UNIVERSITY OF SOUTH AFRICA DEPARTMENT OF QUANTITATIVE MANAGEMENT

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1 UNIVERSITY OF SOUTH AFRICA DEPARTMENT OF QUANTITATIVE MANAGEMENT Contents Page 1 QUANTITATIVE MANAGEMENT Operations Research Financial modelling Research and consulting Postgraduate study Enquiries HONOURS DEGREES Hons BAdmin and Hons BCom in Quantitative Management Hons BSc in Operations Research Modules Syllabi Operations Research Applied statistics and stochastic processes Financial modelling Practical projects Special topics Further studies Design your own honours degree OR/QM and other subjects Admission requirements Hons BSc in Operations Research Hons BAdmin in Quantitative Management Hons BCom in Quantitative Management... 15

2 2.9 General rules Transitional arrangements Exemptions and overlapping Concurrent registration for an undergraduate course or modules for non-degree purposes Reregistration Assignments and examinations Register early! Communication Enquiries regarding honours degrees MASTER S DEGREES Curriculum Syllabi Admission requirements MAdmin and MCom in Quantitative Management MSc in Operations Research General rules Enquiries regarding master s degrees DOCTOR S DEGREES Curriculum Admission requirements DAdmin and DCom in Quantitative Management PhD in Operations Research General rules Thesis proposal Duration of study Reregistration Examination Enquiries regarding doctor s degrees QUANTITATIVE MANAGEMENT

3 The Department of Quantitative Management resides in the College of Economic and Management Sciences of Unisa, and offers postgraduate programmes in the specialisation fields Operations Research and Mathematical modelling Operations Research is the traditional name (popular in Europe) for the discipline that is also known as Management Science or Decision Science in the business world (especially in the USA). We use the term Quantitative Management (QM) when the emphasis is on applications in the business world, and Operations Research (OR) for the more general approach. 1.1 Operations Research Operations Research originated in World War II, when teams of scientists were drawn together from various disciplines in order to solve military logistic problems hence the term operations. Since then the methodology and applications of OR have developed to address a wide spectrum of problems in almost every sector of industry and the business world. Operations Research is multi-disciplinary subject aimed at applications, and cannot be described properly in a few words. The methodology of OR builds on various quantitative subjects, including statistics, mathematics and computer programming, and involves modelling, analytical and numerical techniques. Yet OR has a unique character. It is characterised in particular by a rational and systematic approach to decision problems, often in complex situations of uncertainty and conflict. The departmental website (Section 1.5) contains much more information about OR. The modules and syllabi in Sections 2 and 3 also give an indication of the kind of problems and techniques that belong to OR. 1.2 Financial modelling

4 2 Significant changes in financial market sophistication and complexity over the last decades require an in-depth understanding of the mathematics employed to model various aspects of the markets. It is, for example, necessary to model the stochastic behaviour of financial processes in order to design and price the contingent derivative securities. A solid background in mathematical and financial modelling skills and quantitative techniques is a prerequisite for understanding the technology employed in the financial industry and business world. 1.3 Research and consulting Operations Research and financial modelling are primarily application driven disciplines. Developments in industry and the financial world continually create new problems, which lead to the development of new approaches and techniques. The growing number of research journals that specialise in OR and financial modelling is evidence of the increasing worldwide research in these fields. Several members of the Department do research in OR/QM and related subjects, publish in international research journals and present papers at conferences. Some members are also involved in consulting in practice, including projects involving the evaluation of financial products and investment portfolios, the management of medical funds, multi-criteria decision problems, and cryptography. 1.4 Postgraduate study The multi-disciplinary nature of OR/QM is reflected in the interests of our students. The Department attracts students in the business and management sciences, engineering, and mathematical sciences such as applied mathematics, statistics, computer science and information systems. Their expertise is enhanced by the structured approach, modelling skills and computational techniques of OR/QM.

