Ewch i’r prif gynnwys

Mathemateg, Ymchwil Weithredol ac Ystadegaeth (MMORS)

Blwyddyn Mynediad


Mae'r cynnwys hwn ar gael yn Saesneg yn unig.

Mae hwn yn gyfuniad o Ystadegau ac Ymchwil Weithrediadol yn ogystal ag astudiaeth gyffredinol o Fathemateg mewn cwrs sydd wedi’i deilwra’n ofalus i anghenion y rhai sydd am gadw eu dewisiadau’n agored ac sy’n chwilio am gyfleoedd gyrfa ardderchog.

Cadwch le ar ddiwrnod agored

Trosolwg y cwrs

Gain a deeper understanding of Operational Research and Statistics on the four-year MMORS degree. The course expands on the BSc to prepare you for high-level entry into relevant professions. It’s also a solid base for pursuing a research career.

The MMORS course is the same as the three-year BSc in Mathematics, Operational Research and Statistics with an additional year of study where you will complete a major piece of project work. This could include:

  • a survey of an existing area of mathematical theory not covered in taught modules;
  • an introductory research project;
  • the development of a piece of mathematical software.

Not only will you explore a research topic of your choice, but you will also develop the crucial project and time management skills that graduate employers are looking for. Plus, you will gain the necessary skills, methods and ways of thinking required to analyse and tackle complex organisational problems and become a confident statistical analyst.

 

Nodweddion nodedig

Gwybodaeth arbenigol - Ochr yn ochr â dysgu technegau mathemategol uwch, byddwch chi’n cael yr wybodaeth arbenigol a’r sgiliau i ddelio gyda phroblemau data mawr, a yrrir gan ddata a gwneud penderfyniadau mewn sectorau megis busnes, gofal iechyd a chyllid;

Blwyddyn yn gweithio ar brosiect – Byddwch chi’n cwblhau prosiect mathemategol sylweddol ar lefel uwch yn ystod y bedwaredd flwyddyn.  Bydd hyn yn eich helpu i ddatblygu’r sgiliau rheoli prosiect y mae cyflogwyr graddedigion yn chwilio amdanynt;

Boddhad Myfyrwyr - Cawsom y nifer uchaf o bleidleisiau gan holl Brifysgolion Grŵp Russell yn y prif gategori o Fodlonrwydd Cyffredinol yn Arolwg Myfyrwyr Cenedlaethol 2018;

Cymorth i fyfyrwyr - Yn ogystal â chael eich tiwtor personol eich hun ar ddechrau'r flwyddyn gyntaf, byddwch hefyd yn cael mynediad i diwtorialau wythnosol, labordai cyfrifiadurol dan oruchwyliaeth a sesiynau galw heibio ar gyfer cefnogaeth un-i-un bob dydd.

Achrediadau

Côd UCAS252D
Derbyniad nesafMedi 2020
Hyd4 blwyddyn
Modd (astudio)Amser llawn

Gofynion mynediad

AAA - AAB including A in Maths.   

Cymhwyster Prosiect Estynedig: Fel arfer, bydd ymgeiswyr sydd wedi ennill gradd A yn y Cymhwyster Prosiect Estynedig (EPQ) yn cael cynnig un radd yn is na’r cynnig safonol ar gyfer Safon Uwch. Noder bod yn rhaid bodloni unrhyw ofynion sy’n benodol i’r pwnc o hyd

Derbynnir Tystysgrif Her Sgiliau Bagloriaeth Cymru Uwch yn lle un pwnc Safon Uwch (ar y graddau a restrir uchod) ac eithrio unrhyw bynciau penodol.

DD in any BTEC plus A in Maths at A-level.     

36 points including a minimum grade 6 in HL Mathematics or 666 in 3 HL's including Maths

Gallai cymwysterau amgen gael eu derbyn. Cewch ragor o wybodaeth am ofynion mynediad ar dudalen meini prawf derbyn Ysgol Mathemateg.

IELTS (academic)

O leiaf 6.5 yn gyffredinol gydag o leiaf 5.5 ym mhob is-sgôr.

TOEFL iBT

O leiaf 90 gyda sgôr o 17 o leiaf ar gyfer ysgrifennu, 17 ar gyfer gwrando, 18 ar gyfer darllen ac 20 ar gyfer siarad.

PTE Academic

62 gydag o leiaf 51 yn yr holl sgiliau cyfathrebu.

