| Code | Faculty | Department |
|---|---|---|
| 07130264 | Faculty of Economic and Management Sciences | Department: Statistics |
| Credits | Duration | NQF level |
|---|---|---|
| Minimum duration of study: 3 years | Total credits: 398 | NQF level: 07 |
Statistics is an independent discipline with interdisciplinary applications. The aim of this programme is to prepare the candidates in totality with methods that can be applied for the gathering and interpretation of data and empirical information. Statistics lay the foundation for scientific accountable conclusions, planning and estimation. Candidates are equipped detailed computer and communication skills throughout the course. Statistics is commissioned by all disciplines where it can contribute towards scientific and technological progress, most notably in data science. This qualification trains a statistician to work in a data science environment.
Students who achieved 70% and above in English Home Language (an A or a B), and 80% and above in English First Additional Language (only an A) in the NSC (or equivalent) will be exempted from ALL 124 and therefore do not have to register and pass this module to complete their degrees. Students who achieved 69% and below in English Home Language (a C and below), and 79% and below in English First Additional Language (a B and below) have to register for ALL 124 and will have to pass this module in order to be awarded their degrees.
Students who achieved 70% for English at Cambridge A level or AS level will be exempted from ALL 124.
Important information for all prospective students for 2023
The admission requirements below apply to all who apply for admission to the University of Pretoria with a National Senior Certificate (NSC) and Independent Examination Board (IEB) qualifications. Click here for this Faculty Brochure.
Minimum requirements | ||
Achievement level | ||
English Home Language or English First Additional Language | Mathematics | APS |
NSC/IEB | NSC/IEB | |
5 | 5 | 32 |
Life Orientation is excluded when calculating the APS.
You will be considered for final admission to degree studies if space allows, and if you have a National Senior Certificate (NSC) or equivalent qualification with admission to bachelor’s degree studies, and comply with the minimum subject requirements as well as the APS requirements of your chosen programme.
Applicants with qualifications other than the abovementioned should refer to the Brochure: Undergraduate Programme Information 2023: Qualifications other than the NSC and IEB, available at click here.
International students: Click here.
Transferring students
A transferring student is a student who, at the time of applying at the University of Pretoria (UP) is/was a registered student at another tertiary institution. A transferring student will be considered for admission based on NSC or equivalent qualification and previous academic performance. Students who have been dismissed from other institutions due to poor academic performance will not be considered for admission to UP.
Closing dates: Same as above.
Returning students
A returning student is a student who, at the time of application for a degree programme is/was a registered student at UP, and wants to transfer to another degree at UP. A returning student will be considered for admission based on NSC or equivalent qualification and previous academic performance.
Note:
Closing date for applications from returning students
Unless capacity allows for an extension of the closing date, applications from returning students must be submitted before the end of August via your UP Student Centre.
General Academic Regulations G1 to G15 apply to a bachelor's degree.
With regard to choosing elective modules:
It is recommended that COS 132 be taken as an elective by all students in this programme. Students can then follow one of the following elective options depending on their specific career requirements. Other options are possible subject to consultation with and approval by the programme coordinator.
1. Mathematical Statistics option with major WST 111, WST 121, WST 211, WST 221, WST 212, WST 311, WST 312, (WST 321 or STK 320), STK 353:
Year 1: WTW 114 (16), WTW 124 (16)
Year 2: WTW 211 (12), WTW 218 (12) and WTW 220 (12), WTW 221 (12), WTW 264 (12), WTW 248 (12) or three from EKN 214 (16), EKN 234 (16), EKN 224 (16), EKN 244 (16)
Year 3: Choose three from WTW 310 (18), WTW 382 (18), WTW 354 (18), WTW 364 (18), WTW 381 (18), WTW 389 (18), WTW 320 (18), WST322 (18), EKN 310 (20), EKN 315 (20), EKN 320 (20), EKN 325 (20).