5 3 The mission of the Department is to deliver management scientists and financial experts who are capable of making a significant contribution to the decision-making process at all levels of industry and the business world. Postgraduate study in OR/QM is an excellent opportunity to equip yourself for this. Both science and business students can study for an honours degree, a master s degree, or a doctor s degree. 1.5 Enquiries To find out more about OR/QM, visit our website at or To enquire about postgraduate studies in OR/QM: qm@unisa.ac.za, phone: (012) , fax: (012) , or write to: The Head, Quantitative Management, PO Box 392, UNISA To make enquiries at the Department of Student Admissions and Registrations: post-econ@unisa.ac.za (Hons BCom etc.), post-scientia@unisa.ac.za (Hons BSc etc.), phone: (012) , or fax: (012) Visit the website of Unisa at for general information regarding degrees and modules, study fees, admission, registration, rules and procedures. To obtain Unisa Calendars, brochures and application forms you can also write to:

6 The Registrar (Academic), PO Box 392, UNISA HONOURS DEGREES 4 The Department offers the following honours degrees: the Honours BAdmin and Honours BCom degrees in Quantitative Management; the Honours BSc degree in Operations Research. Study for an honours degree is usually spread over two years and is aimed at students who have achieved good marks in their undergraduate studies in the subject. 2.1 Hons BAdmin and Hons BCom in Quantitative Management The curriculum comprises ten modules chosen from the list below. The modules HONPR1-B and HONPR2-C are compulsory. Applicants in possession of a Masters degree or who can supply proof of having passed a course in research methodology for another formal degree may apply for exemption from the module HONPR1-B. Please note that students who want to obtain admission to the master s degree in future, must take certain modules on honours level. Please see paragraph 2.5. A maximum of four non-compulsory modules may be replaced with Honours modules or papers in related subjects, subject to the approval of the heads of the departments concerned. 2.2 Hons BSc in Operations Research The curriculum comprises ten modules chosen from the list below. The modules HONPR1-B and HONPR2-C are compulsory. Applicants in

7 5 possession of a Masters degree or who can supply proof of having passed a course in research methodology for another formal degree may apply for exemption from the module HONPR1-B. Please note that students who want to obtain admission to the master s degree in future, must take certain modules on honours level. Please see paragraph 2.5. A maximum of four non-compulsory modules may be replaced with Honours modules or papers in related subjects, subject to the approval of the heads of the departments concerned. 2.3 Modules Code Name Prerequisite HONDAN-E HONLIN-R HONNNS-H HONOPT-R HONSIM-G HONFOR-P HONSM1-A HONASM-B HONSM2-B HONFIN-6 HONMD1-Y HONMD2-3 HONINV-4 Decision analysis Linear programming Neural networks Optimisation Simulation Forecasting Stochastic modelling I Applied stochastic modelling Stochastic modelling II Financial mathematics Introduction to the mathematical modelling of derivative instruments I Introduction to the mathematical modelling of derivative instruments II Investment management HONSM1-A HONSM1-A HONSM1-A & HONMD1-Y HONMD1-Y

8 6 HONPR1-B HONPR2-C HONCS1-Y Project I Project II Capita selecta HONPR1-B HONINV-4 is a paper with the weight of two modules, and is taught by the Department of Business Management (also as BELBES-E). HONSM2-B is taught by the Department of Mathematics, Applied Mathematics and Astronomy (also as APM402-4). 2.4 Syllabi The modules can be grouped as follows according to their content: Operations Research HONDAN-E: Decision analysis Modelling techniques for decision problems with one or more objectives. HONLIN-R: Linear programming Linear programming has become an important tool of modern theoretical and applied mathematics. This course is devoted to both theoretical, computational and applied aspects of linear programming models. It intends to instill in the student an ability to recognise potential linear programming problems, to formulate such problems as linear programming models, to employ the proper computational techniques to solve these problems and to understand the mathematical aspects underlying linear programming tools. HONNNS-H: Neural networks Introduction to the theory and application of neural network models such as Hebb, perceptron and backpropagation models as well as associative

9 7 and competitive networks. HONOPT-R: Optimisation Introduction to graph theory and complexity of algorithms; algorithms of combinatorial optimisation, including optimal trees and paths, maximum flow problems and minimum-cost flow problems; the travelling salesman problem; computer implementation. HONSIM-G: Simulation Modelling and operational analysis of industrial processes through simulation; case studies with computer implementation Applied statistics and stochastic processes HONFOR-P: Forecasting Forecasting techniques and applications. HONSM1-A: Stochastic modelling I Review of basic concepts in probability; Poisson processes; discrete-time Markov chains. HONASM-B: Applied stochastic modelling Continuous-time Markov chains, renewal theory and its application; queueing theory; reliability theory. HONSM2-B: Stochastic modelling II Markov chains in continuous time; martingale processes; random walks; Brownian motion and other Markov processes Financial modelling

