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SOUTH AFRICAN QUALIFICATIONS AUTHORITY

REGISTERED QUALIFICATION:

Advanced Diploma in Mathematical Sciences

SAQA QUAL ID	QUALIFICATION TITLE
110055	Advanced Diploma in Mathematical Sciences
ORIGINATOR
Cape Peninsula University of Technology
PRIMARY OR DELEGATED QUALITY ASSURANCE FUNCTIONARY			NQF SUB-FRAMEWORK
CHE - Council on Higher Education			HEQSF - Higher Education Qualifications Sub-framework
QUALIFICATION TYPE	FIELD		SUBFIELD
Advanced Diploma	Field 10 - Physical, Mathematical, Computer and Life Sciences		Mathematical Sciences
ABET BAND	MINIMUM CREDITS	PRE-2009 NQF LEVEL	NQF LEVEL	QUAL CLASS
Undefined	120	Not Applicable	NQF Level 07	Regular-Provider-ELOAC
REGISTRATION STATUS		SAQA DECISION NUMBER	REGISTRATION START DATE	REGISTRATION END DATE
Reregistered		EXCO 0821/24	2019-07-25	2027-06-30
LAST DATE FOR ENROLMENT		LAST DATE FOR ACHIEVEMENT
2028-06-30		2031-06-30

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 this qualification is to develop in-depth theoretical and practical knowledge of the strategies, tools and techniques needed by learners in order to solve problems in financial mathematics and biomathematics. Qualified Bio mathematicians can find jobs in agriculture and nature conservation, in forestry to model changes in forests and vegetation patterns; fisheries to determine the best harvesting strategies; epidemiology to provide insights into disease dynamics and their management. Qualifying learners with Financial Mathematics as an elective will be able to address problems at the interface between mathematics and finance. This qualification aims to develop competence in quantifying and managing investment and risk and apply finite difference and transform methods to option pricing. It enables qualified learners to gain access to jobs in banking, insurance, financial markets as well as business analysts. It empowers graduates to use and apply conceptual knowledge, skills and understanding of advanced mathematics, statistics, programming and numerical methods to solve problems in financial mathematics and biosciences.

This qualification is specifically intended to:

Provide progression pathways for learners who have completed the Diploma in Mathematical Sciences in the Business and Applied Science Streams.

Provide a sound background in advanced Mathematics, Statistics, Numerical Methods and Programming for students interested in pursuing careers or further studies in Financial Mathematics or Biomathematics.

Provide a focus for research activities within the department of Maths and Physics.

Provide learners with a qualification matched to their needs and interests and has links with the current and intermediate job market.

Rationale:
The Advanced Diploma in Mathematical Sciences is designed to empower learners with the knowledge and understanding of core areas in mathematics, statistics and computation using technology to address problems in finance and biosciences, crucial to economic growth and development of the nation. It lays the foundations of mathematical and statistical modelling to enable analysis and projection of financial and bioscience data systems. Through its community service projects, it inculcates values of social responsiveness and community awareness and engagement.

A 3-phase needs analysis was conducted to inform the structure, purpose, outcomes and viability of this qualification.

The first phase involved a literature search and benchmarking of Applied Mathematics with specialisations in Financial Mathematics and Biomathematics, both internationally and nationally. International trends in developments in applications of mathematics were benchmarked with the Society for Industrial Applications of Mathematics and the National Academy of Sciences (NAP).

The second phase involved research into workplace practices through Work Integrated Learning (WIL) and the mathematics and statistics projects that Diploma in Mathematical Sciences learners have completed for business and industry, including Statistics South Africa (StatsSA) South African Centre for Epidemiological Modelling and Analysis (SACEMA) , African Institut of Mathematical Sciences (AIMS), PetroSA, Golden Arrow Bus Services, City of Cape Town Water Department and the Department of Agriculture. The research projects include disease modelling, forecasting Gross Domestic Product (GDP), client satisfaction surveys, optimising Research Octane Numbers in an oil refinery, recycling water, as well assessing water quality. The projects have provided insight into the regional needs in Mathematics and Statistics at the workplace.

An Advisory Committee, comprising representatives from business and industry, and academia was established to give input and direction to this qualification.