2. Mathematics option with major STK 110, STC 122, STK 210, STK 220, WST 212, STK 310, STK 320, STK 353:
Year 1: WTW 114 (16), WTW 124 (16)
Year 2: WTW 218 (12), WTW 211 (12), WTW 220 (12), WTW 221 (12), WTW 264 (12), WTW 248 (12)
Year 3: Choose four from WTW 310 (18), WTW 382 (18), WTW 381 (18), WTW 389 (18), WTW 320 (18)
3. Economics option with major STK 110, STC 122, STK 210, STK 220, WST212, STK 310, STK 320, STK 353:
Year 1: COS 132 (16), COS 122 (16) or INF 154 (10), INF 164 (10), INF 171 (20)
Year 2: EKN 214 (16), EKN 234 (16), EKN 224 (16), EKN 244 (16), INF 261 (7), INF 264 (8)
Year 3: Choose three from EKN 310 (20), EKN 315 (20), EKN 320 (20), EKN 325 (20)
4. Informatics option with major STK 110, STC 122, STK 210, STK 220, WST 212, STK 310, STK 320, STK 353:
Year 1: INF 154 (10), INF 164 (10), INF 171 (20)
Year 2: INF 272 (16), INF 225 (14), INF 261 (14), INF 214 (14), INF 271 (14)
Year 3: Choose 65 credits from INF 315 (15), INF 324 (15), INF 354 (15), INF 370 (35). Note that INF 370 and INF354 must be selected together.
5. Investment Management option with major STK 110, STC 122, STK 210, STK 220, WST 212, STK 310, STK 320, STK3 53:
Year 1: FRK 121 (12) + choose at least 29 credits from COS 132 (16), COS 122 (16), INF 112 (10), INF 154 (10), INF 164 (10), WTW 114 (16), WTW 124 (16)
Year 2: BAC 200 (32), EKN 214 (16), IVM 200 (32)
Year 3: BAC 310 (20), IVM 300 (40)
Note: Please refer to the individual modules for prerequisites.
At least one of the two elective disciplines in which a candidate graduate must be selected from the available disciplines within the Economics and Management Sciences Faculty.
FRK 122 is a terminating module. Candidates will not be able to continue with financial accounting in the second or third year. A student cannot get credits for both FRK 121 and FRK 122.
Specialisation modules: WST 212, STK 310, 320, 353 or WST 212, 311, 312, 321, STK 353.
"Major subject"
To be considered a "major subject" the equivalent of four 14-week modules, including two at 300-level, must be passed provided that:
It is thus the responsibility of students to ensure before registration, that their curricula comply with all the requirements of the applicable regulations.
According to General Academic Regulation G3 students have to comply with certain requirements as set by the Faculty Board.
Application of amended programme regulations
Refer to General Academic Regulation G5.
University of Pretoria Programme Qualification Mix (PQM) verification project
The higher education sector has undergone an extensive alignment to the Higher Education Qualification Sub-Framework (HEQF) across all institutions in South Africa. In order to comply with the HEQSF, all institutions are legally required to participate in a national initiative led by regulatory bodies such as the Department of Higher Education and Training (DHET), the Council on Higher Education (CHE), and the South African Qualifications Authority (SAQA). The University of Pretoria is presently engaged in an ongoing effort to align its qualifications and programmes with the HEQSF criteria. Current and prospective students should take note that changes to UP qualification and programme names, may occur as a result of the HEQSF initiative. Students are advised to contact their faculties if they have any questions.
Minimum credits: 137
Please note this degree is a specialization in Statistics and Data Science.
University of Pretoria Programme Qualification Mix (PQM) verification project
The higher education sector has undergone an extensive alignment to the Higher Education Qualification Sub-Framework (HEQF) across all institutions in South Africa.
In order to comply with the HEQSF, all institutions are legally required to participate in a national initiative led by regulatory bodies such as the Department of Higher Education and Training (DHET), the Council on Higher Education (CHE), and the South African Qualifications Authority (SAQA).
The University of Pretoria is presently engaged in an ongoing effort to align its qualifications and programmes with the HEQSF criteria.
Current and prospective students should take note that changes to UP qualification and programme names may occur as a result of the HEQSF initiative. Students are advised to contact their faculties if they have any questions.
Module content:
Find, evaluate, process, manage and present information resources for academic purposes using appropriate technology.
Module content:
Apply effective search strategies in different technological environments. Demonstrate the ethical and fair use of information resources. Integrate 21st-century communications into the management of academic information.
Module content:
This module is intended to equip students with the competence in reading and writing required in the four high impact modules: Business Management, Financial Accounting, Statistics and Economics. Students will also be equipped to interpret and draw figures and graphs and to do computations and manage relevant formulas. Students attend two lectures per week during semester two.
This module is offered by the Faculty of Humanities.