10 8 HONFIN-6: Financial mathematics Introduction to the classical theory of compound interest, cash flows, annuities and loan schedules; the valuation of securities, Makeham s formula; capital gains tax; volatility of fixed-interest securities, matching of assets and liabilities. HONMD1-Y: Introduction to the mathematical modelling of derivative instruments I Introduction to derivative financial instruments; basic concepts of financial engineering; interest rate structures; binomial pricing models and the Black-Scholes model. HONMD2-3: Introduction to the mathematical modelling of derivative instruments II Introduction to continuous-time models of asset prices; Ito s lemma; Black-Scholes option pricing; other option pricing models; exotic options; modelling of volatility. HONINV-4: Investment management The nature of investments; capital and money markets in South Africa; stock exchanges and stock exchange analysis; portfolio management and selection Practical projects HONPR1-B: Project I Literature survey of selected topics in OR/QM; emphasis on using resources, including electronic resources; introduction to technical

11 9 writing style. HONPR2-C: Project II This module consists of a case study: the modelling and solving of a practical problem through techniques of OR/QM; or a project in financial modelling. A student must contact the lecturer to discuss the choice of his/her problem Special topics HONCS1-Y: Capita selecta This module deals with other topics in OR/QM (e.g. genetic algorithms). The syllabus is not fixed and will be reviewed annually, depending on the interests of students. Please contact the Head of Department to find out more about the content of the module, or to suggest a topic. Note. For more information about the modules, visit the departmental website (Section 1.5). 2.5 Further studies Students who want to obtain admission to a master s degree in future, please note the following: The Department will set certain honnours modules as prerequisites to admission to a master s degree. This will apply from 2007 and you should take it into account in choosing your modules. For admission to the master s degree in OR HONOPT-R and one of HONASM-B and HONSM2-B will be required. Note the prerequisite modules.

12 10 For admission to the master s degree in financial modelling HONMD2-3 and HONSM2-B will be required. Note the prerequisite modules. 2.6 Design your own honours degree You may structure your honours degree to suit your academic background, interests and goals. For example, you can choose a curriculum which emphasises either practice oriented or theoretical knowledge, or which focuses on a specific subject. Furthermore, note that the titles of the degrees do not imply that the modules in the OR group in Section 2.4 are only intended for the Hons BSc students. You may design an OR oriented Hons BCom curriculum if you want to. Similarly, the modules in financial modelling are not only intended for Hons BAdmin or Hons BCom students. If you have a science or engineering background but are interested in financial modelling, you may choose such a curriculum for the Hons BSc. You must, of course, satisfy the registration requirements and prerequisites of the modules that you choose. On the next page we give four examples of focussed curricula for an honours programme that is spread over two years.

13 11 Hons BCom OR/QM for management Year 1 Year 2 HONFIN-6 HONSM1-A HONPR1-B HONDAN-E HONFOR-P HONPR2-C HONASM-B HONOPT-R HONSIM-G HONNNS-H or HONCS1-Y Hons BCom Modelling of financial derivatives Year 1 Year 2 HONFIN-6 HONMD1-Y HONSM1-A HONPR1-B HONDAN-E or HONLIN-R HONINV-4 (= 2 modules) HONMD2-3 HONASM-B or HONSM2-B HONPR2-C Hons BSc OR/QM for management Year 1 Year 2 HONPR1-B HONSM1-A HONLIN-R HONDAN-E HONFOR-P HONPR2-C HONASM-B HONOPT-R HONSIM-G HONNNS-H or HONCS1-Y