The final phase involved research using a questionnaire and interviews with academic institutions and business and industry representatives. This provided valuable information into the type of Mathematics and Statistics and software that is in use in industry and in particular, at the workplace and given us valuable leads as well as endorsement as to the nature and the structure of this qualification. The questionnaire revealed a variety of needs including computation, computer tools to handle large data sets, and applications in finance and applied sciences. Critical areas of Bio- and Financial Mathematics identified include deterministic and stochastic modelling, theoretical and applied statistics, disease modelling and big data analysis. Among the findings were: Software use varied: Matlab, Statistica, Python, Excel, R and Maple. Applications are diverse and included: data analysis, forecasting, prediction, simulation. Findings of Phase 2 and 3 were presented in a research paper entitled, "A survey of Mathematics and Statistics needs in the Workplace" by J. Farmer and T. Sheikh, at the U6 conference held at the Institution in September 2014.

Occupations which require subjects like mathematics, science and Information Technology (IT) dominate the top 100 scarce skills. Among the documents that affirm the need for mathematics and science graduates are" The Joint Initiative on Priority Skills Acquisition", (JIPSA, 2006), "National Development Plan (NDP) for 2010-2030", The Department of Labour's "Job Opportunities and Employment Report" (JOUR, 2016), "Career Junction's Salary and Wage Report" (2016), and "Scarce Skills List (2014)". The Sector Skills Plan drawn up by Finance and Accounting Services Sector Education and Training Authority (FASSET), the Financial and Accounting Sector Education and Training Authority (SETA), reports that shortage of finance and accounting services skills exist at all levels - from clerical to technician, and administrative to professional, and managerial (Fasset, 2016 - 2021).

Applications of mathematics permeate every aspect of the workplace in business, applied sciences and in industry. From planning and design, to monitoring and forecasting production, and quality control, mathematics is applied in all steps of the operations and processes as a powerful tool in the solution of workplace problems. Rapid changes in the workplace, where new technologies are embraced in order to be more globally competitive, have increased the demand for mathematicians who can apply core mathematical knowledge to processes and operations across a number of mathematics based disciplines such as biotechnology, food and geo-technology as well as in the biosciences and finance. In the workplace, the application of mathematical computation with big data, modelling and optimisation, help to improve the efficiency of processes and operations, deal with and accommodate changes in order to make business and industry remain competitive locally, nationally as well as globally.

The report "Frontiers in Massive Data Analysis" (2013) by the National Research Council of the National Academy of Sciences, points out that the rate of data generation of biological, Geographical Information System (GIS), physical, social (Facebook, Twitter), e-commerce, defence, environmental, medical and financial data has surged tremendously. The analysis of this data needs competence in developing new algorithms and inferential strategies, sampling methods, error detection, and innovative computational methods. These form an integral focus of this qualification, which adopts an inter-disciplinary approach spanning relevant areas of mathematics, numerical methods, computer programming, and statistics. It targets the necessary tools to model biological phenomena, and analyse huge amounts of data such as those generated by the human genome project, the spread of disease (HIV, Bird Flu, Malaria) and agri-products (farm output, fisheries,).

The finance industry is also characterised by the extensive use of mathematical tools and models for security pricing, dynamical asset allocation, trading in stock, exchange rates, inflation, GDP, and risk analysis. The increase in financial activity especially on stock markets has seen a corresponding growth in the employment of graduates in mathematics by banks and investment houses. A sound understanding of the mathematics of financial modelling and derivative pricing is essential in order to offer new products, to manage financial risks, and give a finance house a competitive edge in the market. The department is aware of the global financial crises that have hit the property and housing, markets or the banking sector, but also note the measures taken towards correction and recovery.

The career choices are based on learning trajectories established by the 3-year Diploma in Mathematical Sciences that has been on offer since its inception in 2009. The choice of the application domains (electives) for this qualification was informed by the following factors:

Trends on the international, national and regional scene, highlighted above. It is noted that one of the fastest growing areas of employment for mathematical graduates is the financial sector. Banks, insurance companies and investment houses are facing shortages in skilled financial graduates as highlighted by the FASSET. (2015).

Availability of staff with adequate background and experience to offer this qualification. Applied Science qualifications and Finance, Marketing, economics and Business related qualifications in the Diploma in Mathematical Sciences have been offered since its inception in 2009, thus creating an experienced cohort of staff.