Module content:
This module deals with the core principles of economics. A distinction between macroeconomics and microeconomics is made. A discussion of the market system and circular flow of goods, services and money is followed by a section dealing with microeconomic principles, including demand and supply analysis, consumer behaviour and utility maximisation, production and the costs thereof, and the different market models and firm behaviour. Labour market institutions and issues, wage determination, as well as income inequality and poverty are also addressed. A section of money, banking, interest rates and monetary policy concludes the course.
Module content:
This module deals with the core principles of economics, especially macroeconomic measurement the private and public sectors of the South African economy receive attention, while basic macroeconomic relationships and the measurement of domestic output and national income are discussed. Aggregate demand and supply analysis stands core to this course which is also used to introduce students to the analysis of economic growth, unemployment and inflation. The microeconomics of government is addressed in a separate section, followed by a section on international economics, focusing on international trade, exchange rates and the balance of payments. The economics of developing countries and South Africa in the global economy conclude the course.
Module content:
The nature and function of accounting; the development of accounting; financial position; financial result; the recording process; processing of accounting data; treatment of VAT; elementary income statement and balance sheet; flow of documents; accounting systems; introduction to internal control and internal control measures; bank reconciliations; control accounts; adjustments; financial statements of a sole proprietorship; the accounting framework.
Module content:
Property, plant and equipment; intangible assets; inventories; liabilities; presentation of financial statements; enterprises without profit motive; partnerships; companies; close corporations; cash flow statements; analysis and interpretation of financial statements.
Module content:
Budgeting, payroll accounting, taxation – income tax and an introduction to other types of taxes, credit and the new Credit Act, insurance, accounting for inventories (focus on inventory and the accounting entries, not calculations), interpretation of financial statements.
Module content:
The entrepreneurial mind-set; managers and managing; values, attitudes, emotions, and culture: the manager as a person; ethics and social responsibility; decision making; leadership and responsible leadership; effective groups and teams; managing organizational structure and culture inclusive of the different functions of a generic organisation and how they interact (marketing; finance; operations; human resources and general management); contextualising Sustainable Development Goals (SDG) in each of the topics.
Module content:
Value chain management: functional strategies for competitive advantage; human resource management; managing diverse employees in a multicultural environment; motivation and performance; using advanced information technology to increase performance; production and operations management; financial management; corporate entrepreneurship.
Module content:
Inferential concepts. Experimental and observational data. Measures of association, uncertainty and goodness of fit. Sampling error and accuracy of estimation. Introduction to linear regression, reduction of variation due to regression. Conditional distributions of residuals. Simulation based inference: conditional means and prediction intervals. Bivariate data visualisation. Supporting mathematical concepts. Statistical concepts are demonstrated and interpreted through practical coding and simulation within a data science framework.
This module is also presented as a summer school for students who initially elected and passed STK 120 with a final mark of at least 60% and then decides to further their studies in statistics as well as for students who achieved a final mark of between 40% - 49% in STC 122 during semester 2.
Module content:
Descriptive statistics:
Sampling and the collection of data; frequency distributions and graphical representations. Descriptive measures of location and dispersion.
Probability and inference:
Introductory probability theory and theoretical distributions. Sampling distributions. Estimation theory and hypothesis testing of sampling averages and proportions (one and two-sample cases). Supporting mathematical concepts. Statistical concepts are demonstrated and interpreted through practical coding and simulation within a data science framework.
Module content:
Characterisation of a set of measurements: Graphical and numerical methods. Random sampling. Probability theory. Discrete and continuous random variables. Probability distributions. Generating functions and moments.
Module content:
Sampling distributions and the central limit theorem. Statistical inference: Point and interval estimation. Hypothesis testing with applications in one and two-sample cases. Introductory methods for: Linear regression and correlation, analysis of variance, categorical data analysis and non-parametric statistics. Identification, use, evaluation and interpretation of statistical computer packages and statistical techniques.
Module content:
Fundamental concepts of modern operating systems in terms of their structure and the mechanisms they use are studied in this module. After completing this module, students will have gained, as outcomes, knowledge of real time, multimedia and multiple processor systems, as these will be defined and analysed. In addition, students will have gained knowledge on modern design issues of process management, deadlock and concurrency control, memory management, input/output management, file systems and operating system security. In order to experience a hands-on approach to the knowledge students would have gained from studying the abovementioned concepts, students will have produced a number of practical implementations of these concepts using the Windows and Linux operating systems.
