Yearbooks

Programme: MSc Applied Mathematics

Code Faculty Duration Credits Download
02250171 Faculty of Natural and Agricultural Sciences Duration of study: 1 year Total credits: 180

Programme information

The programme compilation consists of two master’s coursework modules of 30 credits each (the choice of modules to be decided by the Head of Department in consultation with the postgraduate coordinator) as well as a dissertation (120 credits).

Full details of the compilation of the curriculum are available in the departmental postgraduate brochure at: http://www.up.ac.za/maths/postgrad

The MSc degree is conferred on the grounds of a dissertation and such additional postgraduate coursework as may be prescribed.

Renewal of registration
As long as progress is satisfactory, renewal of the registration of a master’s student will be accepted for the second year of the study. Registration for a third and subsequent years will only take place when the Student Administration of the Faculty receives a written motivation that is supported by the head of department and Postgraduate Studies Committee.

General
Candidates are required to familiarise themselves with the General Regulations regarding the maximum period of registration and the requirements on the submission of a draft article for publication.

Admission requirements

An appropriate BScHons degree with a minimum of 60% for all modules at honours level. In the selection procedure the candidate’s complete undergraduate and honours academic record will be considered. In particular it is strongly recommended that the following modules be included on honours level: Measure and integration theory Functional analysis Partial differential equations and Numerical analysis.

Admission is also subject to the availability of a suitable supervisor for the study.

 

Promotion to next study year

The progress of all master's candidates is monitored biannually by the supervisor and the postgraduate coordinator. A candidate's study may be terminated if the progress is unsatisfactory or if the candidate is unable to finish his/her studies during the prescribed period.

Subject to exceptions approved by the dean, on recommendation of the head of department, and where applicable, a student may not enter for the master's examination in the same module more than twice.

Pass with distinction

The MSc degree is conferred with distinction to candidates who obtain a final average mark of at least 75% and a mark of at least 75% for the dissertation/mini-dissertation from each of the members of the examination panel. Where a member of the examination panel awards a mark of less than 75% for the dissertation/mini-dissertation, that member of the examination panel must offer, in writing, support for his/her decision, or indicate in writing that he/she supports the examination committee's decision to confer the degree with distinction.

Minimum credits: 180

Core modules

Elective modules

  • Module content:

    *Consult with the Head of Department of Mathematics and Applied Mathematics about the availability of this master’s course in a particular year.
    Mathematics about the availability of this masters module in a particular year.The module focuses on the Hilbertion Sobolev spaces as well as to their applications to elliptic boundary value problems. Topics to be discussed include: Distributions; Sobolev spaces of positive and negative integer orders; Sobolev spaces of traces; Embeddings of Sobolev spaces; Boundary value problems.

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  • Module content:

    *Consult with the Head of the Department of Mathematics and Applied Mathematics about the availability of this master’s module in a particular year.
    Capita selecta from the following: Duality theory. Weak and Weak* topologies. The Krein- Milman theorem. The Stone-Weierstrass theorem. Fixed point theorems. Banach Algebras and the Gelfand transform. C*-algebras and their representations. Semigroups of operators. Functional analysis applied to probability theory and stochastics.

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  • Module content:

    Consult with the Head of the Department of Mathematics and Applied Mathematics about the availability of this master's module in a particular year.
    Lebesgue integral in a general measure space: Basic properties, convergence theorems, convergence in measure. Lebesgue spaces: Completeness, approximation by continuous functions. Complex measures: Absolute continuity, Random-Nikodym Theorem, representation of bounded linear functionals on Lebesgue spaces, Riesz Representation Theorem for bounded linear functionals on the space of continuous functions on a locally convergent Hausdorff space where X is a locally compact Hausdorff space.  Applications to probability.