Trinity ISE II/III

II: dau Ragoriaeth a dau Deilyngdod o leiaf.
III: o leiaf Llwyddo ym mhob cydran.

Cymwysterau eraill a dderbynnir

Os ydych yn ymgeisydd tramor ac nid Saesneg yw eich iaith gyntaf, ewch i'n tudalen am ofynion Iaith Saesneg i gael rhagor o wybodaeth am ba gymwysterau y byddwn yn eu derbyn.

You will require GCSE English Language at grade C or grade 4. 

Dewis

There will be no interviews. Selection is based entirely on A level (or equivalent) performance. Contextual applicants will be guaranteed an offer and will be subject to additional consideration. All applicants will be invited to attend an Open day when they will visit the School of Mathematics. Offers will be made to all applicants who have the potential to satisfy the offer.

Ffioedd dysgu

Myfyrwyr y DU ac UE (2020/21)

Ewch i'n tudalen cyfanswm ffioedd am y wybodaeth ddiweddaraf.

Myfyrwyr tu allan i'r UE (2020/21)

Ewch i'n tudalen cyfanswm ffioedd am y wybodaeth ddiweddaraf.

Costau ychwanegol

There are no additional costs associated with the standard MMORS degree scheme.

Cyfarpar ar gyfer cwrs penodol

What the student should provide:

Calculator that satisfies Cardiff University examination regulations. Students may wish to purchase textbooks but copies are available through the university libraries.

What the University will provide:

Laboratories, computer labs and appropriate software.

Llety

Mae gennym amrywiaeth o breswylfeydd sydd yn gweddu i anghenion a phoced yr unigolyn. Cewch wybod rhagor ar ein tudalennau llety.

Strwythur y cwrs

This is a four year, full-time course. In each year of the programme, you will take modules to the value of 120 credits. In the first year there are compulsory modules in Pure Mathematics, Statistics and Computing in addition to a range of optional modules.

The core modules in Year 2 continue to build your foundational understanding of Mathematics and Statistics, and the subject of Operational Research is introduced.

Year 3 includes a large number of optional modules allowing students to focus on the areas of Pure Mathematics, Operational Research and Statistics that they particularly enjoy. 

Year 4 includes a core 40 credit research dissertation in a topic of your choice, supervised by a leading expert. Research training is enhanced and there are a number of advanced optional modules.

The classification of your degree is based on the grades you achieve in the Modules that you take in years two, three and four.

Mae'r modiwlau a ddangosir yn esiampl o'r cwricwlwm arferol. Byddant yn cael eu hadolygu cyn blwyddyn academaidd 2020/21. Bydd y modiwlau terfynol yn cael eu cyhoeddi erbyn mis Medi 2020

Blwyddyn un

You will take 120 credits in Mathematics. Most modules are compulsory but there is an element of choice allowing you to select between modules in Mechanics and Finance. The modules in Mathematics cover the foundational areas of Calculus, Algebra, Analysis, Computing and Statistics.

Note that the first year is common across all the degree schemes in the School of Mathematics so students can transfer to other degrees in Mathematics at the end of Year One.

Teitl modiwlCôd modiwlCredydau
Elementary Differential EquationsMA100110 credydau
GeometryMA100410 credydau
Foundations of Mathematics IMA100520 credydau
Foundations of Mathematics IIMA100620 credydau
Linear Algebra IMA100810 credydau
Introduction to Probability TheoryMA150010 credydau
Statistical InferenceMA150110 credydau
Computing for MathematicsMA170110 credydau
Fundamental skills for University and BeyondMA190010 credydau

Blwyddyn dau

In year two you will take 120 credits in Mathematics. 80 credits are core and the remaining 40 credits are chosen from a number of optional modules in Pure and Applied Mathematics, as well as additional Statistics and Operational Modules.

The results of Year 2 make up 20% of your final degree classification.

You are required to achieve at least a 55% average and pass at least 100 credits to continue your studies onto Year Three of the scheme. Students who fail to achieve the 55% average will be transferred onto the BSc version of the scheme.

At the end of your second year you have the opportunity to transfer to the three year BSc Mathematics,

Operational Research and Statistics degree scheme. You may also transfer to BSc Mathematics if you have selected the appropriate optional Year Two modules.

