Bachelor of Science Honours in Mathematics

Purpose

It is widely accepted that South Africa has a shortage of well-trained, critically thinking scientists in the fields of the natural sciences, who 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 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 Mathematics to utilise the opportunities for continued personal intellectual growth, gainful economic activity and rewarding contributions to society.

Rationale

The purpose of this honours qualification in Mathematics is to equip a student with further scientific knowledge with the emphasis on Abstract Algebra, Measure and Integration Theory, Functional Analysis, Complex Analysis and research skills 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 Bachelor of Science (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.

Recognition of Prior Learning (RPL)

An applicant who cannot provide formal proof of compliance with the prescribed admission requirements for the Bachelor of Science Honours in Mathematics, 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 institution's RPL policy has been completed successfully. Such recognition is within the sole discretion of the institution and within the context of faculty requirements. This qualification requires that the entrant will already have a BSc or an equivalent standard qualification in the field of Mathematics at the institution or other equivalent institution. The 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. The institution endorses the view that Recognition of Prior Learning constitutes an essential element in deciding on admission to and awarding credits in an explicitly selected teaching-learning programme at honours level.

Entry Requirements

The minimum entry requirement is

• Bachelor of Science Degree with Mathematics passed at Level 7 with at least 60%.

This qualification consists of compulsory and elective modules at Level 8 totalling 120 Credits.

Compulsory Module: 32 Credits

• Project, 32 Credits.

Elective Modules at Level 8

• Advanced Real Analysis, 18 Credits.
• Theory of Differential Equations, 18 Credits.
• Topics in Group Theory, 18 Credits.
• Research Project, 30 Credits.
• Capita Selecta (Maym624), 18 Credits.
• Capita Selecta (Maym623), 18 Credits.
• Capita Selecta (Maym622), 18 Credits.
• Functional Analysis I, 18 Credits.
• Functional Analysis, 24 Credits.
• Topology of Metric and Integration Theory, 24 Credits.
• Capita Selecta (MAYM615), 18 Credits.
• Complex Function Theory, 24 Credits.
• Modern Algebra, 24 Credits.
• Topology, 18 Credits.

1. Demonstrate knowledge of and engagement in Mathematics and 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 Modern Algebra, Complex Function Theory, Measure and Integration Theory, Topology and Functional Analysis.
2. Interrogate multiple sources of knowledge in Modern Algebra, Complex Function Theory, Measure and Integration Theory, Topology and Functional Analysis (area of specialisation) and as an individual and/or in teams evaluate knowledge and processes of knowledge production.
3. 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 Mathematics.
4. Critically review information 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 the field of Mathematics.
6. Demonstrate an understanding of the role of natural sciences in society, appreciate the fundamentals of lifelong learning and understand both the professional and ethical basis of scientific enquiry.

The following Associated Assessment Criteria will be assessed in an integrated manner across the Exit Level Outcomes.

• Demonstrate 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.
• Apply appropriate discipline-related methods of scientific inquiry and independently validate, evaluate and manage sources of information.
• Demonstrate critical reflection on, and understanding and application of, appropriate methods or practices to resolve complex discipline-related problems and thereby introduce change within related practice.
• Demonstrate professional and ethical behaviour within an academic and discipline-related environment with sensitivity towards societal and cultural considerations.
• Effectively communicate scientific understanding and own opinions/ideas in written or oral arguments, using appropriate discipline-related and academic discourse as well as technology.
• Demonstrate 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.

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. Learners are assessed on the application of learned skills in order to ensure that theory evolves into effective practice. Some outcomes of related specialisations across the year are assessed in an integrated manner by means of a project, wherein not only the learner's 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 analyse critically and evaluate effectively a related problem. Report-writing and an oral presentation of the research findings are important aspects of such an assessment.