhichgatgleastgonegofgth
egEU,gwithgagprogramgthatgisgproposed,gandgstategnetworkgsites)
StudygprogramgofgDiscretegmathematicsgandgimplementationgisgcomparablegwithgthegstudygprogramgMat
hematicsg(MSci)gatgthegQueengMarygUniversitygofgLondon
(http://www.qmul.ac.uk/courses/courses.php?course_id=127&dept_id=16&ugcourses=1&course_level=2)
andgthegstudygprogramgatgthegUniversitygofgEssex,gmodulesgMScgDiscretegmathematicsgandgitsgapplicatio
nsgandgMScgStatisticsgandgComputergScience
g(http://www.essex.ac.uk/coursefinder/pdfs/pg/MATH.pdf).
ComparabilitygwithgthegstudygofgMathematicsg(MSCI)gatgthegQueengMarygUniversitygofgLondongisgreflec
tedgingthegsubjects:gcombinatoricsgandggraphgtheoryg(Combinatorics,gEnumerativegandgAsymptoticgCom
binatorics,gExtremalgCombinatorics,gAlgorithmicgGraphgTheory),gprobabilitygtheoryg(ProbabilitygI,gPro
babilitygII,gProbabilitygIIIg),gstatisticsg(IntroductiongtogStatistics,gStatisticalgModellinggI,gStatisticalgMode
llinggII,gAdvancedgStatisticalgModelling,gStatisticalgTheory,gComputationalgStatistics,gBayesiangStatistics)
,gcodinggtheorygandgcryptographyg(CodinggTheory,gCryptography),galgebragandggroupgtheoryg(Algebraic
gStructuresgI,gAlgebraicgStructuresgII,gFieldsgandgGaloisgTheory,gGroupgTheory)gandgdesigngofgexperime
ntsg(DesigngofgExperiments).gCoursesgofgLondon'sgstudiesgaregnumerousgbecausegitgisgfour-yeargstudy.
ComparabilitygwithgstudiesgatgthegUniversitygofgEssexgisgevidentgoverggthegsubjectsgofgGraphgTheory,gCr
yptographygandgCodes,gStochasticgProcessesgandgExperimentalgDesign,gwhichgaregpartgofgthegmodulegM
ScgDiscretegMathematicsgandgitsgApplicationsgandgMScgStatisticsgandgComputergScience.
Performersgofgmentionesgprogramsgemphasizegthatgfinishinggthisgstudygrepresentsgaggoodgbasisgforgthegp
ossiblegdevelopmentgofgscientificgcareergingthegfieldgofgnaturalgsciencesgandgengineering,gbutgalsogallowsge
mploymentgingvariousgareasgwheregisgrequiredgalgorithmicgwaygofgthinkinggandgthegabilitygtoganalysegda
ta.
1.4.gggOpennessgtogtheghorizontalgandgverticalgstudentgmobilitygingnationalgandginternationalghighergeducation
Thisggraduategprogramgcangenrollgbachelorsgwhoghavegcompletedgundergraduategcoursegingmathematicsg
inganygCroatiangorgforeignguniversity.gAftergfinishinggthisgstudy,gmastersgofgmathematicsgwillgbegablegtog
enrollgthegCommongdoctoralgprogramgingmathematicsgatgthegUniversitygJ.J.gStrossmayergingOsijek,gUniv
ersitygofgRijeka,gUniversitygofgSplitgandgthegUniversitygofgZagreb,gasgwellgasgappropriategdoctoralgstudie
sgabroad.
1.5.gCompatibilitygwithgmissiongandgstrategygofgthegUniversitygofgRijeka
AccordinggtogthegStrategyggofgUniversitygofgRijekaggforg2007-
2013,gguniversitygwillgdevotegspecialgattentiongtogthegdevelopmentgofgnaturalgscience.gSincegthisgisgthegfirs
tgnoneducationalggraduategcoursegingmathematicsgatgourguniversity,ggimplementationgofgthisgstudygcertai
nlygcontributesgingachievinggthegstrategicgaimgofgdevelopmentgofgthegnaturalgsciences.gWegalsogexpectgtha
tgthisgstudygwillgcontributegtogthegdevelopmentgofgothergnaturalgsciencesgatgthegUniversitygbygcreatinggpe
rsonnelgwhogcangapplygappropriategmathematicalgmethodsgforgimprovinggthegprocessgofgplanninggandgi
mplementinggexperiments.gOnegofgthegstrategicgaimsgofgthegUniversitygisgdevelopmentgofgresearchgingtheg
fieldgofginformationgandgcommunicationgtechnologies.gSincegcodinggtheorygandgcryptographygaregonegofg
thegmaingcontentgofgthisgprogram,ggstudygalsogcontributesgingachievingggoalgofgdevelopmentgofgICTgresea
rch.