Module content:
This module introduces imperative computer programming, which is a fundamental building block of computer science. The process of constructing a program for solving a given problem, of editing it, compiling (both manually and automatically), running and debugging it, is covered from the beginning. The aim is to master the elements of a programming language and be able to put them together in order to construct programs using types, control structures, arrays, functions and libraries. An introduction to object orientation will be given. After completing this module, the student should understand the fundamental elements of a program, the importance of good program design and user-friendly interfaces. Students should be able to conduct basic program analysis and write complete elementary programs.
Module content:
*Only for students in BSc (Actuarial and Financial Mathematics), BSc (Mathematics), BSc (Applied Mathematics), BSc (Mathematical Statistics), BSc Extended programme – Mathematical Sciences and BCom (Statistics) who comply with the set prerequisites.
Key principles of financial management. Company ownership. Taxation. Introduction to financial statements. Structure of financial statements. Depreciation and reserves. Preparing financial statements. Group financial statements and insurance company financial statements. Interpretation of financial statements. Limitation of financial statements. Issue of share capital.
Module content:
Financial instruments. Use of financial derivatives. Financial institutions. Time value of money. Component cost of capital. Weighted average cost of capital. Capital structure and dividend policy. Capital project appraisal. Evaluating risky investments.
Module content:
Introduction to information systems, information systems in organisations, hardware: input, processing, output, software: systems and application software, organisation of data and information, telecommunications and networks, the Internet and Intranet. Transaction processing systems, management information systems, decision support systems, information systems in business and society, systems analysis, systems design, implementation, maintenance and revision.
Module content:
General systems theory, creative problem solving, the business analyst, systems development building blocks, systems analysis methods, process modelling and data modelling.
Module content:
*This module serves as preparation for students majoring in Mathematics (including all students who intend to enrol for WTW 218 and WTW 220). Students will not be credited for more than one of the following modules for their degree: WTW 114, WTW 158, WTW 134, WTW 165.
Functions, limits and continuity. Differential calculus of single variable functions, rate of change, graph sketching, applications. The mean value theorem, the rule of L'Hospital. Definite and indefinite integrals, evaluating definite integrals using anti-derivatives, the substitution rule.
Module content:
*Students will not be credited for more than one of the following modules for their degree:
WTW 124, WTW 146, WTW 148 and WTW 164. This module serves as preparation for students majoring in Mathematics (including all students who intend to enrol for WTW 218, WTW 211 and WTW 220).
The vector space Rn, vector algebra with applications to lines and planes, matrix algebra, systems of linear equations, determinants. Complex numbers and factorisation of polynomials. Integration techniques and applications of integration. The formal definition of a limit. The fundamental theorem of Calculus and applications. Vector functions and quadratic curves.
Minimum credits: 129
Please note this degree is a specialization in Statistics and Data Science.
University of Pretoria Programme Qualification Mix (PQM) verification project
The higher education sector has undergone an extensive alignment to the Higher Education Qualification Sub-Framework (HEQF) across all institutions in South Africa.
In order to comply with the HEQSF, all institutions are legally required to participate in a national initiative led by regulatory bodies such as the Department of Higher Education and Training (DHET), the Council on Higher Education (CHE), and the South African Qualifications Authority (SAQA).
The University of Pretoria is presently engaged in an ongoing effort to align its qualifications and programmes with the HEQSF criteria.
Current and prospective students should take note that changes to UP qualification and programme names may occur as a result of the HEQSF initiative. Students are advised to contact their faculties if they have any questions.
Module content:
*Module content will be adapted in accordance with the appropriate degree programme. Only one of KOB 281– 284 may be taken as a module where necessary for a programme.
Applied business communication skills
Acquiring basic business communication skills will enhance the capabilities of employees, managers and leaders in the business environment. An overview of applied skills on the intrapersonal, dyadic, interpersonal, group (team), organisational, public and mass communication contexts is provided. The practical part of the module (for example, the writing of business reports and presentation skills) concentrates on the performance dimensions of these skills as applied to particular professions.
Module content:
Statistical problem solving. Causality, experimental and observational data. Probability theory. Multivariate random variables. Discrete and continuous probability distributions. Stochastic representations. Measures of association. Expected values and conditional expectation. Simulation techniques. Supporting mathematical concepts. Statistical concepts are demonstrated and interpreted through practical coding and simulation within a data science framework.
Module content:
Multivariate probability distributions. Sampling distributions and the central limit theorem. Frequentist and Bayesian inference. Statistical learning and decision theory. Simulation techniques enhancing statistical thinking. Supervised learning: linear regression, estimation and inference. Non-parametric modelling. Supporting mathematical concepts. Statistical algorithms. Statistical concepts are demonstrated and interpreted through practical coding and simulation within a data science framework.
