| Code | Faculty | Department |
|---|---|---|
| 02133395 | Faculty of Natural and Agricultural Sciences | Department: Mathematics and Applied Mathematics |
| Credits | Duration | NQF level |
|---|---|---|
| Minimum duration of study: 3 years | Total credits: 434 | NQF level: 07 |
Important information for all prospective students for 2022
Transferring students
A transferring student is a student who, at the time of application for a degree programme at the University of Pretoria (UP) –
A transferring student will be considered for admission based on
Note: Students who have been dismissed at the previous institution due to poor academic performance, will not be considered for admission to UP.
Returning students
A returning student is a student who, at the time of application for a degree programme –
A returning student will be considered for admission based on
Note: Students who have been excluded/dismissed from a faculty due to poor academic performance may be considered for admission to another programme at UP. The Admissions Committee may consider such students if they were not dismissed more than twice. Only ONE transfer between UP faculties will be allowed, and a maximum of two (2) transfers within a faculty.
Important faculty-specific information on undergraduate programmes for 2022
University of Pretoria website: click here
Minimum requirements | ||
Achievement level | ||
English Home Language or English First Additional Language | Mathematics | APS |
NSC/IEB | NSC/IEB | |
5 | 7 | 36 |
Candidates who do not comply with the minimum admission requirements for BSc (Actuarial and Financial Mathematics), may be considered for admission to the BSc – Extended programme – Mathematical Sciences, which requires an additional year of study.
Please note: Progression from the BSc – Extended programme – Mathematical Sciences to the mathematics-intensive programmes will be considered only if students obtained a GPA of 65% in their first-year modules. Students who pass all first-year modules will be advised on alternative academic pathways.
In addition, admission into the BSc (Actuarial and Financial Mathematics) programme will only be considered if students have passed IAS 111 and achieved a minimum mark of 60% in WTW 153 and WST 153.
BSc – Extended Programme – Mathematical Sciences Minimum requirements | ||
Achievement level | ||
English Home Language or English First Additional Language | Mathematics | APS |
NSC/IEB | NSC/IEB | |
4 | 5 | 28 |
Note:
*The BSc – Extended programmes are not available for students who meet all the requirements for the corresponding mainstream programme.
*Please note that only students who apply in their final NSC or equivalent qualification year will be considered for admission into any of the BSc – Extended programmes.
Transfer to the BSc (Actuarial and Financial Mathematics) degree programme
Transfers to the BSc (Actuarial and Financial Mathematics) degree are considered on application. Applications are handled by Student Administration and you should contact them ([email protected]). Applications are not considered during the year, but at the start of each year once the complete academic record for the previous year is available. Applications are generally approved when students meet the requirements specified below. Final admission in all cases is dependent on the capacity of the programme.
Transfer from BSc (Mathematical Statistics) 02133274
Students who have enrolled for the full set of prescribed first year modules for the BSc (Actuarial and Financial Mathematics) degree as part of their BSc (Mathematical Statistics) degree and passed them all outright in one year, will be allowed to transfer at the end of their first year. A dropped subject is considered a fail. Failing a subject and passing it at a Winter or Summer school is also considered a fail. Passing modules with supplementary examinations or very low exam marks are warning signals and a transfer will not be allowed. Students who fall in this category will be allowed to transfer at the end of their second year of study, if they have completed all the prescribed modules for the first and second year of the BSc (Actuarial and Financial Mathematics) in two years.
Transfer from BSc Extended programme – Mathematical Sciences 02130016
In terms of the yearbook, “Admissions from the BSc – Extended programmes to the BSc (Actuarial and Financial Mathematics) programmes will only be considered if students have passed all their first-year modules with an average percentage of at least 60%, passed IAS 111 and achieved a minimum percentage of 60% for WTW 143 and WTW 153.” Note that the admission requirements for IAS 111 and FBS 112 are 60% for each of the first year Mathematics and Mathematical Statistics modules i.e. WTW 133, WTW 143, WST 133 and WST 143.
Transfers from other programmes not included above
Students who meet the grade 12 admission requirements for BSc (Actuarial and Financial Mathematics) are considered. The student’s complete tertiary academic record will be considered. The student should have taken and passed the full credit load in the previous degree for the time the student spent doing that degree. Failed and/or dropped modules will normally disqualify a student from transferring.
