SAQA All qualifications and part qualifications registered on the National Qualifications Framework are public property. Thus the only payment that can be made for them is for service and reproduction. It is illegal to sell this material for profit. If the material is reproduced or quoted, the South African Qualifications Authority (SAQA) should be acknowledged as the source.
SOUTH AFRICAN QUALIFICATIONS AUTHORITY 
REGISTERED QUALIFICATION: 

Doctor of Philosophy in Applied Mathematics 
SAQA QUAL ID QUALIFICATION TITLE
125979  Doctor of Philosophy in Applied Mathematics 
ORIGINATOR
University of Zululand 
PRIMARY OR DELEGATED QUALITY ASSURANCE FUNCTIONARY NQF SUB-FRAMEWORK
CHE - Council on Higher Education  HEQSF - Higher Education Qualifications Sub-framework 
QUALIFICATION TYPE FIELD SUBFIELD
Doctoral Degree  Field 10 - Physical, Mathematical, Computer and Life Sciences  Mathematical Sciences 
ABET BAND MINIMUM CREDITS PRE-2009 NQF LEVEL NQF LEVEL QUAL CLASS
Undefined  360  Not Applicable  NQF Level 10  Regular-Provider-ELOAC 
REGISTRATION STATUS SAQA DECISION NUMBER REGISTRATION START DATE REGISTRATION END DATE
Registered  EXCO 0940/26  2026-06-02  2029-06-02 
LAST DATE FOR ENROLMENT LAST DATE FOR ACHIEVEMENT
2030-06-02   2033-06-02  

In all of the tables in this document, both the pre-2009 NQF Level and the NQF Level is shown. In the text (purpose statements, qualification rules, etc), any references to NQF Levels are to the pre-2009 levels unless specifically stated otherwise.  

This qualification does not replace any other qualification and is not replaced by any other qualification. 

PURPOSE AND RATIONALE OF THE QUALIFICATION 
Purpose:
The purpose of the Doctor of Philosophy in Applied Mathematics is to provide a strong basis for original and independent high-level research work in mathematics, applied mathematics and related fields to enable learners to undertake research in mathematics. Applicable mathematics aimed at solving problems relevant to the needs of the community provides its graduate with a thorough knowledge of applicable mathematics and develops their expertise in applying the methods and tools of mathematics to problems in science and engineering. This qualification will also provide training for a career in mathematics and applied mathematics needed in academia and research institutions. Learners will also be expected to understand, interpret, analyse, and prove research results.

Upon completion of this qualification, the learner will be able to:
  • Demonstrate expertise and critical knowledge using concepts, theories, methods, and techniques covered in Applied Mathematics to create new knowledge.
  • Contribute to scholarly debates around theories of knowledge and processes of knowledge production in Applied Mathematics.
  • Develop new methods, techniques, processes, systems in original and more creative ways appropriate to specialised and complex situations.
  • Apply knowledge and theory in critically reflexive and creative ways to address complex practical and theoretical problems.
  • Identify, formulate, analyse, and interpret information or data in Applied Mathematics to make independent judgements about managing incomplete and inconsistent information or data.
  • Demonstrate intellectual independence, research leadership and management of research and research development in Applied Mathematics by operating independently.
  • Comply with the technical, language and scholarly writing requirements/standards, e.g. referencing techniques as applied in the Doctorate level.

    Rationale:
    The Department of Mathematical Sciences of the institution is already offering an Honours and master's degree in applied mathematics which are in both Ministerial PQM and HEQSF aligned PQM. During the HEQSF Alignment, the Doctor of Philosophy in Applied Mathematics was omitted by error, and the institution was offering it with SAQA ID 19855. This qualification intends to address the learning pathway that is omitted. This qualification primarily offers an open-ended opportunity to develop intellectual and analytical skills as well as develop new Mathematics independently through models or theoretical amendments to Applied Mathematics-related problems for continued personal intellectual growth, gainful economic activity and valuable contributions to society at large. It provides an open-ended research platform through which learners may work with leading researchers in a number of computational and applied fields. The learners will therefore be equipped with the essential skills and knowledge that can be used in a variety of fields, some of which are: Finance, data science, medicine, cosmology, astrophysics, operations research, supply chain and mining, complex manifolds, analytic methods in partial differential equations, Stochastic Calculus with Applications to non-Linear Filtering and computational mathematics.