Module content:
Set theory. Probability measure functions. Random variables. Distribution functions. Probability mass functions. Density functions. Expected values. Moments. Moment generating functions. Special probability distributions: Bernoulli, binomial, hypergeometric, geometric, negative binomial, Poisson, Poisson process, discrete uniform, uniform, gamma,exponential, Weibull, Pareto, normal. Joint distributions: Multinomial, extended hypergeometric, joint continuous distributions. Marginal distributions. Independent random variables. Conditional distributions. Covariance, correlation. Conditional expected values. Transformation of random variables: Convolution formula. Order statistics. Stochastic convergence: Convergence in distribution. Central limit theorem. Practical applications. Practical statistical modelling and analysis using statistical computer packages and the interpretation of the output.
Module content:
Introductory machine learning concepts. Data base design and use. Data preparation and extraction. Statistical modelling using data base structures. Statistical concepts are demonstrated and interpreted through practical coding and simulation within a data science framework.
Module content:
Stochastic convergence: Asymptotic normal distributions, convergence in probability. Statistics and sampling distributions: Chi-squared distribution. Distribution of the sample mean and sample variance for random samples from a normal population. T-distribution. F-distribution. Beta distribution. Point estimation: Method of moments. Maximum likelihood estimation. Unbiased estimators. Uniform minimum variance unbiased estimators. Cramer-Rao inequality. Efficiency. Consistency. Asymptotic relative efficiency.
Bayes estimators. Sufficient statistics. Completeness. The exponential class. Confidence intervals. Test of statistical hypotheses. Reliability and survival distributions. Practical applications. Practical statistical modelling and analysis using statistical computer packages and the interpretation of the output.
Module content:
To use a conceptual understanding of intermediate foundational knowledge of International Financial Reporting Standards (IFRS) in order to prepare, present and interpret company and basic group company financial statements in a familiar business context and to propose clear solutions with adequate justification to solve financial problems in an ethical manner.
Module content:
Macroeconomics
From Wall and Bay Street to Diagonal Street: a thorough understanding of the mechanisms and theories explaining the workings of the economy is essential. Macroeconomic insight is provided on the real market, the money market, two market equilibrium, monetarism, growth theory, cyclical analysis, inflation, Keynesian general equilibrium analysis and fiscal and monetary policy issues.
Module content:
Microeconomics
Microeconomic insight is provided into: consumer and producer theory, general microeconomic equilibrium, Pareto-optimality and optimality of the price mechanism, welfare economics, market forms and the production structure of South Africa. Statistic and econometric analysis of microeconomic issues.
Module content:
Macroeconomics
Application of the principles learned in EKN 214 on the world we live in. We look at international markets and dynamic macroeconomic models, and familiarise the students with the current macroeconomic policy debates. We also take a look at the latest macroeconomic research in the world. The course includes topics of the mathematical and econometric analysis of macroeconomic issues.
Module content:
Microeconomics
From general equilibrium and economic welfare to uncertainty and asymmetric information. In this module we apply the principles learned in EKN 224 on the world around us by looking at the microeconomic principles of labour and capital markets, as well as reasons why the free market system could fail. We touch on the government’s role in market failures. The course includes topics of the mathematical and econometric analysis of microeconomic issues.
Module content:
In this module students are equipped with an understanding of the moral issues influencing human agency in economic and political contexts. In particular philosophy equips students with analytical reasoning skills necessary to understand and solve complex moral problems related to economic and political decision making. We demonstrate to students how the biggest questions concerning the socio-economic aspects of our lives can be broken down and illuminated through reasoned debate. Examples of themes which may be covered in the module include justice and the common good, a moral consideration of the nature and role of economic markets on society, issues concerning justice and equality, and dilemmas of loyalty. The works of philosophers covered may for instance include that of Aristotle, Locke, Bentham, Mill, Kant, Rawls, Friedman, Nozick, Bernstein, Dworkin, Sandel, Walzer, and MacIntyre.
Module content:
Principles of actuarial modelling, cash-flow models, the time value of money, interest rates, discounting and accumulating, level annuities, deferred and increasing annuities, equations of value.
Module content:
Principles of actuarial modelling, cash-flow models, the time value of money, interest rates, discounting and accumulating, level annuities, deferred and increasing annuities, equations of value, loan schedules, project appraisal, elementary compound interest problems, term structure of interest rates.
