Doctor of Philosophy in Mathematics

Purpose

The primary purpose of the qualification Doctor of Philosophy in Mathematics is to facilitate learners with the necessary skills that will enable them in using their highly specialised knowledge, specific skills and applied competencies in addressing complex and challenging problems within the field of Mathematics.

Furthermore, the Doctor of Philosophy in Mathematics will enable learners to either develop or propose new solutions through models or theoretical amendments to Mathematics related problems for continued personal intellectual growth, gainful economic activity and valuable contributions to society.

A second purpose of the qualification is to provide South Africa (and other countries) with specialists in the discipline in order to ensure that the leadership base of innovative and knowledge-based economic and scholarly activity is widened.

A third purpose of the qualification is to provide South Africa (and other countries) with intellectual leaders.

Rationale

The Universityof South Africa (Unisa) has a strategic plan to promote research and to "create a vibrant, pure and applied research culture and conduct relevant and responsive research that impacts positively on development in Africa, globally and in the service of humanity." To this end, the College of Science, Engineering and Technology has a pivotal role to play in imparting knowledge and skills for the knowledge economy, generating new knowledge, capacity building and driving innovation in the fields of science, engineering and computing. The production of postgraduate students is crucial in achieving this task. The shortage of highly skilled people in most professions, particularly in science and mathematics, is well known. Skills at NQF Level 10 are especially of concern, as elaborated in a publication by the Council of Higher Education (Postgraduate Studies in South Africa, 2009). Unisa therefore endeavours to contribute by providing professionals with competent skills and capabilities to ensure sustainable development and enhancement of the engineering field.

The College of Science, Engineering and Technology plans to address the current shortage of the necessary skills, particularly specialised skills and research skills in the country, with this Doctor of Philosophy in Mathematics. Graduates should be able to undertake rigorous research and to communicate the results by means of a thesis that meets internationally acceptable standards of scholarliness and quality.

Recognition of Prior Learning (RPL)

Admission may be granted through RPL to learners who do not meet the minimum entry requirements.

All admissions through RPL must be in accordance with the principles laid down in the Unisa RPL Policy.

This qualification can be achieved wholly or in part through Recognition of Prior Learning.

The Unisa RPL office can supply full details of processes relating to the assessment and accreditation of learning from prior experiences. Evidence can be presented in a variety of forms, including international or previous local qualifications, reports, testimonials mentioning functions performed, work records, portfolios, videos of practice and performance records.

All such evidence should be judged according to the general principle of assessment described in the notes to assessors.

Entry Requirements

The minimum requirement for admission to the Doctor of Philosophy in Mathematics Master of Science Degree in Mathematics, Level 9 with an average of 60% or an equivalent qualification at Level 9 with an average of 60%; or an appropriate Research Master's Degree, Level 9 with an average of 60%.

Learners need to demonstrate adequate mastery of academic English (TOEFL minimum score of 88 for the Internet-based test or a minimum score of 570 for the paper-based test or completion of prior degrees at a university where English is the prime language of instruction).

Adequate exposure to appropriate research methods and methodologies in previous qualifications is required.

Foreign learners need to submit South African Qualifications Authority (SAQA) evaluation of their qualifications (South African National Qualifications Framework (NQF) Level 9 qualification equivalent is required). Applicants with degree structures that are different from South African degrees or with applicable experience that may be relevant for admission will be required to apply for Recognition of Prior Learning (RPL).

The Doctor of Philosophy in Mathematics consists of two compulsory modules at National Qualifications Framework (NQF) Level 10 totalling 360 Credits.

Modules

• Research Proposal, 0 Credits.
• Research Project and Thesis, 360 Credits.

Developmental Outcomes

The Doctor of Philosophy in Mathematics graduate can

1. Produce a variety of strategies to learn more effectively.
2. Play a leading role as a responsible citizen in the life of local, national and global communities.
3. Promote cultural and aesthetic sensitivity across a range of social contexts.
4. Use the educational and career opportunities acquired in the accomplishment of this qualification.
5. Develop entrepreneurial opportunities by drawing on the various knowledge, skills and attitudes acquired in the accomplishment of this qualification.

Specific Outcome

The Doctor of Philosophy in Mathematics graduate can

1. Make an original and significant contribution to knowledge in their area of research.
2. Engage in highly advanced critical thinking and creative problem solving within a focussed research context.
3. Apply principles of sound research practice in collecting, organising and critically evaluating information.
4. Communicate effectively the contents of the discipline and the results of the research.
5. Display technical accuracy in an area of research or within an interdisciplinary context.