Further queries not resolved by the above information, contact the department by sending an email outlining your query with your name and student number to [email protected].
1.1 Requirements for specific modules
A candidate who:
or
or
1.2 Fundamental modules
A student will be promoted to the following year of study if he or she passed 100 credits of the prescribed credits for a year of study, unless the Dean on the recommendation of the relevant head of department decides otherwise. A student who does not comply with the requirements for promotion to the following year of study, retains the credit for the modules already passed and may be admitted by the Dean, on recommendation of the relevant head of department, to modules of the following year of study to a maximum of 48 credits, provided that it will fit in with both the lecture and examination timetable.
General promotion requirements in the faculty
All students whose academic progress is not acceptable can be suspended from further studies.
Minimum credits: 146
Fundamental = 14
Core = 132
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:
The module aims to equip students with the ability to cope with the reading and writing demands of scientific disciplines.
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:
*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:
Professionalism, working in multicultural environments, self-development, propositional logic, financial needs.
Module content:
Financial service providers, investment examples including an introduction to mathematics of finance, life insurance examples including an introduction to contingencies, general insurance examples including an introduction to reserving using run-off triangles, personal self-development.
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:
*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:
Non-linear equations, numerical integration, initial value problems for differential equations, systems of linear equations. Algorithms for elementary numerical techniques are derived and implemented in computer programmes. Error estimates and convergence results are treated.
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.
Module content:
The module serves as an introduction to computer programming as used in science. Modelling of dynamical processes using difference equations; curve fitting and linear programming are studied. Applications are drawn from real-life situations in, among others, finance, economics and ecology.
Minimum credits: 144
Core = 132
Elective = 12
Additional information:
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:
Fundamentals of survival models, select and ultimate life tables, Assurance and annuity functions, basic calculation of premiums and reserves, principles of pricing and reserving.
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:
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:
*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.
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:
Abstract vector spaces, change of basis, matrix representation of linear transformations, orthogonality, diagonalisability of symmetric matrices, some applications.
Minimum credits: 144
Core = 108
Elective = 36
There are two options for electives. Students should select electives according to one of the options.
1. Actuarial Science option: IAS 353, IAS 382
Students who want to try to obtain the maximum possible exemptions from the Actuarial Society examinations, and who meet the prerequisites, should select the Actuarial Science option.
2. Financial Mathematics option: WTW 310, and one of the following modules WTW 320, WTW 382
Students who want to complete the BSc (Actuarial and Financial Mathematics) degree, but are considering an honours degree in Mathematics, should in addition to the Financial Mathematics option take the module WTW 381 for non-degree purposes.
Students who want to complete the BSc (Actuarial and Financial Mathematics) degree, but are considering an honours degree in Applied Mathematics, should take the Financial Mathematics option with any two of the modules WTW 382, WTW 383, WTW386, with one of them for non-degree purposes.
Students who want to complete the BSc (Actuarial and Financial Mathematics) degree, but are considering an honours degree in Mathematical Statistics, should take in addition to either option STK 353 for non-degree purposes.
Students who would like to continue with any of the alternative above-mentioned honours degrees without taking additional credits can switch to the respective undergraduate programme during their third year. Students should note that they still qualify for exemptions from the Actuarial Society subjects if they switch to one of the alternative degrees.
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:
Note: Only one of the modules WST 321 or STK 320 may be included in any study programme.
Stationary and non-stationary univariate time-series. Properties of autoregressive moving average (ARMA) and autoregressive integrated moving average (ARIMA) processes. Identification, estimation and diagnostic testing of a time-series model. Forecasting. Multivariate time-series. Practical statistical modelling and analysis using statistical computer packages, including that of social responsibility phenomena.
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:
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:
Discrete time financial models: Arbitrage and hedging; the binomial model. Continuous time financial models: The Black-Scholes formula; pricing of options and the other derivatives; interest rate models; numerical procedures.
Module content:
Annuities and assurances involving one or two lives, life tables, Calculating premiums and reserves allowing for fixed or variable benefits and premiums, competing risks, profit testing.
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:
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:
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:
Conservation laws and modelling. Fourier analysis. Heat equation, wave equation and Laplace's equation. Solution methods including Fourier series. Energy and other qualitative methods.
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