Module content:
Database design: the relational model, structured query language (SQL), entity relationship modelling, normalisation, database development life cycle; practical introduction to database design. Databases: advanced entity relationship modelling and normalisation, object-oriented databases, database development life cycle, advanced practical database design.
Module content:
Database management: transaction management, concurrent processes, recovery, database administration: new developments: distributed databases, client-server databases: practical implementation of databases.
Module content:
Foundation of databases and query languages which are relevant to the application of information systems within a business environment.
Module content:
Systems analysis. Systems design: construction; application architecture; input design; output design; interface design; internal controls; program design; object design; project management; system implementation; use of computer-aided development tools.
Module content:
*Only for BCom (Investment Management) students and BCom (Statistics and Data Science) .
Functioning of the South African financial system, interest bearing instruments: issuers, institutions and valuation, types of risk and measuring risk, types of return and measuring return, share markets, Financial Market regulation, trading activities in the equity market, share price indices, valuation of ordinary shares, and the fundamental analysis of ordinary shares, industry analysis, technical analysis of shares, investment objectives and investment process, asset allocation, local and international bond markets, bond fundamentals, valuation of bonds, mathematics of fixed interest securities, structure of interest rates and yield curves, duration, convexity introduction to derivatives.
Module content:
Introduction to the world of agricultural economics: where to find practising agricultural economics services, overview of South African Agricultural Economy, scope of agricultural economics. Introduction to consumption and demand: utility theory, indifference curves, the budget constraint, consumer equilibrium, the law of demand, consumer surplus, tastes and preferences, and measurement and interpretation of elasticities. Introduction to production and supply: condition for perfect competition, classification of inputs, important production relationships, assessing short-run business costs, economics of short-run decisions. Isoquants, iso-cost line, least cost combination of inputs, long-run expansion of inputs, and economics of business expansion, production possibility frontier, iso-revenue line and profit maximising combination of products. Introduction to market equilibrium and product prices: market equilibrium in a perfectly competitive market, total economic surplus, changes in welfare, adjustments to market equilibrium, market structure characteristics, market equilibrium in a imperfectly competitive market, government regulatory measures. Introduction to financial management in agriculture: Farm management and agricultural finance, farm management information; analysis and interpretation of farm financial statements; risk and farm planning. Budgets: partial, break-even, enterprise, total, cash flow and capital budgets. Elements of business plan, marketing planning and price risk. Financial structuring and sources of finance for farm business. Time value of money.
Module content:
The agribusiness system; the agricultural value chain, the unique characteristics of agricultural products; marketing functions and costs; historical evolution of agricultural marketing in South Africa. The marketing environment. Consumer behaviour and consumer trends. Introduction to supply and demand analysis. Developing a marketing plan and strategies for agricultural commodities; market analysis; product management; distribution channels for agricultural commodities, the agricultural supply chain. Introduction to the agricultural futures market. Marketing in the 21st century. Online marketing, social media. Market structure.
Module content:
This is an introduction to linear algebra on Rn. Matrices and linear equations, linear combinations and spans, linear independence, subspaces, basis and dimension, eigenvalues, eigenvectors, similarity and diagonalisation of matrices, linear transformations.
Module content:
Calculus of multivariable functions, directional derivatives. Extrema and Lagrange multipliers. Multiple integrals, polar, cylindrical and spherical coordinates.
Module content:
*This module is recommended as an elective only for students who intend to enrol for WTW 310 and/or WTW 320. Students will not be credited for more than one of the following modules for their degree: WTW 220 and WTW 224.
Properties of real numbers. Analysis of sequences and series of real numbers. Power series and theorems of convergence. The Bolzano-Weierstrass theorem. The intermediate value theorem and analysis of real-valued functions on an interval. The Riemann integral: Existence and properties of the interval.
Module content:
Abstract vector spaces, change of basis, matrix representation of linear transformations, orthogonality, diagonalisability of symmetric matrices, some applications.
Module content:
Vectors and geometry. Calculus of vector functions with applications to differential geometry, kinematics and dynamics. Vector analysis, including vector fields, line integrals of scalar and vector fields, conservative vector fields, surfaces and surface integrals, the Theorems of Green, Gauss and Stokes with applications.
Module content:
*Students will not be credited for both WTW 162 and WTW 264 or both WTW 264 and WTW 286 for their degree.
Theory and solution methods for ordinary differential equations and initial value problems: separable and linear first order equations, linear equations of higher order, systems of linear equations. Laplace transform.
