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Honours BSc in Applied MathematicsHonneurs BSc in Toegepaste Wiskunde

Students who enrol for the Honours Programme in Applied Mathematics must complete a 32-credit research project, as well as six 16-credit semester modules that may be chosen freely from the list of modules below. Students may take up to a maximum of two of these six modules at other divisions or departments (see for example the postgraduate modules offered by Computer Science and Mathematics). Studente wat vir die Honneursprogram in Toegepaste Wiskunde inskryf moet 'n 32-krediet navorsingsprojek voltooi, asook ses 16-krediet semestermodules wat vryelik uit die lys van modules hieronder gekies kan word. Studente mag tot 'n maksimum van twee van hierdie ses modules by ander afdelings of departemente neem (sien bv. Rekenaarwetenskap en Wiskunde se nagraadse modules).

Contact the postgraduate coordinator of Applied Mathematics, Dr Willie Brink (), for further information. Kontak Toegepaste Wiskunde se nagraadse koördineerder, Dr Willie Brink (), vir verdere inligting.

Year moduleJaarmodule

10557-772 Research Project in Applied MathematicsNavorsingsprojek in Toegepaste Wiskunde Coordinatorkoördineerder: Dr Roux

Honours students choose a topic at the start of the year and work independently, under the guidance of his/her project advisor, on the chosen problem. A report is submitted at the end of the year, and a short oral presentation is given. The module also involves students learning generic research skills. Honneursstudente kies aan die begin van die jaar 'n onderwerp en werk selfstandig, onder leiding van sy/haar projekadviseur, aan die gekose probleem. Aan die einde van die jaar word 'n verslag ingehandig en 'n kort mondelinge voordrag gelewer. Die module behels ook dat studente generiese navorsingsvaardighede aanleer.

First semester modulesEerste semester modules

36323-776 Numerical methodsNumeriese Metodes  (1st semester) Dr Hale, Prof. Weideman

Focus on numerical methods for matrix computations. Effective solution of square linear systems, least squares problems, the eigenvalue problem. Direct and iterative methods, special attention to sparse matrices and structured matrices. Numerical instability and ill-conditioning. Model problems from partial differential equations and image processing. Fokus op numeriese metodes vir matriksbewerkings. Effektiewe oplos van vierkantige lineêre stelsels, kleinste-kwadrate probleme, die eiewaarde probleem. Direkte en iteratiewe metodes, klem op yl matrikse en matrikse met struktuur. Numeriese onstabiliteit en sleg-geaardheid. Modelprobleme uit parsiële differensiaalvergelykings en beeldverwerking.

62820-775 Numerical Simulation of FluidsNumeriese Vloeisimulasie  (1st semester) Prof. Smit

General numerical methods for solving flow equations; finite difference/volume methods; procedures for the simulation of diffusive and convective processes; boundary values; solving algorithms such as the SIMPLE range; introduction to CFX. Algemene numeriese metodes vir die oplos van vloeivergelykings; eindige-verskil/volume metodes; prosedures vir simulasie van diffusiewe en konvektiewe prosesse; randwaardes; algoritmes soos die SIMPLE-reeks; inleiding tot CFX.

10643-774 Partial Differential EquationsParsiële Differensiaalvergelykings  (1st semester) Dr Cloete

Derivation of simple partial differential equations (PDEs) from first principles, Fourier analysis, separation of variables and transform techniques for linear second-order PDEs, characteristics, Lagrange's method for first-order PDEs, finite differences.
* Students who took Applied Mathematics 364 are not allowed to take this module.
Herleiding van eenvoudige parsiële differensiaalvergelykings (PDVs) uit eerste beginsels, Fourier analise, skeiding van veranderlikes en transform-tegnieke vir lineêre tweede-orde PDVs, karakteristieke, Lagrange se metode vir eerste-orde PDVs, eindige verskille.
* Studente wat Toegepaste Wiskunde 364 geneem het, word nie toegelaat om hierdie module te neem nie.

62839-791 Porous mediaPoreuse Media (1st semester) Dr Diedericks

Differential and integral calculus of volume averages in two phase media and its use in the mathematical modelling of transport processes in porous media; the rectangular unit cell model. Differensiaal- en integraalrekening van volumegemiddeldes in twee-fasige media; die modellering van vloeiprossesse in poreuse media; die reghoekige eenheidselmodel.

62855-796 Statistical Pattern RecognitionStatistiese Patroonherkenning  (1st semester) Prof. Herbst

Parametric and non-parametric estimation of probability density functions, Bayesian classification techniques, hidden Markov models, linear and non-linear discriminant analysis, Kalman filters, particle filters.
* This module is also offered on 3rd-year level, for Computer Science students (CS315).
Parametriese en nie-parametriese afskatting van waarskynlikheidsdigtheidsfunksies, Bayesiese klassifikasie-tegnieke, verskuilde Markov-modelle, lineêre en nie-lineêre diskriminant-analise, Kalman-filters, partikelfilters.
* Hierdie module word ook op 3dejaarsvlak aangebied, vir Rekenaarwetenskapstudente (RW315).