ThegprogrammegisgalsogadjustedgwithgthegStrategygofgUniversitygofgRijekag2014.-2020.
• Increasegthegnumbergofgstudentsgingengineering,gbiomedicine,gbiotechnologygandgnaturalgsciences,
ginginformationgandgcommunicationgtechnologygandginginterdisciplinarygstudiesgrelatedgtogthesegfi
elds
Theregisgnotgmanygcandidatesgwithgthisgprofilegingtheglaborgmarket.gAccordinggtogthegStrategygofgUniver
, SveučilištegugRijecig•gUniversitygofgRijeka
TrggbraćegMažuranićag10g•g51g000gRijekag•gCroatia
T:g(051)g406-500g•gF:g(051)g216-671;g216-091
W:gwww.uniri.hrgg•gE:
sitygofgRijekag(2014.-
2020.),gstrategicggoalgofgUniversitygisgtogincreasegentrygquotasgandgthegnumbergofggraduatesgongstudygpro
grammesgrelatedgtognaturalgsciences.
• Achievegfavorablegratiogofgstudentsgperglecturer
Entrygquotagofg15genablesgagfavorablegratiogofgstudentsgperglecturergongthegDepartmentgstudies.
• Increasegeligibilitygingthegregimegofginternalgmobility
Thegprogrammegensuresgeligibilitygingthegregimegofginternalgmobilitygwithgtheglargegnumbergofgelectivegc
oursesgingthisgstudygprogrammegbeinggcompulsorygongothergstudygprogrammesg(studiesgongDepartmentg
ofgMathematics,gDepartmentgofgInformaticsgorgDepartmentgofgPhysics).
• Increasegthegportiongofge-learninggingstudygprogrammes
Almostgallgcoursesgusegadvancedgtoolsgforge-
learning,gwhichgcausesgqualitygchangesgingeducation.gForgthegmajoritygofgcourses,gtheregisgagversiongofgag
coursegongMudRi,ge-
learninggsystemgofgUniversitygofgRijeka,gatgthegsamegtimegkeepingghighgstandardsgofgeducationgquality,ge
speciallygcommunicationgbetweengprofessorsgandgstudents.gThegneededgICTginfrastructuregisgsecured,gie.
gcomputergandgsoftwaregsupportgforgeducationalgactivitiesgandge-learning.
• Ensuregregulargmonitoringgofgstudents'gsatisfaction
Studygprogrammegpredictsgefficientgadministrationgofgmeasuresgforgmonitoringgandgimprovementgofgstu
dents'gsuccessgwhichgisgconductedgbygthegdepartment'sgBoardgforgqualitygassurance.
• Determinegtheglistgofgpracticalgcompetenciesgwhichgaregguaranteedgaftergfinishinggthegstudiesgand
gadjustgthegstudygprogrammesgingtheg(re)accreditationalgprocedure.
1.6.gInstitutionalgdevelopmentgstrategygofgstudygprogramsg(compatibilitygwithgthegmissiongandgstrategicgaimsgof
gtheginstitution)
Thisgstudy,gasggfirstgnoneducationalgcoursegingmathematicsgatgthegUniversitygofgRijeka,gisgextremelygimp
ortantgforgimplementinggthegstrategygofgdevelopmentgprogramsgatgthegDepartmentgofgmathematics.gWega
lsogexpectgconnectinggwithgothergprogramsgofgcomponentsgofgthegUniversityg(mainlyguniversitygdepartme
nts)gthatgshouldgrecognizegthegprograms'gpotentialgingthegdevelopmentgofgcompetenciesgforgfuturegresear
chers.
Ongtheg65.gmeeting,gongOctoberg20th,g2014.,gThegCouncilgofgthegDepartmentgofgMathematicsghasgaccepte
dgthegStrategygofgUniversitygofgRijekag2014.-
2020.gasgagstrategicgdocumentgofgthegDepartmentgofgMathematics,gUniversitygofgRijeka,gandgdefinedgprio
ritizedgstrategicggoalsgofgthegDepartment.gSomegofgthegstrategicggoalsgrelatedgtogeducationgare:
• Increasegthegnumbergofgstudentsgwhogenrolledginggraduategstudies
• Increasegthegnumbergofgstudentsgwhoggraduated
• Determinegtheglistgofgpracticalgcompetenciesgwhichgaregguaranteedgaftergfinishinggthegstudiesgand
gadjustgthegstudygprogrammesgingtheg(re)accreditationalgprocedure
• Increasegthegportiongofge-learninggingstudygprogrammes
ThegimplementationgofgGraduateguniversitygstudiesgDiscretegMathematicsgandgApplicationsgisgingaccorda
ncegwithgthegafore-
mentionedgmissiongandgitgcontributesgtogrealisationgofgstrategicggoalsgofgDepartmentgofgMathematics,gUn
iversitygofgRijeka.