Minimum credits: 132
Please note this degree is a specialization in Statistics and Data Science.
University of Pretoria Programme Qualification Mix (PQM) verification project
The higher education sector has undergone an extensive alignment to the Higher Education Qualification Sub-Framework (HEQF) across all institutions in South Africa.
In order to comply with the HEQSF, all institutions are legally required to participate in a national initiative led by regulatory bodies such as the Department of Higher Education and Training (DHET), the Council on Higher Education (CHE), and the South African Qualifications Authority (SAQA).
The University of Pretoria is presently engaged in an ongoing effort to align its qualifications and programmes with the HEQSF criteria.
Current and prospective students should take note that changes to UP qualification and programme names may occur as a result of the HEQSF initiative. Students are advised to contact their faculties if they have any questions.
Either BAC 300 or BAC 310 can be selected but not both.
INF 370 and INF 354 must be selected together.
Module content:
Supervised learning. Linear and non-linear regression. Ordinary least squares and maximum likelihood estimation. Violations of the assumptions, residual analysis. Cross validation. Statistical inference. Bootstrap inference. Supporting mathematical concepts. Statistical concepts are demonstrated and interpreted through practical coding and simulation within a data science framework.
Module content:
Stationary and non-stationary univariate time series. Properties of ARIMA processes. Identification, estimation and diagnostic testing of a time series models. Forecasting. Multivariate time series. Supervised learning: introduction to generalised linear models. Modelling of binary response variables, logistic regression. Supporting mathematical concepts. Statistical concepts are demonstrated and interpreted through practical coding and simulation within a data science framework.
Module content:
Data exploration. Data wrangling. Statistical coding. Algorithmic thinking. Sampling: basic techniques in probability, non-probability, and resampling methods. Text mining and analytics. Machine learning: classification and clustering. Statistical concepts are demonstrated and interpreted through practical coding and simulation within a data science framework.
Module content:
Multivariate statistical distributions: Moments of a distribution, moment generating functions, independence. Multivariate normal distribution: Conditional distributions, partial and multiple correlations. Distribution of quadratic forms in normal variables. Multivariate normal samples: Estimation of the mean vector and covariance matrix, estimation of correlation coefficients, distribution of the sample mean, sample covariance matrix. Principal component analysis.The linear model: Models of full rank, least squares estimators, test of hypotheses.The generalised linear model: Exponential family mean and variance, link functions, deviance and residual analysis, test statistics, log- linear and logit models. Practical applications: Practical statistical modelling and analysis using statistical computer packages and interpretation of the output.
Module content:
Definition of a stochastic process. Stationarity. Covariance stationary. Markov property. Random walk. Brownian motion. Markov chains. Chapman-Kolmogorov equations. Recurrent and transient states. First passage time. Occupation times. Markov jump processes. Poisson process. Birth and death processes. Structures of processes. Structure of the time-homogeneous Markov jump process. Applications in insurance. Practical statistical modelling, analysis and simulation using statistical computer packages and the interpretation of the output.
Module content:
BAC 300 includes both company and complex group company statements and the outcome of BAC 300 is:
To use a conceptual understanding of comprehensive and integrated foundational knowledge of International Financial Reporting Standards (IFRS), basic foundational knowledge of IFRS for small and medium-sized enterprises (IFRS for SMEs) and basic foundational knowledge of Generally Recognised Accounting Practice (GRAP), in order to proficiently prepare, present and interpret company and complex group company financial statements in an unfamiliar business context and to propose appropriate solutions with compelling justification to solve financial problems in an ethical manner.
Module content:
Public finance
Role of government in the economy. Welfare economics and theory of optimality. Ways of correcting market failures. Government expenditure theories, models and programmes. Government revenue. Models on taxation, effects of taxation on the economy. Assessment of taxation from an optimality and efficiency point of view. South African perspective on public finance.
Module content:
Poverty and inequality are among the greatest contemporary challenges of economic development in the World. This course provides an overview of different economic explanations of underdevelopment and policy options to fostering household and individual welfare. We will investigate key development issues such as poverty, inequality, migration, the role of institutions (policy and governance), among others, as they are encountered by developing countries in general and South Africa in particular. During the course, we put special emphasis on the interplay between theory and data.