14 12 Hons BSc Modelling of financial derivatives Year 1 Year 2 HONPR1-B HONFIN-6 HONMD1-Y HONSM1-A HONFOR-P or or HONSIM-G HONLIN-R HONPR2-C HONINV-4 (= 2 modules) HONMD2-3 HONSM2-B 2.7 OR/QM and other subjects It is possible that you are also interested in other subject areas and want to combine it with OR/QM. You may replace at most four of the (noncompulsory) modules with modules in related subjects. To register for modules offered by other departments, you must satisfy the prerequisites of the modules and obtain permission from the heads of departments concerned. Here are some examples of topics in honours modules that are offered by other departments and are related to OR/QM: Applied Mathematics Optimal control Business Management Risk management Computer Science and Information Systems Data structures and algorithms, Parallel algorithms, Artificial intelligence (expert systems) Geography and Environmental studies Geographical information systems (GIS)

15 13 Mathematics Graph theory, Discrete mathematics Statistics Statistical techniques, Regression, Multivariate analysis, Time series, Probability and stochastic processes Transport Economics and Logistics Transport logistics 2.8 Admission requirements To be admitted to an honours degree in the Department of Quantitative Management you must 1. comply with the general rules, admission and registration requirements for honours degrees as set out in Part 1 of the Unisa Calendar; 2. be proficient in the use of a spreadsheet (eg. Excel, Lotus, Quattro Pro, StarOffice or Gnumeric); 3. have access to a computer and printer with the software necessary for requirement 2; and 4. satisfy the admission requirements of the relevant honours degree as set out in Part 4 or 7 of the Calendar. All admissions are subject to approval by the Head of Department. The degree-specific admission requirements (i.e. condition 4 above) are set out in the following paragraphs. (N.B. It remains your responsibility to consult the official version in Part 4 or 7 of the Unisa Calendar.)

16 Hons BSc in Operations Research To be admitted to the Hons BSc in OR you must comply with requirements 1 3, hold a Bachelor s degree, and have passed Operations Research (or an equivalent course) as a major subject. NB: A graduate who does not comply with the last requirement may gain admission to the Hons BSc in OR by first passing the required courses for nondegree purposes (NDP) or the National Certificate in Datamatrics Hons BAdmin in Quantitative Management To be admitted to the Hons BAdmin in Quantitative Management you must comply with requirements 1 3 and hold a BAdmin degree and have passed Quantitative Management (or an equivalent course) as a major subject; or hold another degree and have passed at least six BAdmin courses, including Quantitative Management as a major subject; Economics I; a course on second-year level in one of the following subjects: # Development Administration, # Municipal Government and Administration, or # Public Administration; a course on first-year level in one of the following subjects:

17 15 # Accounting, # Business Management, # Industrial Psychology, or # Statistics. N.B. A graduate who does not comply with one of the above two requirements may gain admission to the Hons BAdmin in Quantitative Management by first passing the required courses for nondegree purposes (NDP) Hons BCom in Quantitative Management To be admitted to the Hons BCom in Quantitative Management you must comply with requirements 1 3 and hold a BCom or BCompt degree, or another approved degree in the Economic and Management Sciences, and have passed Quantitative Management (or an equivalent course) as a major subject; or hold another degree, and have passed at least the following BCom courses: Quantitative Management as a major subject; Accounting I or Accounting IA; Business Management I; and Economics I; or have obtained the Certificate in the Theory of Accounting at a recognised university, have qualified for or hold the CA(SA), and have passed at least the following courses: Quantitative Management as a major subject; Business Management I; and

18 16 Economics I. N.B. A graduate who does not comply with one of the above three requirements may gain admission to the Hons BCom in Quantitative Management by first passing the required courses for nondegree purposes (NDP). 2.9 General rules The official rules regarding honours degrees, admission, registration, etc. are contained in Parts 1 and 4 of the Unisa Calendar. In this section we only emphasise a few matters Transitional arrangements If you registered for an honours degree before 2000, you are fully accommodated in the modular structure. Each paper that you passed before 2000 carries the weight of two modules. The following restrictions also apply to the choice of modules: Paper passed HOPLIN-3 HOPMOD-9 HOPSTR-N HOPSTG-B HOPPRP-6 Modules that cannot be taken HONLIN-R HONDAN-E HONFOR-P HONSM1-A, HONSM2-B HONPR1-B, HONPR2-C Exemptions and overlapping If you passed modules for an uncompleted honours degree at another recognised university, you may be exempted from at most four corresponding modules. This must also fit in with the requirements in Section 2.7. If you passed modules or courses for a completed postgraduate