1.7. gOthergimportantginformationg-gingthegopiniongofgthegproposer
AlthoughgthegproposedgstudygisgfirstgnoneducationalggraduategcoursegstudygimplementedgbygthegDepart
mentgofgmathematics,gUniversitygofgRijeka,gandgdifferentgbygitsgcontentgandglearninggoutcomesgfromgexis
tinggcoursesgofgmathematicsgingRepublicgofgCroatia,gwegwantgtogemphasizegthatghegwillgnotgrepresentgagsi
gnificantgadditionalgburdengingtermsgofgteachergload.gIngfact,gsomegcompulsorygandgallgofgelectivegcourse
sgaregalreadygimplementedg(asgcompulsorygorgelective)gwithingthegframeworkgofgexistinggstudiesgperform
edgbygthegDepartmentgofgmathematics,gDepartmentgofgphysicsgandgDepartmentgofginformatics,gUniversit
ygofgRijekag(seegsectiong3.4).gAlso,g6gnewgcoursesg(36gECTS)gwillgbegofferedgasgangelectivegcoursesgtogstud
entsgofgexistinggprogramsgingthegDepartmentgofgmathematics,gasgwellgasgothergcomponentsgofgthegUnivers
itygofgRijeka.
, SveučilištegugRijecig•gUniversitygofgRijeka
TrggbraćegMažuranićag10g•g51g000gRijekag•gCroatia
T:g(051)g406-500g•gF:g(051)g216-671;g216-091
W:gwww.uniri.hrgg•gE:
2. GENERALgPART
2.1. Titlegofgstudygprogrammeg
Discretegmathematicsgandgitsgapplications
2.1.1. Typegofgstudygprogrammeg
Universityggg
2.1.2. Levelgofgstudygprogrammeg
gGraduate
2.1.3. Areagofgstudygprogrammeg(scientific/artistic)g–gindicategthegtitleg
Mathematics
2.2. Studygprogrammegcoordinator
UniversitygofgRijeka
2.3. Implementor/sgofgstudygprogrammeg
Departmentgofgmathematicsg–gUniversitygofgRijeka
2.4. Durationgofgstudygprogrammeg(indicateggpossibilitiesgofgpart-timegstudy,glonggdistancegstudy)g
Studyglastsg4gsemesters,gtheregisgnogpossibilitygofgattendinggclassesgingworkinggtime,gneithergthroughgdist
anceglearning.
2.4.1. ECTSgcreditsg–gminimalgnumbergofgcreditsgrequiredgforgcompletiongofgstudygprogrammeg
120gECTS
2.5. Enrolmentgrequirementsgandgselectiongprocedureg
Candidatesgwhogachievedgmathematicalgcompetenciesgdescribedgbygthegfollowingglearninggoutcomesgcang
enrollgthegstudygprogramme:
1. axiomaticallygandginductivelygconstructgthegfieldsgofgrealgandgcomplexgnumbers
2. describegangalgebraic,gmetricalgandgtopologicalgstructuregofgEuclideangspacegRn
3. determineglimitsgofgagfunction,gcontinuitygandguniformgcontinuity,gandgothergpropertiesgofgagfunc
tiongfromgRngtogRmg
4. analysegalgebraicgstructuresgandgdifferentiategbasicgpropertiesgofggroups,grings,gfieldsgandgvectorg
spaces
5. differentiategpropertiesgofgaglineargoperatorg
6. axiomaticallygconstructgEuclideanggeometrygwithgthegoverviewgofgitsghistoricalgdevelopmentg
7. formulategpropertiesgandgexistencegconditionsgofgregulargpolygonsgandgpolyhedra
8. formulategandganalyseggraphgproperties
9. formulategbasicgnotionsgofgdescriptivegstatistics
10. usegbasicgnotionsgrelatedgtogbinarygquadraticgforms
11. describegsetgoperationsgongfinitegandginfinitegsets
12. applygandgunderstandgpropertiesgofgrealgelementarygfunctionsgandgfundamentalgcomplexgfunctio
nsgofgagcomplexgvariableg
13. applygandgunderstandgusegofgdifferentialgcalculusginggeometrygandgingtheganalysisgofgpropertiesgo
fgfunctionsgthatgareggivengingangexplicit,gimplicitgandgparametricgform
