Postgraduate Diploma in Mathematical Sciences

Purpose

The purpose of the Postgraduate Diploma in Mathematical Sciences qualification is to consolidate and deepen learners' understanding and thus equip learners with the analytical, technical, and professional skills, methods and tools required to perform as analytical problem solvers at a high level. In achieving this purpose, the qualification will empower learners to excel in careers such as Analyst or Data Scientist.

This qualification is an interdisciplinary and specialised qualification that integrates knowledge, skills and methods from both Applied Mathematics and Statistics and is at the same time infused with specialisation in the emerging sub-discipline of Data Science. It aims to use a rigorous mathematical approach by empowering learners with theoretical knowledge and technical and professional skills from these disciplines, to serve in a range of business and industry careers as Analysts, Data Scientists, Junior Lecturers, or similar.

The qualification is also designed to prepare learners for master's level studies in Applied Mathematics, Statistics, or Data Science through the deepening of their knowledge and understanding of theories, methodologies and practices in these disciplines, as well as the development of their ability to formulate, undertake and resolve more complex theoretical and practice-related problems and tasks through the selection and use of appropriate methods and techniques.

Graduates of this qualification will be able to articulate vertically to master's degrees in mathematical sciences and its subdisciplines. Moreover, graduates will have been equipped with ethical training and digital and professional citizenship to be able to conduct themselves in a caring and ethical manner in their careers.

Upon completion of the qualification, qualifying learners will be able to

• Demonstrate understanding of the fundamental theories, concepts, and models within Applied Mathematics, Statistics, and Data Science, and articulate them using symbolic mathematical expressions.
• Select an appropriate mathematical or statistical model or technique for a given unfamiliar problem and construct the model in terms specific to the problem.
• Demonstrate the ability to acquire, quality-check, clean, merge, transform, and wrangle large, complicated data sets using data science software and programming.
• Select and apply appropriate computational algorithms and techniques to correctly implement the chosen mathematical or statistical model(s) in software.
• Create and correctly interpret visually attractive and appropriate graphical and numerical output related to the implementation of a model or method in Applied Mathematics, Statistics, or Data Science.

Rationale

According to the Department of Home Affairs' 2021 Critical Skills List, and DHET's associated 2020 List of Occupations in High Demand, two of the critical occupations required in the country are Data Scientist (and Statistical and Mathematical Assistant. The planned Level 8 qualification thus contributes toward addressing the shortage of two occupations deemed critical to the national economy.

The Postgraduate Diploma in Mathematical Sciences is an interdisciplinary programme, based on a core curriculum in Applied Mathematics, Statistics and Data Science, with domain-specific applications in Business and Applied Sciences. The design team adopted an interdisciplinary approach as Applied Mathematics and Statistics supply core theory and methods that are then applied to the emerging discipline of Data Science to create a powerful and versatile toolkit for problem-solving in business, industry, and academia. The students' deep roots in Mathematics and Statistics will establish them as specialist Data Scientists and set them apart from many professionals who adopt the self-designation "Data Scientist" after doing short courses in machine learning with little appreciation for the mathematical and statistical foundations thereof. Indeed, major advances in data science usually stem from a combination of techniques drawn from applied mathematics and statistics. Machine Learning algorithms applied to Big Data are a huge growth area in the Fourth Industrial Revolution labour economy. Graduates of this qualification will be poised to capitalise on these new opportunities, and in so doing, to ensure that South Africa keeps apace with this global revolution.

Business intelligence (BI) uses software and services to provide insights that inform an organization's strategic business decisions. BI tools access and analyse data sets and present analytical findings in reports, summaries, dashboards, graphs, charts, and maps to provide users with detailed intelligence about the state of the business for decision-making support. The Postgraduate Diploma includes subjects that reinforce BI and thus enables students to package and communicate quantitative information in a form in which business leaders currently expect to receive such information.

With this professionally oriented qualification in hand, and more importantly the technical skills (e.g., advanced analytical and modelling skills, problem-solving, computational and programming skills in a variety of software applications) and professional skills (e.g., versatility, adaptability, professionalism, lifelong learning, community service, information literacy, and critical thinking) with which we will equip our students, graduates will be well prepared to further specialise at Masters Level or pursue job opportunities as data scientists and data analysts in a variety of sectors including financial services, retail, government, health care, research, etc. The Research Project component will provide the student with a choice between a professionally oriented "business case" that entails solving a business problem for a real-world client (e.g., the student's employer, which could be in a variety of sectors and domains of application) or a more traditional research project for students who aim to continue to Masters level.