19 17 qualification which correspond to modules of the honours degree, then you may not register for these modules Concurrent registration for an undergraduate course or modules for non-degree purposes You may register for an undergraduate course for non-degree purposes (NDP) concurrently with an honours degree only with special permission of Senate. In this case, you may register for at most one undergraduate course, or the corresponding number of modules on the same level. Moreover, you may do this only if the NDP course or modules are related to you honours degree, or if you submit a written motivation and it is acceptable to the University. NB You must apply for permission for concurrent registration before the closing date for registration for the undergraduate course or modules Reregistration If your progress through the curriculum is too slow you may be refused permission to reregister. Each student is evaluated individually, but as a guideline you may assume that reregistration is normally only permitted if you have passed at least two modules after one study year, and four modules after two study years Assignments and examinations Each module has assignments which you must do in preparation for the examination Some of these assignments are compulsory, and have to be submitted by the closing date in order to be admitted to the examination. You are strongly advised to do all assignments and to submit your solutions for evaluation before the closing dates.

20 18 The module HONSM2-B and the paper HONINV-4, which are taught by other departments, have their own admission and examination rules. Contact the relevant lecturers to find out what they are. Postgraduate examinations are written in January or February, and there is no supplementary examination. Fixed dates will be given on which a student with extraordinary circumstances may take a special examination on invitation of the Head of the Department Register early! Postgraduate studies in general rely heavily on the use of prescribed books. The University, in collaboration with its official booksellers, does everything in its power to ensure that there are enough books for its students. Nevertheless, it does happen that an unforeseen increase in students (possibly from other educational institutions prescribing the same book) depletes the stocks by early March. Moreover, the academic year is short and you should exploit all the available time. Hence, you are well advised to register as early as possible in the year (to obtain the necessary information), to buy the prescribed books and to start studying Communication In order to improve communication, students are requested to furnish valid addresses on registration forms and to inform the University and the Department immediately of change of address Enquiries regarding honours degrees Use the contact numbers in Section 1.5 for general enquiries about the degrees. For more detail about the content of specific modules you may contact the relevant lecturers; get their contact details from the departmental

21 19 website (Section 1.5) or phone (012) To discuss possible curricula, exemptions and admission, contact Prof B Swart: swartb@unisa.ac.za, phone: (012) , fax: (012) , or make an appointment in advance and visit her at office AJH You may also contact the Head of Department at: qmhod@unisa.ac.za 3 MASTER S DEGREES The Department offers the following master s degrees: the MAdmin and MCom degrees in Quantitative Management; the MSc degree in Operations Research. 3.1 Curriculum The curriculum of a master s degree consists of two papers chosen from the list of master s papers, and a dissertation of limited scope (DIS661-V), which carries the weight of three papers. The papers are chosen in consultation with the Head of Department and must be passed before the dissertation is attempted. The list of papers is:

22 20 Code MOPKOM-D MOPOPT-4 MOPSP1-R MOPSP2-S Name Combinatorial analysis and heuristics Optimisation theory Special topic : Credit Risk Models Special topic : Interest Rate Modelling One of the papers may be replaced with a postgraduate paper (or two fourth-level modules) in a related subject, subject to the approval of the heads of departments concerned and the Executive Committee of the College. 3.2 Syllabi MOPKOM-D: Combinatorial analysis and heuristics NP-complete problems, geometric theory of linear programming, polyhedra and optimisation, matroids and greedy algorithms. MOPOPT-4: Optimisation theory The course aims at presenting a broad range of practical optimisation techniques. Both analytical and algorithmic issues related to these techniques are discussed. This is valuable both as a means for learning existing material and for developing new results. Ways for using these techniques as well as appropriate software to deal with real-life problems are also indicated. Prerequisites The general prerequisites for the following two courses are at least eight modules in the modelling of financial processes at the Honours level which are the equivalent of: HONMD1-Y; HONMD2-3; HONSM1-A; HONSM2-B; HONFIN-6; HONINV-4; HONPR1-B; and HONPR2-C.