The choice of Financial Mathematics as an elective follows naturally from earlier courses in, for example, Economics, Finance, Marketing and Financial Markets, Econometrics 3, Financial Mathematics 3, in the Diploma in Mathematical Sciences. Likewise, the choice of Biomathematics follows naturally from courses in Physics, Chemistry, Bioscience, Biomathematics 3, Biostatistics 4, Applied sciences 2 and 3 in the Diploma course. There is a growing need for trained professionals who understand the languages of both biology and mathematics.

The requirements of potential employers: In this respect a questionnaire asking future employers to rate graduate attributes highlighted important attributes that this qualification must focus on.

The main aim of the Higher Education Qualifications Sub-Framework (HEQSF)-aligned Advanced Diploma in Mathematical Sciences is to develop in-depth theoretical and practical knowledge, and understanding of the tools and techniques in order that graduates can solve problems in biosciences and financial industry at HEQSF Level 7. Job opportunities for graduates of the Advanced Diploma exist as data analysts, data capturers, as well as quality controllers and in teaching. Bio-mathematicians can find jobs in agriculture and nature conservation, in forestry to model changes in forests and vegetation patterns; fisheries to determine the best harvesting strategies; epidemiology to provide insights into disease dynamics and their management. Graduates with Financial Mathematics as an elective will have access to jobs in banking, insurance, financial markets as well as business analysts.

LEARNING ASSUMED TO BE IN PLACE AND RECOGNITION OF PRIOR LEARNING

Recognition of Prior Learning (RPL):
Recognition of Prior Learning (RPL) is a process of identifying the knowledge and skills of an applicant against the admission requirements of a qualification. The process involves the identification, mediation, assessment and acknowledgement of knowledge and skills obtained through informal, non-formal or formal learning. The RPL process is multi-dimensional and multi-contextual in nature, aimed at the individual needs of applicants and is handled in accordance with an institutional RPL policy. The RPL process includes guidance and counselling, as well as the preparation of a body of evidence to be presented by the RPL candidate to meet institutional requirements. An appeal procedure is also in place to accommodate queries. RPL in this qualification will relate to gaining access to the qualification or credits as described in institutional guidelines.

The outcome of recognition of prior learning is that learners are judged to have completed the credits that will be formally recorded on their transcript.

Entry Requirements:
The minimum requirements for entry are:

A Diploma in Mathematical Sciences at Level 7.

A Diploma in Mathematical Technology at Level 6.

A 360 Credit Bachelor's Degree with majors in Mathematics or Statistics at Level 6.

RECOGNISE PREVIOUS LEARNING?

QUALIFICATION RULES

This qualification consists of compulsory and elective modules at National Qualifications Framework (NQF) Level 7 totalling 120 Credits.

Compulsory Modules, 96 Credits:

Complex Analysis, 12 Credits.

Matrix Theory and Linear Algebra, 12 Credits.

Mathematical Statistics, 12 Credits.

Non-Linear and Partial Differential Equations, 12 Credits.

Numerical Methods, 12 Credits.

Data Science, 12 Credits.

Programming and Data Base Development, 12 Credits.

Workplace Project, 12 Credits.

Elective Modules, 24 Credits (select any two):

Biostatistics, 12 Credits.

Business Analytics, 12 Credits.

Biomathematics, 12 Credits.

Financial Mathematics, 12 Credits.

EXIT LEVEL OUTCOMES

1. Use and apply conceptual knowledge, skills and understanding of advanced mathematics, statistics, programming and numerical methods to solve problems in financial mathematics and biosciences.
2. Select and apply a range of methods, strategies, techniques and appropriate knowledge to solve problems in mathematics and statistics and areas of application.
3. Identify, analyse, evaluate, critically reflect on and address routine and complex problems, applying appropriate evidence-based solutions and theory-driven arguments.
4. Ttake decisions and act ethically and professionally, and justify those decisions and actions drawing on appropriate ethical values and approaches within a supported environment.
5. Develop appropriate processes of information gathering for a given context or use and to independently validate the sources of information.
6. Manage processes in unfamiliar and variable contexts, recognising that problem solving is context driven.
7. Identify, evaluate and address his or her learning needs in a self-directed manner, and to facilitate appropriate collaborative learning processes.
8. Take full responsibility for his or her work, decision-making and use of resources, and limited accountability for the decisions and actions of others in varied or ill-defined contexts.

ASSOCIATED ASSESSMENT CRITERIA

Associated Assessment Criteria for Exit Level Outcome 1:

Use and apply integrated knowledge and understanding of advanced mathematics including complex variables, matrices and Systems of Ordinary and partial Differential Equations in order to solve well defined problems accurately.

