Bachelor of Science Honours in Applied Mathematics and Statistics

Purpose

The purpose of the Bachelor of Science Honours in Applied Mathematics and Statistics is to consolidate and deepen learners' expertise in the theoretical aspects of stochastic modelling and its applications and to develop research capacity in the methodologies and techniques within disciplines at the interface of Applied Mathematics and Statistics. The qualification demands a high level of theoretical engagement and intellectual independence that will prepare learners for research-based postgraduate studies in either Mathematical Statistics or Stochastically oriented Applied Mathematics.

The qualification will further equip learners with scientific knowledge regarding the interface of applied mathematical disciplines and statistically oriented disciplines, and the applications of this interface to challenges that require stochastic modelling. Expert knowledge at the forefront of the field will enable innovative problem-solving from a value-driven perspective, continued personal intellectual development, value-added economic activity and rewarding contributions to the community. Learners will be equipped to understand the complexities of various research methods, methodologies, and skills to select, apply and transfer appropriate procedures, processes, and techniques to solve unfamiliar and abstract problems.

The qualification will also equip learners with the tools necessary for them to enter a path to

• Research academic in Mathematical Statistics or Stochastically oriented Applied Mathematics,
• Professional academic scientists in their disciplines following careers in fields like Data Science, Banking, Mining, Naval Operations Research, and Biological Data Analysis (where such fields demand expertise in stochastic phenomena and statistical data),
• Follow professional careers as Government Analysts, Financial Risk Analysts, Investment analysts, Market researchers, Operational researchers, and Statisticians.

Upon completion of the qualification, a qualifying learner will be able to

• Demonstrate an ability to assimilate information from various sources within the wider fields of Applied Mathematics and Mathematical Statistics and, more specifically, to critically evaluate and review the information in the specialised fields of Probability Theory, Stochastic Processes, Numerical Analysis and Partial Derivative Equations.
• Demonstrate an ability to select, apply and critically judge the effectiveness of the implementation of a range of computer-based statistical and numerical methods to address unique real-world problems that include stochastic effects.
• Demonstrate an ability to use a range of specialised skills to identify, analyse and address complex or abstract problems, drawing systematically on the body of knowledge and methods appropriate to the interface of Applied Mathematics and Statistics.
• Demonstrate a depth of understanding of the role of the natural sciences in society, appreciate the fundamentals of lifelong learning and understand both the professional and ethical basis of scientific enquiry.
• Demonstrate an ability to access, process and manage information to demonstrate that the learner can critically review the information gathered; to synthesise data, its evaluation and the processes in specialised contexts to develop creative responses to problems and related issues based on objective and applicable analysis processes.
• Communicate effectively in a variety of formats (oral, written, visual and electronic) to diverse audiences and to evaluate knowledge and processes of knowledge production.

Rationale

The need for experts skilled in the theoretical aspects of stochastic modelling is widely recognised and growing in importance daily. A critical shortage of academics exists in Mathematical Statistics that leads to the need for a qualification equipping learners with the skills and knowledge necessary to pursue a career in which a mastery of the theoretical aspects of stochastic modelling is crucial as well as the specific need for a qualification in Applied Mathematics and Statistics exists, accessible to a wide range of learners with an undergraduate background in (Applied) Mathematics as well as Statistics.

The qualification is shaped in a particular and creative manner to address the needs highlighted in the NRF report. There has been wide consultation by various role players on ways to address the shortage of researchers in Mathematical Statistics, a need that this qualification aims to help rectify. Although the need for researchers in Mathematical Statistics was one of the main reasons for the identification of this qualification, this is by no means the only area of activity where the qualified learners will be able to operate.

The qualification is also aimed at equipping learners from a broad spectrum of adherent disciplines with the skills and knowledge necessary for dealing with the theoretical aspects of stochastic modelling and its applications. More specifically, this qualification has been designed to be accessible to learners with an undergraduate background in an adherent mathematically oriented discipline (like actuarial studies), which includes skill in mathematical statistics equivalent to at least a second-year level. Although this degree is designed to offer a pipeline to further studies and, ultimately, research in this subfield, learners who do not wish to carry on with a master's degree will be able to compete for jobs in a variety of industries. In justifying the local viability, the qualification design will not attempt to address all the industries requiring these skills but instead focus on the industry experiencing the most critical need, namely the dire shortage of academics skilled in Mathematical Statistics.

This qualification is designed to alleviate the nationwide critical shortage of senior academic statistics personnel by providing learners with the necessary skills required for enrolment in a research-oriented MSc (Mathematical Statistics). Modules in this qualification will equip learners with a more advanced background in mathematics necessary for such studies, which is non-negotiable for many of the more modern cutting-edge subdisciplines in Mathematical Statistics. The industry's growing demand for Mathematical Statistics graduates has two relevant consequences. Firstly, universities struggle to attract the interest of the crop of graduates currently being produced since they cannot compete with remuneration packages from industries such as banking, insurance, etc. Secondly, the demand for Mathematical Statistics academics is increasing due to the increasing number of learners in disciplines such as Actuarial Science, Quantitative Risk Management, Data Science, etc. This growing imbalance between the Master's and PhD graduates is currently being produced, and the demand ensures a sustainable market appetite within Statistics Departments across South Africa.

The shortage of academics in Mathematical Statistics played a significant role in the rationale for this program. However, the modelling of stochastic phenomena is increasingly popular in a wide range of fields. Therefore, a number of the elective modules in this program will equip learners with a range of skills which will enable them to solve problems of a stochastic nature. One of the objectives of this degree is to equip learners with the skills necessary to continue with postgraduate studies in fields requiring stochastic modelling, in particular, Mathematical Statistics.