Module content:
Economic analyses
Identification, collection and interpretation process of relevant economic data; the national accounts (i.e. income and production accounts, the national financial account, the balance of payments and input-output tables); economic growth; inflation; employment, unemployment, wages, productivity and income distribution; business cycles; financial indicators; fiscal indicators; social indicators; international comparisons; relationships between economic time series - regression analysis; long-term future studies and scenario analysis; overall assessment of the South African economy from 1994 onwards.
Module content:
Economic policy and development: Capita select
The course provides an introduction to growth economics and also to some topics on development economics. Firstly, historical evidence is covered and then the canonical Solow growth model and some of its empirical applications (human capital and convergence). Secondly, the new growth theory (the AK and the Romer models of endogenous growth) are covered. Some of the development topics to be covered include technology transfer, social infrastructure and natural resources.
Module content:
Survival models and the life table, estimating the lifetime distribution, proportional hazard models, the binomial and Poisson models, exposed to risk, graduation and statistical tests, methods of graduation.
Module content:
A review of current trends which are relevant to the application of information systems within a business environment.
Module content:
Application of systems analysis and design in a practical project; programming; use of computer-aided development tools.
Module content:
*Only for BCom (Investment Management) students and BCom (Statistics and Data Science).
Efficient market hypothesis, portfolio management, asset allocation, construction of efficient investment portfolios, asset pricing models (CAPM and APT), equity portfolio management strategies, performance evaluation of investment portfolios, restructuring of investment portfolios, measuring of financial risk exposure, futures market in South Africa, the use of futures contracts in financial risk management, pricing and the valuation of futures contracts, swaps and forward rate agreements, option markets in South Africa and the valuation of options, option payoffs and trading strategies, warrants and convertible securities, alternative evaluation techniques, real estate investment, venture capital, rights issues and capitalisation issues, immunisation, switching and trading strategies in the bond market, fixed income portfolio strategies, CFA Institute Code of Ethics and Standards of Professional Conduct.
Module content:
Historical evolution of South African agricultural policy. Agriculture and the state (communicating the legislative process in detail): reasons for government intervention (government and stakeholder engagement). Theoretical aspects of agricultural policy. Introduction to agricultural policy analysis. Welfare principles, pareto optimality. Macroeconomic policy and the agricultural sector. International agricultural trade (including inter-governmental communication).
Module content:
The modern food and agribusiness system. Key drivers in the global context. Whole farm planning including business planning, financial analysis and financial modelling, capital acquisition and creditworthiness, time value of money and the investment decision, Decision making in agriculture under risk and uncertain cirmumstances and risk management. Operational and strategic management. Business plan and scenario planning assignments.
Module content:
Bayes estimation. Loss distributions. Reinsurance. Risk models. Ruin theory. Credibility theory. Extreme value theory. Copulas. Practical statistical modelling and analysis using statistical computer packages.
Module content:
Topology of finite dimensional spaces: Open and closed sets, compactness, connectedness and completeness. Theorems of Bolzano-Weierstrass and Heine-Borel. Properties of continuous functions and applications. Integration theory for functions of one real variable. Sequences of functions.
Module content:
Series of functions, power series and Taylor series. Complex functions, Cauchy- Riemann equations, Cauchy's theorem and integral formulas. Laurent series, residue theorem and calculation of real integrals using residues.
Module content:
Mean variance portfolio theory. Market equilibrium models such as the capital asset pricing model. Factor models and arbitrage pricing theory. Measures of investment risk. Efficient market hypothesis. Stochastic models of security prices
Module content:
Group theory: Definition, examples, elementary properties, subgroups, permutation groups, isomorphism, order, cyclic groups, homomorphisms, factor groups. Ring theory: Definition, examples, elementary properties, ideals, homomorphisms, factor rings, polynomial rings, factorisation of polynomials. Field extensions, applications to straight-edge and compass constructions.
Module content:
Matrix exponential function: homogeneous and non-homogeneous linear systems of differential equations. Qualitative analysis of systems: phase portraits, stability, linearisation, energy method and Liapunov's method. Introduction to chaotic systems. Application to real life problems.
Module content:
Direct methods for the numerical solution of systems of linear equations, pivoting strategies. Iterative methods for solving systems of linear equations and eigenvalue problems. Iterative methods for solving systems of nonlinear equations. Introduction to optimization. Algorithms for the considered numerical methods are derived and implemented in computer programmes. Complexity of computation is investigated. Error estimates and convergence results are proved.
Module content:
Axiomatic development of neutral, Euclidean and hyperbolic geometry. Using models of geometries to show that the parallel postulate is independent of the other postulates of Euclid.
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