Teitl modiwlCôd modiwlCredydau
Operational ResearchMA026120 credydau
Complex AnalysisMA200310 credydau
Series and TransformsMA200410 credydau
Real AnalysisMA200610 credydau
Linear Algebra IIMA200820 credydau
Multivariable and Vector CalculusMA201020 credydau
Foundations of Probability and StatisticsMA250020 credydau
Teitl modiwlCôd modiwlCredydau
Modelling with Differential EquationsMA023210 credydau
Introduction to Number Theory IMA201110 credydau
Programming and StatisticsMA250110 credydau
Finance II: Investment ManagementMA280010 credydau
Problem SolvingMA290010 credydau

Blwyddyn tri

The modules in Year Three are closely aligned to the research interests of the School. 120 credits of Optional Modules are chosen. There are a broad range of optional modules, enabling you to focus on areas of particular interest. At least 50% of your Year Three modules should be in the areas of Operational Research or Statistics. There are no core modules in Year Three.

The results of Year Three make up 30% of your final degree classification.

At the end of your third year you have the option to graduate with a BSc degree.

Teitl modiwlCôd modiwlCredydau
Regression Analysis and Experimental DesignMA350220 credydau
OptimisationMA360320 credydau

Blwyddyn pedwar

In Year Four, the course develops research training and enhanced mathematical skills. There is also a major piece of project work, in which you will apply the knowledge and skills learnt in the first four years of the degree to tackle some practical or theoretical problems. This gives you the opportunity to develop presentation and communication skills, in addition to applying your mathematical skills to a research topic of your choice.

Training for the dissertation will be provided at the beginning of Year Four with a number of additional lectures covering research and communication skills.

There are a range of optional modules available in Pure Mathematics, Statistics and Operational Research.

The results of Year Four make up 50% of your final degree classification.

Teitl modiwlCôd modiwlCredydau
MMath ProjectMA490040 credydau
Teitl modiwlCôd modiwlCredydau
Measure TheoryMA400720 credydau
Combinatorial and Analytic Number TheoryMA401120 credydau
Advanced Topics in Analysis: Sobolev Spaces and Viscosity SolutionsMA401520 credydau
Statistics of Big DataMA451120 credydau
Credit Risk ScoringMA451210 credydau
Advanced Use of Statistical PackagesMA451310 credydau
Convex OptimisationMA460020 credydau
Stochastic Search and OptimisationMA460120 credydau
Supply Chain ModellingMA460610 credydau
Healthcare ModellingMA460910 credydau
Reading ModuleMA490120 credydau
Reading ModuleMA490220 credydau
Mae'r Brifysgol wedi ymrwymo i ddarparu amrywiaeth eang o opsiynau modiwl lle’n bosibl. Ond byddwch yn ymwybodol er y byddwn yn gwneud pob ymdrech i gynnig dewis, gall hyn gael ei gyfyngu mewn rhai amgylchiadau. Y rheswm am hyn yw'r ffaith mai dim ond nifer cyfyngedig o leoedd sydd ar gael ar rai modiwlau, a gaiff eu dyrannu ar sail y cyntaf i'r felin. Mae'n ofynnol i fodiwlau eraill sicrhau isafswm nifer o fyfyrwyr cyn gallu eu cynnal, er mwyn gwneud yn siŵr y gellir cyflwyno addysg o ansawdd priodol. Gall modiwlau gael eu cyfyngu oherwydd gwrthdaro yn yr amserlen hefyd, ac er bod y Brifysgol yn ymdrechu i amharu cyn lleied â phosibl ar eich dewis, byddai'n syniad da i chi ofyn am gyngor gan yr Ysgol berthnasol am y dewisiadau modiwl sydd ar gael.

Dysgu ac asesu

Sut caf fy addysgu?

Core knowledge is taught through a mixture of lectures, exercise classes, small-group tutorials and guided study. Mathematics is a hierarchical discipline so the structure of the course is systematic, building on fundamental understanding.

The first two years are focussed on providing a foundational understanding. The following two years cover a range of contemporary subject material, reflecting research interests in the School. Throughout the delivery of the programme, wherever possible, recent research results are used to illustrate and illuminate the subject.

In year one, there are regular small-group tutorial sessions in mathematics modules. Exercises are an integral part of all lecture-based modules, these allow you to apply your knowledge and improve your problem-solving skills. Extra exercise or examples classes are currently held in all mathematics modules. In these a lecturer will discuss additional problems with you, give general oral feedback and provide model solutions for further reflection.