Apply mathematics concepts, theorems, algorithms and procedures to solve problems in a range of contexts including investment, risk analysis, disease modelling, genetics using standard methods.

Apply knowledge of advanced programming using appropriate software (R, Matlab, SAS) to find analytical and/or qualitative solutions of well-defined problems in financial and biomathematics.

Use and apply appropriate statistical models, probability theorems, parametric and non-parametric statistical tests (z, t, F, Chi) to analyze and monitor processes, and trends in Financial Mathematics and Biomathematics.

Apply appropriate techniques and tools of multivariate statistics (regression, Principal component analysis, Factor and Discriminant analysis) in the analysis and interpretation of financial or biosciences data sets.

Know, understand and competently apply principles, strategies methods and techniques competently in Financial Mathematics in a range of contexts (investment analysis, asset management, valuation of stocks, risk assessment, and property finance).

Apply knowledge from substantive sub-disciplines such as Biostatistics and Business Analytics in the solution of problems in Financial Mathematics and Biomathematics.

Use knowledge of standard data mining software (SAS, the R language), as appropriate, in the solution of practical problems.

Associated Assessment Criteria for Exit Level Outcome 2:

Formulate conceptual and quantitative models that translate and represent real world problems in finance and biosciences using appropriate representation (Systems of Ordinary, Partial Differential Equations.

Use and apply core knowledge to competently model problems in Biosciences including population and, disease modelling (Malaria, TB, Cancer), cellular and molecular biology, biochemistry, and microbiology.

Construct and use appropriate time series models and algorithms for forecasting investments, production schedules.

Select and implement correct numerical techniques for a range of problems.

Use computational tools (Mat Lab, R) and statistical packages such as EXCEL, Statistical Package for the Social Sciences (SPSS) or SAS to manipulate data bases, for simulation and modelling and computing solutions to a range of problems.

Know and use phases of data mining i.e. the business understanding phase, the data understanding phase, the exploratory data analysis phase, the modelling phase, the evaluation phase, and the deployment phase competently in large data analysis.

Associated Assessment Criteria for Exit Level Outcome 3:

Use a structured analytical approach to problem solving in Financial Mathematics and Biomathematics, bearing in mind the assumptions made and consequences of their violation.

Identify correct mathematical structures (e.g. differential or difference equations, individual-based models, directed graphs) embedded within a given conceptual model.

Solve competently open-ended problems and routine problems by formulating the problems in precise terms, identifying key variables, assumptions, and limitations of solutions.

Critically analyse the results of a mathematical model, and propose changes to the model as appropriate and necessary.

Conduct independent, in-depth enquiry within the specialised disciplines to an academically acceptable standard.

Associated Assessment Criteria for Exit Level Outcome 4:

Understand and abide by professional responsibilities and ethical norms that go in handling financial data and bioscience research.

Check answers and solutions to models and problems for validity, reliability and accuracy.

Understand the appropriate limitations and power of using analytical methods for solutions to finance and bioscience problems.

Justify and correctly validate conclusions, decisions, and outcomes of investigations and projects.

Associated Assessment Criteria for Exit Level Outcome 5:

Access, evaluate and synthesise scientific or financial information for analysis and decision-making in routine and complex contexts.

Ensure academic integrity and social responsibility in compiling reports by correctly citing references, rewording text, etc.

Use appropriate referencing conventions in quoting research and show respect for the intellectual property of others by giving due credit.

Demonstrate written, visual, and/or oral presentation skills to communicate scientific/financial knowledge correctly.

Construct mathematical arguments, identifying assumptions and conclusions and present arguments and conclusions accurately and clearly.

Use correct language to produce clear and coherent written documents, which follow appropriate scientific/business conventions.

Communicate effectively online and work with others using collaborative tools such as the Blackboard.

Associated Assessment Criteria for Exit Level Outcome 6:

Solve problems and work within the systems and frameworks of scientific and financial mathematics.

Demonstrate knowledge and understanding of financial instruments, asset pricing, portfolio selection and optimisation.

Source, analyse and critically evaluate financial or bio data from a range of sources including electronic databases.

Associated Assessment Criteria for Exit Level Outcome 7:

Reflect on and manage own learning needs with minimum guidance appropriate initiative and responsibility.