23 21 Note that both courses assume some knowledge of distribution theory (STA202-M), measure theory and probability theory. MOPSP1-R (Special Topic): Credit Risk Modelling The concept of risk is integral to the world of finance. Many types of risk have been identified and studied to enable companies to optimise the way in which they take financial risk. The aim of the course is to study the valuation of default-risky bonds within the context of credit risk. Contents: Overview of risk and credit risk; basics of contingent claims analysis; credit risk valuation models S synopsis plus full text of three research papers; a general framework; credit derivatives. MOPSP2-S (Special Topic): Interest-rate Models A general introduction to the bond market, pricing of bonds, and the term-structure of interest-rates is given. The main part of the course then deals with martingale models for the short rate; forward rate models and the Heath-Jarrow-Morton framework; change of numeraire; LIBOR and swap market models. 3.3 Admission requirements All admissions are subject to approval by the Head of Department, but the formal requirements are as follows: MAdmin and MCom in Quantitative Management To be admitted to the MAdmin or MCom in Quantitative Management you must 1. hold an Hons BAdmin or Hons BCom degree, 2. have passed eight of the modules (or the equivalent thereof) prescribed for the Hons BCom degree in Quantitative

24 22 Management (please note that some Hons-modules may be a prerequisite for MCom); and 3. have a good academic record (60%+ average in the honours degree) MSc in Operations Research To be admitted to the MSc in Operations Research you must 1. hold an honours degree; 2. have passed eight of the modules (or the equivalent thereof) prescribed for the Hons BSc degree in Operations Research (please note that some Hons-modules may be a prerequisite for MSc); and 3. have a good academic record (60%+ average in the honours degree). 3.4 General rules Consult the official rules regarding master s degrees, admission, registration, etc. in Parts 1, 4 and 7 of the Unisa Calendar. N.B. The study fees for a master s degree are payable annually and are independent of the number of modules for which you register in a given year. 3.5 Enquiries regarding master s degrees Use the contact numbers in Section 1.5 for general enquiries about the degrees.

25 23 Contact the Head of Department or Prof JS Wolvaardt to discuss possible curricula, special topics, dissertations and admission. His contact details are as follows: dial: (012) , fax: (012) , or make an appointment in advance and visit him at office AJH Please do not register before contacting the Department. 4 DOCTOR S DEGREES The Department offers the following doctor s degrees: the DAdmin and DCom degrees in Quantitative Management; the PhD degree in Operations Research. 4.1 Curriculum The curriculum of a doctor s degree consists of a thesis on an approved topic. 4.2 Admission requirements All admissions are subject to approval by the Head of Department, but the formal requirements are as follows: DAdmin and DCom in Quantitative Management To be admitted to the DAdmin or DCom in Quantitative Management you must

26 24 1. hold an MAdmin or MCom degree, respectively; 2. have passed at least five of the papers (or the equivalent number of modules) prescribed for the master s and/or honours degree in Quantitative Management; and 3. have a good academic record PhD in Operations Research To be admitted to the PhD in Operations Research you must 1. hold a master s degree; 2. have passed at least five of the papers (or the equivalent number of modules) prescribed for the master s and/or honours degree in Operations Research; and 3. have a good academic record. 4.3 General rules The official rules regarding honours degrees, admission, registration, etc. are contained in Parts 1, 4 and 7 of the Unisa Calendar. In this section we only emphasise a few matters Thesis proposal Before your application for registration can be considered you must submit a thesis proposal to the Head of Department. You are advised to contact him before embarking on the preparation of a thesis proposal. His contact details are given in Section Duration of study Unless otherwise decided by Senate, the degree may not be awarded before you have registered for this degree at Unisa for at least two years Reregistration

27 25 Reregistration is annually subject to the recommendation of the Head of Department and may be refused in any year on the grounds of unsatisfactory progress. If you think that your progress in a given year was unsatisfactory, or if you want to defer your studies, you are advised to contact the Head of Department before applying for reregistration in the subsequent year Examination Only the thesis is examined, but you may be called up for questioning before the examiners make a final recommendation regarding the result. 4.4 Enquiries regarding doctor s degrees Use the contact numbers in Section 1.5 for general enquiries about the degrees. Contact the Head of Department or Prof JS Wolvaardt to discuss thesis proposal and admission. His contact details are as follows: wolvajs@unisa.ac.za dial: (012) , fax: (012) , or make an appointment in advance and visit him at office AJH UNISA

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