Assessment Criteria Associated with Developmental Outcomes

1. Show evidence of highly advanced study and research skills, selection, analysis and evaluation.
2. Deal constructively with diversity and display appropriate conflict-resolution skills:

• Use the knowledge, skills and attributes required in studying towards the doctorate in the service of the community at large (local and global).
• Apply what they know and study in culturally diverse contexts.
• Apply what they know and study at different levels, from personal to academic contexts.
• Contribute significantly to the community, country in which they live.
• Interact with their peers locally, nationally and internationally.

3. Value cultural diversity

• Manage diversity and the opinions of others.
• Use various skills to draw out the cultural accomplishments and contents of others (e.g., listening skills, empathy, sympathy open-mindedness, etc.).

4. Identify the doctorate skills which are highly valued in the workplace within the relevant discipline

• Use the skills required for efficiency in most jobs: imaginative intelligence, emotional maturity, effective communication skills, thoughtful accuracy and interpersonal sensitivity.
• Deal effectively with unknown problems and tasks set them on the job, in the real world, by drawing upon the skills from the Doctor of Philosophy (critical thinking, problem-solving, conflict resolution, etc.).
• Demonstrate a work ethic that shows responsibility and accountability towards the employer and the client or community.

5. Create job opportunities in whatever situation they find themselves

• Have a realistic view of their own worth and value to contribute to their local community and global society.
• Communicate that value to others in the real world.
• Demonstrate a healthy self-esteem and confidence in their knowledge, skills and attitudes as required to complete the Doctor of Philosophy qualification.
• Deal with various complex situations with flexibility and adaptability.

Assessment Criteria Associated with Specific Outcomes

1. Expand, redefine and reconfigure existing knowledge within the broader context of the field or inter/multi-disciplinary fields:

• Show that his/her thesis/research project can be recognised by experts in the field.
• Produce a thesis which is publishable entirely or in part.

2. Achieve a high degree of abstraction when analysing and synthesising information within an area of research

• Attain a high level of epistemological sophistication when reflecting on information within an area of research.
• Make sound evaluations on the basis of independently generated criteria.
• Autonomously analyse, synthesise and evaluate information.
• Design new creative systems based on sound principles.

1. Document the problem statement and aims and objectives, the research design or plan, modus operandi, results and conclusions in an academically respectable and acceptable manner:

• Analyse data.
• Apply theory to practice.
• Show critical acumen in evaluating sources, specifically primary material.
• Develop a logical argument.
• Display expert, innovative and highly specialised knowledge in the area of research or within an interdisciplinary context.

4. Present material clearly and systematically

• Argue logically in order to support his/her findings.
• Use acceptable style and presentation.
• Provide an advanced critical overview of the material.

5. Document research with complete accuracy

• Use a systematic and consistent approach to technical issues such as the layout of the dissertation or other required project.

Integrated Assessment

All assessments are conducted in line with the principles of assessment as defined in the University of South Africa (UNISA) Assessment Policy.

Submitted proposals are assessed and approved by the supervisor and Departmental Research and Higher Degrees Committee to be ratified by the College Research and Higher Degrees Committee.

When a learner's thesis is nearing completion, he/she informs the Registrar of his/her intention to submit if for examination at least two months before the anticipated date. After consultation with the co-supervisor (where applicable), the supervisor gives the learner permission to submit.

Assessment will include input from three external examiners, and all must be recognised experts in their fields and must not be attached to or affiliated with UNISA. At least one of the external examiners should be from a county other than South Africa. All examiners are recommended by the Department Chairperson and/or Departmental Research and Higher Degrees Committee and their names are forwarded for appointment by the College Management Committee.

The completed report of the panel of examiners is regarded as the examiners' final recommendation. The result of the doctoral thesis is based on a judicious appraisal of the examiners' reports.

After the result of the learner's thesis has been approved, the non-examining chairperson makes the examiners' report available to the Chairperson of the Department, the supervisor, the co-supervisor, the learner and the other examiners if requested.

In addition, learners must demonstrate the ability to engage in the field of Mathematics in an integrative way, dealing with Information Science challenges strategically and effectively. It is recommended for this ability to be demonstrated by the publication of at least one article based on the research, in a scientific peer reviewed journal.