Carry out an independent investigation or project using textbooks and other available literature, searching databases and interacting with colleagues and staff to source relevant information.

Develop and use effective learning strategies and skills (note taking, summarising, critical review of research) that suit personal needs and contexts appropriate to National Qualifications Framework (NQF) Level 7.

Seek and make use of feedback, and self-evaluate own work objectively.

Be self-directed and proficient in solving problems and understanding new material.

Manage time effectively e.g. by completing tasks to a required standard in keeping with the requirements of NQF Level 7 and within stipulated timeframe and deadlines.

Associated Assessment Criteria for Exit Level Outcome 8:

Critically challenge assumptions and modify or adapt mathematical or statistical models as appropriate.

Implement principles and concepts of data analysis with integrity, security and confidentiality.

Evaluate the appropriateness of different approaches to problem solving.

Integrated Assessment:
Integrated assessment forms part of continuous assessment at the institution and takes the form of an appropriate mix of both formative and summative assessment methods. Assessment policy and practices at the institution promote constructive alignment of the curriculum, learner centred-learning and assessment, and the importance of feedback to enhance learner engagement. Assessment practices should be fair, reliable and valid. It should also be in keeping with academic disciplinary and professional field norms and standards.

Formative assessment is aimed at enhancing student learning and provides students with an opportunity to reflect critically on their own learning and to improve their own levels of personal accountability and time management. Formative assessment usually consists of a variety of assessment tasks relevant to the field of study.

In this qualification, it will consist of a variety of tasks such as problem-solving individual and/or group assignments and projects, case studies, class discussions, quizzes, and poster and project presentations.

Summative assessment will take place at the end of a section of work/quarter or semester and is aimed at assessing learner's attainment against the learning outcomes of the qualification and subject(s). Summative assessments are internally and externally moderated based on institutional policy and requirements. In this qualification, summative assessment will consist of written assessments in the form of written class tests and examination as well as Mathematics lab reports conducted during and at the end of the academic semester.

Integrated assessment often cuts across a number of modules of a qualification and is aimed at the holistic development of learners and contributes to learners' personal and professional development in the field of study in terms of foundational, practical and reflexive competence.

Integrated assessment in this qualification will take place in the form a project and learners will be assessed holistically by means of written project reports, an oral presentation related to the needs and requirements of the industry and field of study. Emphasis is placed on the integration of knowledge, skills and abilities in Mathematics, Statistics and Computing.

INTERNATIONAL COMPARABILITY

The international comparability exercise was conducted in terms of institutional requirements and guidelines which include the following: determining the scope of the benchmarking exercise; the selection of a variety of reputable Higher Education institutions internationally; the selection of comparable qualifications and aspects from these qualifications; analysis and evaluation of programme design of the selected qualifications; and conclusions and recommendations for curriculum renewal at the institution. This qualification compares favourably with the following qualifications:
Country: United States of America (USA).
Institution: Michigan Institute of Technology, Florida Institute of Technology.
Qualification: Graduate Diploma in Financial Mathematics and Biomathematics.

Country: Austria:
Institution: Vienna Institute of Technology.
Qualification: Graduate Diploma in Financial Mathematics and Biomathematics.

Country: China:
Institution: Hong Kong University of Technology.
Qualification: Graduate Diploma in Financial Mathematics and Biomathematics.

Country: Australia:
Institution: School of Mathematics and Statistics at the University of New South Wales (UNSW).
Qualification: Graduate Diploma in Mathematics and Statistics.

Conclusion:
The Mathematics modules are similar and include complex variables, as well as Partial Differential Equations. A direct comparison with the content of these qualifications enabled a successful benchmarking of the courses offered in the Advanced Diploma. The qualification from Australia includes specialisations in fields such as Medical Statistics, Financial Mathematics and Industrial Statistics. Typical core modules are Computational Methods for Finance, Continuous Time Financial Modelling, Data Mining and its Business Applications and Discrete Time Financial Modelling. All these have parallels in this qualification.

ARTICULATION OPTIONS

This qualification allows possibilities for both horizontal and vertical articulation.

Horizontal Articulation:

Advanced Diploma in Statistics, Level 7.

Advanced Diploma in Mathematics, Level 7.

Vertical Articulation:

Postgraduate Diploma in Mathematical Sciences in Financial Mathematics, Level 8.

Postgraduate Diploma in Mathematical Sciences in Biomathematics, 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.	Cape Peninsula University of Technology