In year four, more student participation is expected as some lectures take the form of seminars.

Sut y caf fy nghefnogi?

At the start of each year a guide to module aims, learning outcomes, methods of assessment, module syllabuses, and reading lists will be made available to you. You will also be allocated a personal tutor in the School of Mathematics. This will be a member of academic staff who can give pastoral support and academic advice as well as helping you with module selection and career planning. Regular meetings with your Personal Tutor will be scheduled to give you the opportunity to discuss your individual progress and develop generic skills such as team work and presentation skills.

All lecturing staff can be contacted by email and have either an ‘open door’ policy for students with specific queries about course material, or a system to book meeting times. The Director of Learning and Teaching of the School of Mathematics can advise you on academic issues, and each year of study has a year co-ordinator who can offer advice on administrative issues. The School also has an Education and Students Manager who can assist with administrative queries. The Undergraduate Office in Mathematics, is a further source of information.

Further learning support is also available via the University-wide Maths Support Service. This provides relaxed and informal drop-in sessions where you are encouraged to discuss any elements of your studies with a tutor in a one-to-one or small group basis.

You will have access through the Learning Central website to relevant multimedia material, presentations, lecture handouts, bibliographies, further links, electronic exercises and discussion circles. Opportunities for you to reflect on your abilities and performance are available through the Learning Central ‘Personal Development Planning’ module.

Before commencing your dissertation, additional lectures will provide preparation covering research and communication skills. Core computing modules in Years One and Two will provide the foundation for any computing work required for the dissertation. The additional lectures will cover practical issues such as working with a supervisor, format and structure of a dissertation, referencing and how to produce academic writing. They will also cover the skills required to independently perform mathematical research.

The University offers a range of services including the Careers Service, the Counselling Service, the Disability and Dyslexia Service, the Student Support Service, and excellent libraries and resource centres. The School of Mathematics has a designated Disability and Diversity Officer and ensures that reasonable adjustments are made for students with disabilities.

An extensive programme of careers lectures and workshops is delivered within the School of Mathematics and an in-house Careers Consultant is available.

Sut caf fy asesu?

Most modules have closed book written examinations at the end of the autumn or spring semesters, with some also having an element of continuous assessment. This may include problem-solving exercises, written reports, computer programs and oral presentations. Feedback on progress is typically provided through a combination of discussion in class, written comments on submitted work and review of outline solutions to problems. You are encouraged to discuss any queries related to specific modules with individual lecturers. All students can review their examination scripts and discuss their performance with the corresponding module lecturer.

Your major research project in year four is assessed through a written report (85% of the mark) and an oral examination (15% of the mark).

The pass mark for each module is 40%. Students can progress to resit as long as they have failed no more than 60 credits. They can progress to the following year as long as they have failed no more than 20 credits.

The grade of your final degree is currently based on 20% from your Year Two studies, 30% from Year Three and 50% from Year Four.  An average of at least 55% in Year Two is required to continue on this programme. Students failing to achieve this average will be transferred to the three year BSc in Mathematics, Operational Research and Statistics degree scheme.

Feedback:

Written feedback and outline solutions on in-course assessment give you an opportunity to reflect on your progress. Further feedback is provided in examples classes and tutorials (in year one) to review problems in more detail and discuss potential solutions. You should discuss any queries related to specific modules with individual lecturers.

The majority of coursework in the School of Mathematics is formative, meaning that the mark given does not form part of your overall mark for the module. This is to encourage students to learn the intrinsic value of completing the work for the educational benefit rather than just to gain a given mark. This ensures that students will carefully consider their feedback and use it to improve and develop their understanding of the material.

In Year One, you are required to regularly submit work to ensure your understanding of the course material is progressing. Detailed formative feedback is provided to help you identify your strengths and weaknesses and areas that need further work. It also enables staff to identify means of supporting you. This continues in later years of the course, though the frequency of submitted work will vary from module to module.

Pa sgiliau bydda i’n eu hymarfer a’u datblygu?