Recognition of Prior Learning (RPL)

RPL will be applied according to the institutions' General Academic Rules (2019:3-4), Rules 1.6 and 1.7 and Rules for Teaching, Learning and Assessment (2023), as follows:

• Admission and advanced standing on the grounds of recognition of prior learning

> An executive dean may, by means of the recognition of prior learning (RPL) in accordance with the university's Rules for Teaching, Learning and Assessment (2019), grant a learner who does not meet the minimum admission requirements admission to a qualification of a qualification, or grant advanced standing to a learner by exempting the learner from the recognised modules required for the completion of a particular qualification.

The faculty must ensure that quality assurance processes that address the specificities of the RPL process (including applications, assessment, and reporting and management systems) are implemented; and that administrative and support systems, both prior to and subsequent to RPL assessment, are in place.

Only proven informal or non-formal learning may be taken into consideration by means of RPL; the process of equivalence-setting between such learning and formal modules must be documented, and its outcome must be recorded on the official learner record. Where a learner was granted exemption for one or more modules as a consequence of RPL, the remaining HEMIS credits required for the qualification must be obtained by completing the relevant qualification. The maximum portion of a qualification from which a learner may be exempted by means of RPL is fifty percent of the credits of the full qualification. Not more than 10% of a cohort of learners in an academic qualification can be admitted through an RPL process.

Entry Requirements

The minimum entry requirement for this qualification is

• Bachelor of Science in Applied Mathematics, NQF Level 7.

Or

• Bachelor of Science in Applied Statistical Sciences, NQF Level 7.

Or

• Bachelor of Science in a Cognate field, NQF Level 7.

This qualification consists of the following compulsory and elective modules at National Qualifications Framework Level 8, totalling 128 Credits.

Compulsory Modules at Level 8, 56 Credits

• Multivariate Statistics, 12 Credits.
• Research Report, 32 Credits.
• Stochastic Processes II, 12 Credits.

Elective Modules at Level 8, 72 Credits, (Select six modules)

• Measures and Integration Theory I, 12 Credits.
• Numerical Analysis, 12 Credits.
• Theory of partial differential equations, 12 Credits.
• Introduction to partial differential equations, 12 Credits.
• Financial modelling, 12 Credits.
• Applied matrix analysis, 12 Credits.
• Financial driven statistics I, 12 Credits.
• Real and complex analysis, 12 Credits.
• Numerical methods for partial differential equations, 12 Credits.
• Financial modelling II, 12 Credits.
• Financial modelling III, 12 Credits.
• Control theory, 12 Credits.
• Stochastic processes II, 12 Credits.
• Measures and integration theory II, 12 Credits.
• Introduction to harmonic analysis, 12 Credits.

1. Apply an integrated knowledge of the interface of Applied Mathematical and Statistically oriented disciplines and critical understanding and application of this interface relevant to modelling stochastic phenomena such as those encountered in Financial Modelling.
2. Demonstrate an ability to assimilate information from various sources within the wider fields of Applied Mathematics and Mathematical Statistics and, more specifically, to critically evaluate and review the information in the specialised fields of Probability Theory, Stochastic Processes, Numerical Analysis and Partial Derivative Equations.
3. Demonstrate an ability to select, apply and critically judge the effectiveness of the implementation of a range of computer-based statistical and numerical methods to address unique real-world problems that include stochastic effects.
4. Demonstrate an ability to use a range of specialised skills to identify, analyse and address complex or abstract problems, drawing systematically on the body of knowledge and methods appropriate to the interface of Applied Mathematics and Statistics.
5. Demonstrate a depth of understanding of the role of the natural sciences in society, appreciate the fundamentals of lifelong learning and understand both the professional and ethical basis of scientific enquiry.
6. Demonstrate an ability to access, process and manage information to demonstrate that the learner can critically review the information gathered; to synthesise data, its evaluation and the processes in specialised contexts to develop creative responses to problems and related issues based on objective and applicable analysis processes.
7. Communicate effectively in a variety of formats (oral, written, visual and electronic) to diverse audiences and to evaluate knowledge and processes of knowledge production.
8. Demonstrate an in-depth understanding of the context and systems by empowering the learner to operate effectively within a system.
9. Manage the process of learning to demonstrate the ability to critically apply learning strategies which address the professional field of ongoing learning focuses and needs, inclusive of the ongoing learning needs of other persons and/or groups of people.
10. Take accountability for the decisions and actions of self and others where applicable, and demonstrate intellectual independence, research leadership and management of research in a financial or statistical discipline.

The following Associated Assessment Criteria are assessed in an integrated manner across all Exit Level Outcomes

• Analyse, evaluate and apply the fundamental terms, concepts, facts, principles, rules and theories in the discipline.
• Apply appropriate discipline-related methods of scientific inquiry and independently validate, evaluate and manage sources of information.
• Apply appropriate methods or practices to resolve complex discipline-related problems and thereby introduce changes within related practice is critically reflected.
• Display professional and ethical behaviour within an academic and discipline-related environment, with sensitivity towards societal and cultural considerations.
• Communicate scientific understanding and own opinions or ideas, written or oral arguments, using appropriate discipline-related and academic discourse, as well as technology are communicated.
• Illustrate effective functioning as a member and/or leader of a team or a group in scientific projects or investigations, with self-directed management of learning activities and responsibility for own learning progress is demonstrated.