Faculty of Natural and Honours programme 2015 BSc · PDF fileHonours project topics: ... mathematical physics 776 15 2 ... the final year should include at least four of the following

http://www.up.ac.za/maths/postgrad

Department of Mathematics and Applied Mathematics

Honours programme 2015

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Faculty of Natural andAgricultural Sciences

Honours programme 2015

Study programmes

BSc Honours in Mathematics

BSc Honours in Applied Mathematics

Stream 1: Applied analysis

Stream 2: Differential equations and modelling

BSc Honours in Mathematics of Finance

BSc Honours in Financial Engineering

Application: Online on the UP student portal or go to the CSC (Client

Service Centre) in person.

Web address: http://www.up.ac.za/maths/postgrad

click on “Postgraduate matters” and choose “Postgraduate Study

Programmes”. Go to “Honours” at point 2.

Syllabi, course prerequisites, etc: Refer to the Postgraduate

Regulations and Syllabi of the Faculty of Natural and Agricultural

Sciences (available on UP web under Faculty, go to quick link

“Yearbooks”).

Honours project topics:

Go to “Postgraduate matters” on the departmental homepage.

Duration of study: The minimum duration is one year of full-time study

or two years of part-time study. A student must complete his or her

study for an honours degree, in the case of full-time students, within

two years from the first examination to the final examination and in the

case of part-time students, within three years from the first examination

to the final examination. Under special circumstances, the Dean, on

the recommendation of the head of department, may give approval

for a limited extension of this period.

Note: There are no supplementary examinations in honours modules.

Lecture times: Normally presented at 17:30 or 17:00.

BSc Honours in Mathematics

Admission requirements

An appropriate BSc degree with a minimum of 60% for each

Mathematics/Applied Mathematics module on third-year level.

In the selection procedure the candidate’s complete undergraduate

academic record will be considered. In particular, it is required that the

candidate has completed the following modules each with a mark of

at least 60%: real analysis on third-year level and algebra on third-year

level. (UP modules WTW 310 and WTW 381)

Programme composition

The programme compilation consists of seven honours modules of

15 credits each (five compulsory and two elective) as well as the

mandatory project (30 credits).

Code Module Credits Semester

Core modules:

WTW 710 Functional analysis 710 15 1

WTW 724Axiomatic set theory and mathematical logic 724

15 1

WTW 731 Algebra 731 15 1

WTW 734Measure theory and probability 734

15 1

WTW 790 Topology 790 15 2

Research:

WTW 795 Project 795 30 year

Elective modules:

WTW 727 Special topics 727 15 2

WTW 733 Numerical analysis 733 15 1

WTW 763 Finite element method 763 15 2

WTW 764 Stochastic calculus 764 15 2

WTW 772Mathematical methods and models 772

15 1

WTW 776Partial differential equations of mathematical physics 776

15 2

A total of at least 135 credits is required

BSc Honours in Applied Mathematics Stream 1: Applied analysis


A BSc degree in Mathematics, Applied Mathematics or equivalent

Bachelor’s degree with at least a 60% average in the third-year level

Mathematics/Applied Mathematics subjects.


academic record will be considered. In particular, it is required that

the final year should include at least four of the following third-year

level modules or equivalent: partial differential equations, dynamical

systems (ordinary differential equations), real analysis, complex analysis,

numerical analysis or continuum mechanics. (UP modules WTW 386,

WTW 382, WTW 310, WTW 320, WTW 383 or WTW 387)


The programme compilation consists of seven honours modules of 15

credits each as well as the mandatory project (30 credits). It is required

that students select the stream and the modules according to the

prerequisites of the modules.

Stream 1: Applied analysis


Research:


Core modules:


WTW 734 Measure theory and probability 734 15 1

WTW 776Partial differential equations of mathematical physics 776

15 2

Elective modules:

Four (4) electives from below. The selection must contain at least one of WTW 787 or WTW 764 and at least one of WTW 733 or WTW 763.