    Envisaged occupations for the graduates are:
  • Academics/ researchers.
  • Actuarial analysts.
  • Risk analysts / Business Analysts/Credit Analysts.
  • Investment banking.
  • Data analysts/ data scientists.
  • Quantitative analysts.
  • Machine Learning/ Artificial intelligence specialists.
  • Astronomy.
  • Applied Mathematicians.
    Learner will develop willingness to work collaboratively with other researchers in the same field or other fields requiring their expertise. 
    		•

    LEARNING ASSUMED TO BE IN PLACE AND RECOGNITION OF PRIOR LEARNING 
    Recognition of Prior Learning (RPL):
    RPL for access:
    All potential learners who are not in possession of a master's degree in applied mathematics need to provide proof of an equivalent qualification. Those who claim that they have achieved relevant prior learning which should give them access to the qualification need to apply to the Head of the Department of Mathematics for recognition of prior learning. Potential learners who want to be credited for prior learning need to apply in writing to the Head of the Department of Mathematics clearly stating the title(s) of the module or modules they want to be credited for, as well as the basis on which they believe the accreditation should be granted.

    The Recognition of Prior Learning in this qualification will be conducted in accordance with the Policy and Procedures for Recognition of Prior Learning (RPL) of the University. RPL is regarded as one of the critical mechanisms for achieving redress and equity and accelerating access in the university.

    This policy and set of procedures will be used in the admission of a learner to a learning programme where the minimum requirements have not been met (excluding mature age exemption category of exemption for admission to undergraduate qualifications), but the learner has evidence that the requirements can be met through RPL.

    The principles of RPL are subscribed to and will be implemented in a flexible manner. The principle of flexible and open access will, however, be offset against the provision that this should not be to the detriment of the potential learner and that his/her chances of success are reasonable. The Committee will assess competencies of these learners in order to determine whether they are eligible or not. Only 10% of the cohort of learners will be admitted through RPL.

    Entry Requirements:
  • Master's degree in applied mathematics, NQF Level 9. 
    		•

    RECOGNISE PREVIOUS LEARNING? 
    Y 

    QUALIFICATION RULES 
    This qualification consists of the following compulsory modules at National Qualifications Framework, Level 10, totalling 360 Credits.

    Compulsory Modules, Level 10, 360 credits:
  • Thesis in Applied Mathematics, 360 Credits. 
    		•

    EXIT LEVEL OUTCOMES 
    1. Critically demonstrate expertise and knowledge using concepts, theories, methods, and techniques covered in Applied Mathematics to create new knowledge.
    2. Contribute to scholarly debates around theories of knowledge and processes of knowledge production in Applied Mathematics.
    3. Develop new methods, techniques, processes, and systems in original and more creative ways appropriate to specialised and complex situations.
    4. Apply knowledge and theory in critically reflexive and creative ways to address complex practical and theoretical problems.
    5. Identify, formulate, analyse, and interpret information or data in Applied Mathematics to make independent judgements about managing incomplete and inconsistent information or data.
    6. Demonstrate intellectual independence, research leadership and management of research and research development in Applied Mathematics by operating independently.
    7. Comply with the technical, language and scholarly writing requirements/standards, e.g. referencing techniques as applied in the Doctorate level. 

    ASSOCIATED ASSESSMENT CRITERIA 
    Associated Assessment Criteria for Exit Level Outcome 1:
  • Illustrate expertise and specialist knowledge.
  • Reveal originality of approach in the thesis.
  • Consult relevant and authoritative scientific sources and theories.
  • Illustrate a thorough understanding of the principles and theories in Applied Mathematics.