Studying this course will enable you to acquire and develop a range of valuable skills, both discipline specific and more generic ‘employability skills’. You will:

  • Demonstrate the effective self-management and organisational skills needed to undertake a substantial project in an area of mathematics of your choice
  • Enhance your IT, information retrieval and handling skills
  • Develop your ability to apply logical and analytic thinking to problems in other disciplines
  • Demonstrate commitment to lifelong learning through engaging in a process of personal development planning
  • Develop the skills of objectivity, creativity and independent thinking
  • Develop your knowledge of core Mathematics concepts such as calculus and analysis, proof, algebra and modelling.
  • Increase your understanding of the principles and techniques of proof
  • Develop skills that will enable you to sustain a critical argument and to communicate ideas and theories in writing and through oral presentation
  • Learn how to solve well-defined, open-ended problems and identify key issues
  • Conduct independent research using source materials such as textbooks, scientific journals and electronic databases
  • Use precise calculations in appropriate situations
  • Develop your ability to undertake independent learning and effectively manage your time

Beth yw deilliannau dysgu’r cwrs/rhaglen?

The Learning outcomes for this Programme describe what you will be able to do as a result of your study at Cardiff University. They will help you to understand what is expected of you and academic staff will focus on precisely what they want you to achieve within each Module. 

Knowledge & Understanding:

Students completing the Programme will demonstrate:

  • An ability to analyse and interpret data and to apply modern statistical methods
  • An ability to use the latest operational research techniques to solve real life problems
  • An understanding of the underlying principles and mathematical theories underpinning modern statistics and operational research
  • An understanding of the ideas of proof, calculus, algebra, analysis and applied mathematics

Intellectual Skills:

Students completing the Programme will demonstrate:

  • The ability to formulate and solve mathematical models
  • The skills of using analytical and logical thinking to draw conclusions based on quantitative information.
  • Communication skills and the ability to communicate mathematical knowledge and understanding
  • Plan and conduct a piece of novel research

Professional Practical Skills:

Students completing the Programme will be able to:

  • Use a number of modern software packages
  • Assimilate and communicate detailed mathematical arguments

Transferable/Key Skills:

Students completing the Programme will demonstrate:

  • Logical reasoning
  • Independent thinking
  • Critical thinking
  • The ability to apply mathematical skills to solve problems
  • Use of information technology and library resources
  • Time and workload management
  • The ability to conduct independent research

Gyrfaoedd a lleoliadau gwaith

Rhagolygon gyrfa

Mae graddedigion y cwrs MMORS yn aml yn symud ymlaen i wneud PhD ac uwch-astudiaethau eraill. Yn 2017-18, dywedodd 89% o raddedigion yr Ysgol a oedd ar gael i weithio eu bod mewn cyflogaeth a/neu astudiaethau pellach ymhen chwe mis ar ôl graddio. Mae rhai o’n cynfyfyrwyr bellach yn gweithio yn y Swyddfa Ystadegau Gwladol (ONS) a’r Swyddfa Feteorolegol.

Cefnogaeth Gyrfaoedd Mathemateg

Yn semestr gwanwyn eich blwyddyn gyntaf, bydd amrywiaeth o ddosbarthiadau meistr ar gael i chi i helpu i gefnogi eich rhagolygon gyrfa i’r dyfodol.  Mae’r dosbarthiadau’n ymdrin â phrofiad gwaith, CV a llythyrau esboniadol, ffurflenni cais, technegau cyfweliad, a chyflwyniad i LinkedIn.

Mae gennym ni fwrdd swyddi myfyrwyr sy’n cael ei ddiweddaru’n rheolaidd, gydag amrywiaeth o gyfleoedd i raddedigion, gwirfoddoli, interniaethau a lleoliadau. Ar ben hynny, rydym ni’n trefnu rhaglen lawn o gyflwyniadau gan fyfyrwyr a chyflogwyr bob blwyddyn gyda chyflogwyr fel Grŵp Bancio Lloyds, HSBC, PwC, Sefydliad a Chyfadran yr Actiwarïaid, Sainsburys, Network Rail, GSK, y Swyddfa Ystadegau Gwladol (ONS), Llywodraeth Cymru, y Weinyddiaeth Amddiffyn, Dŵr Cymru, a’r Swyddfa Feteorolegol.

Lleoliadau

There is the option of transferring to our Year of Study Abroad degree scheme, which would involve an additional fifth year spent at a university abroad.

Astudio yn Gymraeg

Mae hyd at 36% o'r cwrs hwn ar gael drwy gyfrwng y Gymraeg. Cysylltwch â'r Tiwtor Derbyn am wybodaeth bellach.

Nid oes data Unistats ar gael ar gyfer y cwrs hwn eto.

Nid oes data Unistats ar gael ar gyfer y cwrs hwn eto.

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