It has been mentioned how the Postgraduate Diploma in Mathematical Sciences will provide graduates who can help to supply the shortage in critical skills and high-demand occupations identified by the South African government, such as Statistical and Mathematical Assistant and Data Scientist. It is therefore clear that the graduates of this qualification will make an important contribution to society and the national economy. It is anticipated that the programme will also be an attractive option for international students from other African countries that similarly consider Data Science, Applied Mathematics, and Statistics to be critical skills.

Recognition of Prior Learning (RPL)

RPL for access

The Institution's Recognition of Prior Learning Policy is informed by the CHE RPL Policy. RPL may be used to grant access to a qualification programme, but this exemption does not translate to credits being awarded for these subjects and a student who, on the basis of RPL, is granted exemption from doing some subjects in the qualification programme will complete the qualification with a total number of credits that is less than the normally required number of credits for the qualification in question.

Not more than 10% of a cohort of learners in a higher education programme should be admitted through an RPL process. The institution's RPL Policy also states that any learner wishing to continue their studies after an absence of ten years or more must apply via RPL. In such cases, the student must provide detailed information about their activities during their absence from formal studies.

Entry Requirements

The minimum entry requirement for this qualification is

• Bachelor of Science in Mathematical Sciences or Statistical Sciences, NQF Level 7.

Or

• Advanced Diploma in Mathematical Sciences, NQF Level 7.

This qualification consists of the following compulsory modules at National Qualifications Framework Level 8 totalling 120 Credits.

Compulsory Modules, NQF Level 8, totalling 120 Credits

• Machine Learning 5A, 12 Credits.
• Machine Learning 5B, 12 Credits.
• Research Project, 24 Credits.
• Advanced Programming for Data Science, 12 Credits.
• Data Engineering and Visualisation, 12 Credits.
• Convex Optimisation, 12 Credits.
• Mathematical Modelling, 12
• Bayesian Statistics, 12 Credits.
• Computational Methods, 12 Credits.

1. Demonstrate understanding of the fundamental theories, concepts, and models within Applied Mathematics, Statistics, and Data Science, and articulate them using symbolic mathematical expressions.
2. Select an appropriate mathematical or statistical model or technique for a given unfamiliar problem and construct the model in terms specific to the problem.
3. Demonstrate an ability to acquire, quality-check, clean, merge, transform, and wrangle large, complicated data sets using data science software and programming.
4. Select and apply appropriate computational algorithms and techniques to correctly implement the chosen mathematical or statistical model(s) in software.
5. Create and correctly interpret visually attractive and appropriate graphical and numerical output related to the implementation of a model or method in Applied Mathematics, Statistics, or Data Science.
6. Solve sophisticated theoretical or professionally oriented research problems in Applied Mathematics, Statistics, or Data Science by undertaking a comprehensive research project.
7. Address ethical and practical issues such as plagiarism, protection of personal information, cybersecurity, and non-disclosure in an academic and professional context.
8. Produce insightful academic or professional information and communicate it effectively to a range of audiences, thereby offering actionable solutions to problems appropriate to the context.
9. Apply, in a self-critical manner, learning strategies for online and face-to-face classes and consultations, which effectively address the learners' professional and ongoing personal learning needs as well as those of others.
10. Take full responsibility for one's work and capably defend methodological decisions and interpretations.

Associated Assessment Criteria for Exit Level Outcome 1

• Define and defend fundamental concepts and principles in mathematics, statistics, and data science (e.g., calculus, linear algebra, mathematical statistics, basic programming).
• Apply knowledge of fundamental concepts to include more specialised or complex theories and contexts.
• Provide a verbal rationale and formal derivation of various mathematical, statistical, and data analysis methods and techniques.
• Relate the understanding of mathematical and statistical concepts and methods to problems in data science, especially those involving Big Data.
• Draw on different sources of knowledge as part of the learning process, including books, journals, web sources, and consultations with lecturers and peers.

Associated Assessment Criteria for Exit Level Outcome 2

• Describe the basic characteristics of and rationale for a variety of well-known mathematical and statistical models that are useful in Applied Mathematics and Data Science.
• Evaluate the advantages and disadvantages of a given method or technique for a given problem or context, informed by criteria such as theoretical soundness, computational efficiency, violation of model assumptions, and empirical performance.
• Apply the knowledge gained from the selection of an appropriate mathematical or statistical model or technique for a given unfamiliar problem to select the most appropriate method or technique for a given problem or context.

Associated Assessment Criteria for Exit Level Outcome 3

• Acquire or extract data sets from online sources or databases, using queries or scraping techniques where necessary.
• Perform exploratory analysis and quality checks of a given data set, characterising the architecture and relevant features of the data.
• Apply knowledge and import data sets from a variety of file types into statistical and data science software.