    Associated Assessment Criteria for Exit Level Outcome 2:
  • Apply theory, knowledge and research methods creatively to complex theoretical and practical problems to sound theoretical conclusions.
  • Show the thesis to contribute to new knowledge in the field of Applied Mathematics through substantial, independent study and advanced scholarship resulting in the interpretation and expansion of knowledge.

    Associated Assessment Criteria for Exit Level Outcome 3:
  • Apply a comprehensive and in-depth understanding of the relevant research techniques and their application.
  • Illustrate a critical understanding of the most advanced research methodologies, techniques and technologies in Applied Mathematics.
  • Show a logical progression from the research objectives and aims in the research design.
  • Show an ability to identify, conceptualise, design and implement research that addresses complex problems at the cutting edge of Applied Mathematics in the thesis.
  • Display an ability to apply, select and manage appropriate statistical software, instruments and techniques in the analysis of data or research samples.
  • Master appropriate techniques that research has the methodological challenges appropriately are shown.

    Associated Assessment Criteria for Exit Level Outcome 4
  • Demonstrate an advanced level of competence in addressing problems that are directly or indirectly relevant to the topic.
  • Prove evidence of ability to conduct innovative research in Applied Mathematics.
  • Prove the ability to engage with current research in the discipline or field of study.

    Associated Assessment Criteria for Exit Level Outcome 5
  • Display the ability to identify, analyse, synthesise, and evaluate quantitative and/or qualitative data.
  • Display the ability to select, apply and manage appropriate mathematical software, instruments, and experimental techniques in the analyses of quantitative data or research samples.
  • Provide evidence that shows an understanding of the principles and theories used in the field of Applied Mathematics.

    Associated Assessment Criteria for Exit Level Outcome 6
  • Prove the ability to engage with current research in Applied Mathematics.
  • Display an ability to present and communicate academic/professional work appropriate to the context and level of the study.

    Associated Assessment Criteria for Exit Level Outcome 7
  • Illustrate the capacity to achieve technical, linguistic, and scholarly writing requirements/standards.
  • Illustrate the ability of the candidate's thesis to form a meaningful and integrated unit.

    Integrated Assessment
    Assessment criteria for the Doctoral Thesis will solely be determined by the quality of the thesis that will be sent out for external examination. The examiner will ensure that the learner has addressed five sub-categories of requirements that render a doctoral manuscript worthy of submission to the external examiners.

    The external examiners in turn will assess the manuscript on the basis of the very same criteria. These criteria include:
  • the focus of the study as captured by the thesis title.
  • the quality of the literature review regarding the conceptual and theoretical focus.
  • the methodological issues and the described research process; (iv)presentation of the findings as well as the synthesis of the entire study and the conclusions and recommendations.
  • the adherence to the technical and ethical standards.

    Through the supervision process, the supervisor will make the candidate aware of the key elements of each of the sub-categories that necessarily must be addressed. For each of the expositions, each of the elements pertaining to each of the five sub-categories is posed in the form of questions, the very same of which will be posed to the external examiners. 
    		•

    INTERNATIONAL COMPARABILITY 
    The qualification is comparable to the international qualifications from the following countries:

    Country: Kenya
    Institution: Maseno University
    Qualification: Doctor of Philosophy in Applied Mathematics
    NQF Level: 10
    Duration: 3 years (Full-time), often featuring 1 year of coursework followed by 2+ years of research.

    Entry requirements:
  • Master's degree in applied mathematics, Pure Mathematics, or Applied Statistics from Maseno University or other recognized universities.

    Purpose/Rationale:
    The purpose of the Doctor of Philosophy in Applied Mathematics is to develop advanced research capacity in Applied Mathematics. The qualification emphasises the production of original research that contributes to knowledge in the field, as well as the development of independent research skills.

    ELOs / Content / Modules:
    The qualification is largely research-based, with a strong emphasis on independent study under supervision. Learners are expected to conceptualise, plan, and execute a substantial research project, culminating in a thesis. Formal coursework is minimal or absent, reinforcing the research-intensive nature of both qualifications.