WTW 750 Mathematical optimisation 750 15 1



WTW 772 Mathematical methods & models 772 15 1

WTW 787 Continuum mechanics 787 15 2


BSc Honours in Applied Mathematics Stream 2: Differential equations and modelling


A BSc degree in Mathematics, Applied Mathematics or equivalent

Bachelor’s degree with at least a 60% average in the third-year level

Mathematics/Applied Mathematics subjects.


academic record will be considered. In particular, it is required that

the final year should include at least four of the following third-year

level modules or equivalent: partial differential equations, dynamical

systems (ordinary differential equations), real analysis, complex analysis,

numerical analysis or continuum mechanics. (UP modules WTW 386,

WTW 382, WTW 310, WTW 320, WTW 383 or WTW 387)


The programme compilation consists of seven honours modules of 15

credits each as well as the mandatory project (30 credits). It is required

that students select the stream and the modules according to the

prerequisites of the modules.

Stream 2: Differential equations and modelling


Research:


Core modules:


WTW 735Main principles of analysis in

applications 73515 1



WTW 772Mathematical methods and

models 77215 1

WTW 776Partial differential equations of

mathematical physics 77615 2

WTW 787 Continuum mechanics 787 15 2


BSc Honours in Mathematics of Finance


An appropriate BSc degree with a minimum of 60% for each

Mathematics/Applied Mathematics module on third-year level.



candidate has completed the following modules each with a mark

of at least 60%: real analysis on third-year level and linear algebra on

second-year level. (UP modules WTW 310 and WTW 211 / WTW 221)


The programme compilation consists of seven honours modules

of 15 credits each (six compulsory and one elective) as well as the



Core modules:


WTW 732Mathematical models of financial

engineering 73215 1


WTW 734 Measure theory and probability 734 15 1

WTW 762Mathematical models of financial

engineering 76215 2


Research:

WTW 792

OR

WTW 795

Project 792 or Project 795 30 year

Elective modules:



WTW 772 Mathematical methods & models 772 15 1

WTW 776Partial differential equations of

mathematical physics 77615 2

LMO 710 Linear models 710 15 1


MVA 710 Multivariate analysis 710 15 1



BSc Honours in Financial Engineering


An appropriate Bachelor’s degree with a minimum of 60% for all

modules on third-year level.



candidate has completed the following modules each with a mark of at

least 60%: calculus, differential equations and linear algebra on second-

year level. (UP modules WTW 218, WTW 286 and WTW 211 / WTW 221)


The programme compilation consists of a number of compulsory

and elective honours modules of 15 – 16 credits each as well as the



Core modules:

BAN 780 Industrial analysis 780 16 1

WTW 732Mathematical models of

financial engineering 73215 1


WTW 762Mathematical models of

financial engineering 76215 2

Fundamental module:


Elective modules:

WTW 712 Modern portfolio theory 712 15 year


WTW 735Main principles of analysis in applications 735

15 1


ISE 780 Systems engineering 780 16 1





TRA 720 Analysis of time series 720 15 2

Any other postgraduate module from this department as approved by the Postgraduate Coordinator, provided that the prerequisites are met.


Code Prerequisites

WTW 710 Analysis WTW 310

WTW 712Admissions test could be required / enrolment for WTW 732 is required

WTW 724

WTW 727 WTW 710, WTW 731, WTW 734 and WTW 724

WTW 731 Algebra WTW 381

WTW 732

WTW 733


WTW 735

Calculus at second-year level (e.g. WTW 218) and one

third-year level module on analysis or applications of

analysis, e.g. WTW 310, WTW 382, WTW 383 or WTW 386

WTW 750Multivariate Calculus and Linear Algebra;

both on second-year level

WTW 762 WTW 732 or Financial Engineering WTW 364

WTW 763 WTW 733 is strongly recommended

WTW 764 WTW 734

WTW 772

WTW 776 WTW 710 or WTW 735

WTW 787


Contact personsDepartment of Mathematics and Applied Mathematics

Honours academic advisors: Prof JE van den Berg: MathematicsProf NFJ van Rensburg: Applied MathematicsDr AJ van Zyl: Maths of Finance and Financial EngineeringDr R Kufakunesu: Maths of Finance and Financial Engineering

Contact person in Department Ms Y McDermot Tel: 012 420 3550 Email: [email protected] Office: Mathematics room 1-24

Faculty of Natural and Agricultural SciencesContact person in Faculty (Agricultural Sciences Building) Ms M Maine Email: [email protected]

Bursaries and fees Please consult the CSC (Client Service Centre)

Prerequisites for WTW modules

Documents

Faculty of Natural and Honours programme 2015 BSc · PDF fileHonours project topics: ... mathematical physics 776 15 2 ... the final year should include at least four of the following