Second semester modulesTweede semester modules

62847-792 Computer VisionRekenaarvisie  (2nd semester) Dr Brink

Image interpolation; feature detection and matching; the SVD with application in face recognition; projective geometry; homogeneous coordinates; intersection of parallel lines and the line at infinity; homographies; removing perspective distortion; model estimation with RANSAC; camera models; epipolar geometry; the fundamental matrix; image rectification; the essential matrix; 3D reconstruction.
* This module is also offered on 3rd-year level, for Computer Science students (CS364).
Beeldinterpolasie; kenmerkdeteksie en -passing; die SVD met toepassing in gesigsherkenning; projeksie-meetkunde; homogene koördinate; snyding van parallelle lyne en die lyn by oneindig; homografieë; verwydering van perspeksie-distorsie; modelafskatting met RANSAC; kamera modelle; epipolêre meetkunde; die fundamentele matriks; beeldregstelling; die essensiële matriks; 3D rekonstruksie.
* Hierdie module word ook op 3dejaarsvlak aangebied, vir Rekenaarwetenskapstudente (RW364).

64572-793 Digital Image ProcessingDigitale Beeldverwerking  (2nd semester) Dr Coetzer

Basic grey-scale transformations and image enhancement techniques in the spatial domain; Fourier analysis in two dimensions and image enhancement techniques in the Fourier domain; image restoration; morphological filters; image compression techniques; image segmentation, representation, description and recognition. Basiese grysskaal-transformasies en beeldverbeteringstegnieke in die fisiese ruimte; Fourier-analise in twee dimensies en beeldverbeteringstegnieke in die Fourier-ruimte; die herstel van beelde; morfologiese filters; tegnieke vir beeldkompaktering; beeldsegmentasie, -voorstelling, -beskrywing en herkenning.

10542-782 Graph theoryGrafiekteorie  (2nd semester) Dr Grobler

Broad introduction to graph theory. Problems such as enumeration of graphs; optimal paths in networks; optimal spanning trees; centres and medians; planarity; vertex and edge colouring; Eulerian graphs and Hamiltonicity; tournaments; domination and independence; and Ramsey theory. Breë inleiding tot grafiekteorie. Probleme soos enumerasie van grafieke; optimale paaie in netwerke; optimale spanbome; senters en mediane; planariteit; punt- en lynkleuring; Euler-grafieke en Hamilton-grafieke; toernooie; dominasie en onafhanklikheid; en Ramsey-teorie.

10728-794 Tensor AnalysisTensoranalise (2nd semester) Dr Fidder-Woudberg

Development of a physical understanding of the mathematical concepts associated with general and Cartesian tensor analysis; introductory differential geometry; curvilinear coordinate systems; coordinate transformations; development of a sound foundation for advanced mathematical modelling in scientific and engineering research environments. Ontwikkeling van 'n fisiese begrip van die wiskundige konsepte van algemene en Cartesiese tensoranalise; inleidende differensiaalmeetkunde; kromlynige koodinaatstelsels; assetransformasies; vorming van 'n stewige grondslag vir gevorderde wiskundige modellering in wetenskaplike- en ingenieursomgewings.

MSc in Applied MathematicsToegepaste Wiskunde

Students who enrol for the Masters Programme in Applied Mathematics must complete a thesis on the topic of their choice (within the expertise of one of the division's lecturers). The thesis is presented during an oral examination and internal as well as external examiners are appointed to assist in the examination of the thesis. The programme normally spans two academic years of full-time study.

Contact the postgraduate coordinator of Applied Mathematics, Dr Willie Brink (), for further information.
Studente wat vir die Magisterprogram in Toegepaste Wiskunde ingeskryf is moet 'n tesis oor die onderwerp van hul keuse (binne die navorsingsveld van een van die afdeling se dosente) voltooi. Die tesis word tydens 'n mondelinge eksamen voorgelê en interne sowel as eksterne eksaminatore word aangestel vir die eksaminering van die tesis. Die program strek normaalweg oor twee akademiese jare van voltydse studie.

Kontak Toegepaste Wiskunde se nagraadse koördineerder, Dr Willie Brink (), vir verdere inligting.

PhD in Applied MathematicsToegepaste Wiskunde

Students who enrol for the Doctoral Programme in Applied Mathematics must complete a dissertation on the topic of their choice (within the expertise of one of the division's lecturers). Results of the dissertation must be original and must contribute to the relevant field. The dissertation is defended during a public oral examination. Internal as well as external examiners are appointed to assist in the examination of the dissertation. The programme normally spans three academic years of full-time study.

Contact the postgraduate coordinator of Applied Mathematics, Dr Willie Brink (), for further information.
Studente wat vir die Doktorale Program in Toegepaste Wiskunde ingeskryf is, moet 'n proefskrif oor die onderwerp van hul keuse (binne die navorsingsveld van een van die afdeling se dosente) voltooi. Resultate van die proefskrif moet oorspronklik wees en 'n bydra maak tot die betrokke veld. Die proefskrif word tydens 'n openbare mondelinge eksamen verdedig. Interne sowel as eksterne eksaminatore word aangestel om die proefskrif te eksamineer. Die program strek normaalweg oor drie akademiese jare van voltydse studie.

Kontak Toegepaste Wiskunde se nagraadse koördineerder, Dr Willie Brink (), vir verdere inligting.