Bachelor of Science Honours in Applied Mathematics

Purpose

The purpose of this qualification is to equip a student with further scientific knowledge with the emphasis on Numerical Analysis, Partial Differential Equations, Control Theory and Optimization and Mathematical Modelling. Expertise 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. Students 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 students with the tools necessary for them to enter a path to be professional academic scientists in their particular disciplines, namely (industrial) applied mathematicians and teachers following careers at institutions like the CSIR, MRC, MINTEK, ESKOM, SASOL, SABS, DENEL, AECI, Mittal Steel SA, NECSA, Mining (e.g., gold, platinum, coal, etc.), Financial institutions (e.g., ABSA, SANLAM, OLD MUTUAL, etc.), SABC and Higher educational institutions. Concerning information, the students will learn to critically review the information gathering process and to synthesise data and develop creative responses to problems and issues. Most South African Universities insist on a BSc Honours level qualification as the minimum entry level for further postgraduate study, therefore a further purpose of the qualification is to stimulate and prepare students for further academic study and research by the provision of the required knowledge, skills and insight to develop as researchers on a high academic level.

Rationale

It is widely accepted that South Africa has a shortage of well-trained, critically thinking scientists in the fields of the natural sciences, which are capable of proceeding towards independent, high quality research. This qualification is aimed at providing South Africa with significant numbers of graduates in the natural sciences who are able to undertake advanced research under the guidance of an expert through the acquisition of the necessary research skills and tools in the specific field of Applied Mathematics. These young scientists will ensure the broadening of the local leadership base of innovative and knowledge based economic and scholarly activity. The second rationale of this qualification is to provide students with the necessary knowledge, specific skills, applied competence and professional attitude in the field of Applied Mathematics to utilise the opportunities for continued personal intellectual growth, gainful economic activity and rewarding contributions to society.

Recognition of Prior Learning (RPL)

An applicant who cannot provide formal proof of compliance with the prescribed admission requirements for this qualification, but with prior learning and relevant work experience may be admitted to the Honours Degree study after the procedure for Recognition of Prior Learning in terms of the University's RPL policy has been completed successfully. Such recognition is within the sole discretion of the University and within the context of faculty requirements. This qualification requires that the entrant will already have a Bachelor of Science (BSc) or an equivalent standard qualification in the field of Applied Mathematics at this institution or other University or equivalent institution. This institution subscribes to the principles underlying outcomes-based, source-based and lifelong learning. In this context, considerations of articulation and mobility play an important role. This institution endorses the view that Recognition of Prior Learning (RPL) constitutes an essential element in deciding on admission to and awarding credits in an explicitly selected teaching-learning programme at Honours level.

RPL does not only imply assessment to determine the level of skills and knowledge comparable to Level 7 the candidate already possesses, but also the skills and knowledge the candidate has to master additionally prior to being accepted for the honours qualification. The assessment processes involved with RPL are the same as those followed for awarding credits in the formal graduate setting. An RPL candidate seeking credits for previously acquired skills and knowledge, must still comply with all the requirements as stated for modules, programmes and qualifications. The difference lies in the route of the assessment, since RPL assessment may be holistic in nature taking the context of the programme as well as the prior knowledge and experience of the person who is being assessed into account.

Entry Requirements

The minimum requirements for admission into the Honours studies are

• Bachelor of Science (BSc) Degree with Applied Mathematics passed at Level 7.

This qualification comprises elective and compulsory modules at Level 8.

Elective Modules, Level 8

• Complex Function Theory (WISN673), 24 Credits.
• Theory of Dynamical Systems (APMM612). 18 Credits.
• Algebra, Real and Complex Analysis (APMM611), 18 Credits.
• Calculus Variations (APMM623), 18 Credits.
• Capita Selecta (APMM622), 18 Credits.
• Differential Geometry (APMM621), 18 Credits.
• Symmetries of Differential Equations (APMM616), 18 Credits.
• Capita Selecta (APMM615), 18 Credits.
• Optimal Control Theory (APMM614), 18 Credits.
• Theory of Differential Equations (MAYM612), 18 Credits.
• Control Theory and Mechanical Systems (TGWN675), 24 Credits.
• Control Theory and Optimization Of Financial Systems (TGWN674), 24 Credits.
• Partial Differential Equations (TGWN673), 24 Credits.
• Functional Analysis (WISN675), 24 Credits.
• Capita Selecta (APMM613), 18 Credits.

Compulsory Modules, Level 8

• Research Project (APMM625), 32 Credits.
• Project (TGWN671), 32 Credits.

1. Demonstrate advanced knowledge of and engagement in Applied Mathematics and an understanding of the theories, research methodologies, methods and techniques relevant to this field of study, as well as be able to apply this knowledge in the context of Numerical Analysis, Differential equations, Control theory and Optimal control, Complex Function theory and Functional Analysis.
2. Demonstrate the ability to interrogate multiple sources of knowledge in Numerical Analysis, Differential equations, Control theory and Optimal control, Complex Function theory and Functional Analysis (area of specialisation) and as an individual and/or in teams evaluate knowledge and processes of knowledge production.
3. Demonstrate the 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 field of Applied Mathematics.
4. Review information critically gathering, synthesis of data, evaluation and management processes in specialised contexts in order to develop creative responses to problems and issues.
5. Produce and communicate information by effectively presenting and communicating academic and professional or occupational ideas and texts to a range of audiences, offering creative insights, meaningful interpretations and solutions to problems and issues appropriate to this field of Applied Mathematics.
6. Understand 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.

Associated Assessment Criteria will be assessed in an integrated manner to the Exit level Outcomes

• A systematic and integrated knowledge and understanding of, and an ability to analyse, evaluate and apply the fundamental terms, concepts, facts, principles, rules and theories is achieved.
• The ability to apply appropriate discipline-related methods of scientific inquiry and independently validate, evaluate and manage sources of information is demonstrated.
• An understanding and application of, appropriate methods or practices to resolve complex discipline-related problems and thereby introduce change within related practice is critically reflected.
• Professional and ethical behaviour within an academic and discipline-related environment, with sensitivity towards societal and cultural considerations is displayed.
• Scientific understanding and own opinions/ideas, written or oral arguments, using appropriate discipline-related and academic discourse as well as technology are communicated.
• 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.

Integrated Assessment

Opportunities for both continuous formative and summative assessments throughout the year of study are imbedded in the curriculum design of this qualification. Formative assessments include written and practical assignments, class and semester tests, whereas summative assessment includes written and practical examinations. Students are assessed on the application of learned skills in order to ensure that theory evolves into effective practice. Some outcomes of related specializations across the year are assessed in an integrated manner by means of a project, wherein not only the students evidence of the mastering of discipline-specific knowledge and skills is assessed, but also writing and communication skills, computer literacy and his/her ability to analyze critically and evaluate effectively a related problem. Report-writing and an oral presentation of the research findings are important aspects of such an assessment.