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  • Module content:

    *Consult with the Head of the Department of Mathematics and Applied Mathematics about the availability of this master’s module in a particular year.
    Finite dimensional dynamical systems: Autonomous and non-autonomous systems of differential equations, dynamical systems, linear and nonlinear systems, existence and uniqueness of solutions, extension of solutions, maximal solution and maximal interval of existence, phase space and phase portrait. Stability theory for equilibria and periodic orbits using linear approximation, Liapunov's method and other energy methods and discrete dynamical systems (Poincarè map). Introduction to strange attractors. Application to mechanics and population models. Infinite dimensional dynamical systems: Semigroups, first and second order abstract differential equations, Sobolev spaces, finite dimensional approximation. Application to heat conduction and mechanical vibration. Examples of nonlinear systems.

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  • Module content:

    Content will vary from time to time depending on the availability of expertise in the Department.

    View more

  • Module content:

    *Consult with the Head of the Department of Mathematics and Applied Mathematics about the availability of this master's module in a particular year.
    Finite element interpolation theory.  Finite element approximation of elliptic boundary value problems and eigenvalue problems.  Finite element approximation of parabolic and hyperbolic initial value problems.  Applications in a project.

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Minimum credits: 180

Core modules

Elective modules

  • Module content:

    *Consult with the Head of Department of Mathematics and Applied Mathematics about the availability of this master’s course in a particular year.
    Mathematics about the availability of this masters module in a particular year.The module focuses on the Hilbertion Sobolev spaces as well as to their applications to elliptic boundary value problems. Topics to be discussed include: Distributions; Sobolev spaces of positive and negative integer orders; Sobolev spaces of traces; Embeddings of Sobolev spaces; Boundary value problems.

    View more

  • Module content:

    *Consult with the Head of the Department of Mathematics and Applied Mathematics about the availability of this master’s module in a particular year.
    Capita selecta from the following: Duality theory. Weak and Weak* topologies. The Krein- Milman theorem. The Stone-Weierstrass theorem. Fixed point theorems. Banach Algebras and the Gelfand transform. C*-algebras and their representations. Semigroups of operators. Functional analysis applied to probability theory and stochastics.

    View more

  • Module content:

    Consult with the Head of the Department of Mathematics and Applied Mathematics about the availability of this master's module in a particular year.
    Lebesgue integral in a general measure space: Basic properties, convergence theorems, convergence in measure. Lebesgue spaces: Completeness, approximation by continuous functions. Complex measures: Absolute continuity, Random-Nikodym Theorem, representation of bounded linear functionals on Lebesgue spaces, Riesz Representation Theorem for bounded linear functionals on the space of continuous functions on a locally convergent Hausdorff space where X is a locally compact Hausdorff space.  Applications to probability.

    View more

  • Module content:

    *Consult with the Head of the Department of Mathematics and Applied Mathematics about the availability of this master’s module in a particular year.
    Finite dimensional dynamical systems: Autonomous and non-autonomous systems of differential equations, dynamical systems, linear and nonlinear systems, existence and uniqueness of solutions, extension of solutions, maximal solution and maximal interval of existence, phase space and phase portrait. Stability theory for equilibria and periodic orbits using linear approximation, Liapunov's method and other energy methods and discrete dynamical systems (Poincarè map). Introduction to strange attractors. Application to mechanics and population models. Infinite dimensional dynamical systems: Semigroups, first and second order abstract differential equations, Sobolev spaces, finite dimensional approximation. Application to heat conduction and mechanical vibration. Examples of nonlinear systems.

    View more

  • Module content:

    Content will vary from time to time depending on the availability of expertise in the Department.

    View more

  • Module content:

    *Consult with the Head of the Department of Mathematics and Applied Mathematics about the availability of this master's module in a particular year.
    Finite element interpolation theory.  Finite element approximation of elliptic boundary value problems and eigenvalue problems.  Finite element approximation of parabolic and hyperbolic initial value problems.  Applications in a project.

    View more


The information published here is subject to change and may be amended after the publication of this information. The General Regulations (G Regulations) apply to all faculties of the University of Pretoria. It is expected of each student to familiarise himself or herself well with these regulations as well as with the information contained in the General Rules section. Ignorance concerning these regulations and rules will not be accepted as an excuse for any transgression.

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