Associated Assessment Criteria for Exit Level Outcome 4

• Apply knowledge of and select software platforms, packages, and functions appropriate for the implementation or fitting of a mathematical or statistical model, method, or technique.
• Apply the various elements of a systematic and algorithmic modelling process (e.g., machine learning) in a logical and properly sequenced manner.
• Construct and apply mathematical modelling techniques and use sensitivity analysis to predict real-world outcomes under different conditions.
• Apply computational and numerical methods to obtain approximations for quantities for which exact analytical solutions are infeasible.

Associated Assessment Criteria for Exit Level Outcome 5

• Create aesthetically attractive and easily interpretable visualisations of data and models, including static graphs and interactive dashboards.
• Present tables and other numerical displays of relevant output from a mathematical or statistical model or method accurately.
• Interpret graphical and numerical results correctly in the context of the given problem, while recognising the assumptions and limitations inherent in the methods used.

Associated Assessment Criteria for Exit Level Outcome 6

• Describe the quantitative features of a real-world problem in a specialised domain of application (e.g., finance, economics, ecology, epidemiology) and identify relevant variables and data that can be brought to bear.
• Present the findings of the modelling and analysis in a clear, nuanced way that solves the research problem and achieves research objectives.
• Apply practical and actionable recommendations resulting from the project to a client or stakeholder or the wider community of practice.

Associated Assessment Criteria for Exit Level Outcome 7

• Protect personal or other confidential information in data sets using encryption, anonymisation, or pseudonymisation in accordance with relevant legislation.
• Apply knowledge and understanding to uphold and adhere to principles of beneficence and informed consent in research and professional work involving human subjects.
• Undertake research having obtained ethical clearance from a Research Ethics Committee to undertake research.

Associated Assessment Criteria for Exit Level Outcome 8

• Interpret software output and model results with an appropriate level of detail and precision and in a way understandable to a non-technical audience.
• Communicate and discuss analysis and research in a written format (e.g., case study or research report) in a well-structured, well-formatted, academically literate, and grammatically and stylistically sound manner.
• Present analysis and research orally in an engaging and audience-appropriate manner, with effective use of visuals (e.g., slides) and public speaking skills.
• Apply a mathematical document preparation system to effectively represent complicated mathematical expressions, quantitative output, and graphical representations in slides or a written report.

Associated Assessment Criteria for Exit Level Outcome 9

• Develop and implement a work plan and progress reports for academic and professional projects including a major year-long research project.
• Identify and access sources of academic and non-academic support required (e.g., lecturer or supervisor consultations, academic writing services at Fundani Centre for Higher Education Development).
• Collaborate successfully with peers on group projects and equitably manage workloads with the group.
• Conduct research, projects, experiments, and investigations to required standards in a substantive area within one or more of the Mathematical Sciences subdisciplines.

Associated Assessment Criteria for Exit Level Outcome 10

• Respond and adapt to feedback, including criticism, through formative and continuous assessments such as supervisor consultations and draft documents.
• Articulate the contributions and limitations of one's own work (individual or group), particularly in the case of a major research project and other smaller projects and case studies.
• Create and adhere to a budget, in the case of a project that requires financial input.

INTEGRATED ASSESSMENT

Formative assessment

Formative Assessments in this qualification will take several forms. These include lecturer-learner interactions during contact sessions, one-on-one or small-group consultations between learners and lecturer outside of class, and small tutorial tasks in which the lecturer monitors the learners' ability to replicate some problem-solving, analytical, or computational procedure demonstrated by the lecturer. They also include self-study assignments, programming exercises, and practical reports. It also may include practice versions of online tests conducted via the Blackboard e-Learning platform.

Formative assessments will include consultations with the academic supervisor and a research proposal and ethics protocol submitted to the Faculty Research Committee and Research Ethics Committee.

Summative Assessments

Summative assessments will include tests and examinations to be performed in time- and space-controlled environments. However, because of the circumstances just mentioned, such tests and examinations will need, for most modules in the course, to be conducted in computer laboratories, with submissions made electronically.

Summative assessments for this module will include an oral presentation and Q&A session with a panel of academic and professional experts and a written research or technical report.

The Research Project module will not have a summative assessment in the form of a test or exam.

In general, assessment is continuous and consists of both formative, summative and integrated elements. Assessment is aligned with the rationale, purposes, and aims of the qualification, the intended learning outcomes, and the designed and implemented curriculum, and is integral to the methodology of the teaching and learning processes.

The Final Integrated Summative Assessment task will carry a weight of 50% in each module, with the remaining 50% split between other formative and summative assessment tasks.