    Similarities:
  • The South African (SA) qualification is comparable to the Maseno University (MU) qualification, where a learner must have completed a master's degree or equivalent in Applied Mathematics or a related field of study to be eligible.
  • The qualification at both institutions is primarily based on original research rather than extensive coursework, culminating in a thesis.
  • The research focus for both qualifications involves mathematical modelling, numerical analysis, differential equations, and applications in sciences, such as mathematical biology, epidemiology, or fluid dynamics.
  • The research focus in both places involves mathematical modelling, numerical analysis, differential equations, and applications in sciences, such as mathematical biology, epidemiology, or fluid dynamics. While also focusing on applied mathematical modelling, the research at Maseno is geared toward the Kenyan context and broader African developmental needs, often aligned with their School of Graduate Studies.

    Country: United States of America
    Institution: University of Wisconsin-Stout
    Qualification: Doctor of Philosophy in Applied Mathematics
    Credits: 60+ Credits
    Duration: 4-5 years, depending on the research pace and preparation.

    Entry requirements:
    Master's degree or equivalent qualification.

    Purpose/Rationale:
    The purpose of the qualification aims to produce learners with strong analytical, problem-solving, and research capabilities in Applied Mathematics. Provide training focuses on advanced coursework, independent study, and specialized knowledge in areas like computational mathematics, numerical analysis, and mathematical modelling.

    ELOs / Content / Modules:
    The institution offers greater flexibility through specialisation or concentration areas. The programme includes elements of hands-on learning and applied experiences, which support the development of technical and industry-relevant skills.

    Similarities:
  • Both institutions require a doctoral thesis based on original research that contributes to the field of applied mathematics.
  • Both typically involve a minimum of two years of full-time study, although doctoral degrees often take longer.
  • The qualifications are generally aimed at developing expertise in modelling, simulation, and analysis to solve complex, practical challenges in science, industry, and technology.

    Differences:
  • The South African qualification focuses heavily on academic, industrial, and social research relevant to South Africa, including topics like differential equations, Lie groups, and mathematical modelling for disease dynamics.
  • The University of Wisconsin-Stout, as a polytechnic university, has a focus that is generally more tightly integrated with industrial, engineering, and technology-focused applications in the U.S. context. 
    		•

    ARTICULATION OPTIONS 
    This qualification provides opportunities for horizontal and vertical articulation options.

    Horizontal Articulation:
  • Doctor of Philosophy in Mathematics, NQF Level 10.
  • There are no qualifications registered at NQF Level 10 at the Occupational Qualifications Sub-framework.

    Vertical Articulation:
  • Doctor of Philosophy in Applied Mathematics is already at the highest NQF Level 10; thus, there is no formal vertical articulation to a higher qualification.

    Diagonal Articulation:
  • Specialised Occupational Diploma: Accountant in Practice, NQF Level 8. 
    		•

    MODERATION OPTIONS 
    N/A 

    CRITERIA FOR THE REGISTRATION OF ASSESSORS 
    N/A 

    NOTES 
    N/A 

    LEARNING PROGRAMMES RECORDED AGAINST THIS QUALIFICATION: 
     
    NONE 


    PROVIDERS CURRENTLY ACCREDITED TO OFFER THIS QUALIFICATION: 
    This information shows the current accreditations (i.e. those not past their accreditation end dates), and is the most complete record available to SAQA as of today. Some Primary or Delegated Quality Assurance Functionaries have a lag in their recording systems for provider accreditation, in turn leading to a lag in notifying SAQA of all the providers that they have accredited to offer qualifications and unit standards, as well as any extensions to accreditation end dates. The relevant Primary or Delegated Quality Assurance Functionary should be notified if a record appears to be missing from here.
     
    1. University of Zululand 


    All qualifications and part qualifications registered on the National Qualifications Framework are public property. Thus the only payment that can be made for them is for service and reproduction. It is illegal to sell this material for profit. If the material is reproduced or quoted, the South African Qualifications Authority (SAQA) should be acknowledged as the source.