# Undergraduate Course List

### Mathematical Statistics Stream

Please see the Science Faculty Handbook for more information on course requirements

The aim of STA1006S is to provide students who intend to major in Mathematical Statistics with a solid foundation in the mathematical aspects of statistics required in the training of a professional statistician. The material for STA1006S places more emphasis on the theoretical and mathematical aspects of Statistics than STA1000S. As a result, the course will be taught at a much faster pace than STA1000S. The breadth and depth of the STA1006S syllabus means that the course demands from the students a hard working attitude and an effective study strategy.

STA2004F is a rigorous introduction to the foundations of mathematical statistics and aims to provide students with a deeper understanding of the statistical concepts covered in STA1006S. The course is intended for students studying mathematical or actuarial science. STA2004F is divided into two broad sections: (1) Probability and Distribution Theory and (2) Statistical Inference. During the first part of the course, students will learn to derive the distributions of random variables and their transformations, and explore the limiting behaviour of sequences of random variables. The last part of the course covers the estimation of population parameters and hypothesis testing based on a sample of data.

STA2005S consists of three sections. The first five weeks focus on the general linear model, regression theory as well as the practical application of multiple regression using R. The second five weeks cover the design and analysis of experiments (completely randomized, randomised block and latin square designs, factorial experiments, and we briefly introduce random effects). The last two weeks cover basic non-parametric statistics. The course covers the theory but there is also a strong emphasis on applying the theory to data and the analysis of data using statistical software.

STA3041F comprises two distinct sections. The first six weeks focus on Stochastic Processes; an introduction to discrete Markov chains, followed by Branching Processes, Counting of Events and Ruin Theory. In the second part of the course different methods for the analysis of Time Series are presented. These include AR processes, MA processes, ARIMA processes and a brief introduction to Garch modelling.

This third year second semester course consists of two sections:

**Decision and Risk Theory**covers the structure of decision making under uncertainty; game theory and non-probabilistic decision criteria; probabilistic decision criteria, expected value and utility; use of Bayes’ theorem; value of information; Bayesian statistical analysis for Bernoulli and normal sampling; empirical Bayes and credibility theory; loss and extreme value distributions; and the Monte Carlo method.**Generalized Linear Models**introduces the exponential family of distributions and covers the definition of a GLM, estimation and inference of GLMs, applications of GLMs to insurance and other data, including logistic, Poisson and log-linear models as well as models for continuous responses with skew distributions.

The course covers the analysis and modelling of stochastic processes. Topics include Poisson processes, Markov chains, random walks, measure theoretic probability, martingales, stopping theorems, Brownian motion, stochastic integration and Ito calculus.

### Applied Statistics Stream

Please see the Commerce Faculty Handbook for more information on course requirements

This course provides an introduction to the study of Statistics and explores some of the foundations of the discipline including exploratory data analysis, probability and probability distributions, statistical inference, tests of association and regression. Tutorials are split between classroom sessions which focus on solution of exam type problems, and computer lab sessions in which Excel is used as a platform both to explore statistical theory and to perform statistical calculations.

The objective of this course is to introduce first year students to the basic concepts of linear algebra and differential calculus. The course simplifies these concepts by covering a vast range of real life applications such as the rate of change and finding optimum solutions to linear programming problems. This course is primarily intended for EBE and Humanities students. The course outline includes Linear Algebra, differentiation, logarithmic and exponential functions, applications of differentiation, integration, linear programming and compound interest.

This course provides an introduction to the study of Statistics within a biological context and explores some of the foundations of the discipline including exploratory data analysis, probability and probability distributions, statistical inference and regression. Practical data analysis skills are taught in lab sessions that use Excel as a platform, and students will learn how to apply the statistical theory being covered in lectures to real data sets. These skills will be important and relevant to students when they need to analyse data for research projects in other courses.

Exploratory data analysis and summary statistics. Probability theory. Random variables. Probability mass and density functions. Binomial, Poisson, exponential, normal and uniform distributions. Sampling distributions. Confidence intervals. Introduction to hypothesis testing. Tests on means, variances and proportions. Determining sample size. Simple linear regression and measures of correlation.

Functions and graphs: straight lines, polynomials, exponential and logarithmic functions; Differential calculus; The Mathematics of Finance; Matrix algebra; Linear Programming; Binomial Theorem. Emphasis will be placed on areas of interest to Commerce students, including applications to Economics.

The course aims to equip students with practical experience and skills in analysing data, using some statistical techniques frequently used in the sciences. The skills include designing experiments, choosing appropriate statistical methods for visual display and statistical modelling of data, model checking, interpretation and reporting of statistical results, and understanding limitations of statistical methods and data. By the end of the course the student should have gained enough confidence to transfer these skills to new problems or data sets in their own profession.

This course is designed to extend the student’s basic statistical knowledge, acquired in STA1000F/S. Applied techniques which have direct application in all the management functional areas such as Marketing, Finance, Production, Human Resource Management and Information Systems will be addressed. Students will be introduced to analysis of variance, simple and multiple regression, model building, time series analysis and non-parametric techniques. Students will continue to analyze data using Excel.

This course explores some aspects of probability theory that are particularly relevant to statistics. Such aspects include the notions of random variable, joint probability distributions, expected values and moment generating functions, just to mention a few. The course also intends to familiarize students with statistical data analysis techniques such as the Chi-square test of independence and the Matched-pairs designs. The course outline includes univariate distributions and moments of univariate distributions, moments of bivariate distributions, distributions of sample statistics and regression analysis.

STA3022F covers the application of multivariate statistical techniques. These have the aim of uncovering relationships between two or more variables. Students are exposed to a wide range of methods, including many of the most popular methods currently used in industry and general research. The focus of the course is on practical application and interpretation of results from these methods, rather than the underlying theory. Extensive use is made of examples and students are given practical training on applying the methods using statistical software.

STA3030F provides a thorough introduction to the underlying principles of inferential statistics. Inference lies at the heart of statistical thinking. It provides a systematic approach for assessing how uncertainty introduced by sampling affects our ability to make meaningful statements about a range of phenomena. Since much of scientific and business research is based on experimenting with or observing a sample, statistical inference has become, to a large extent, the workhorse of modern research. The focus of the course is on providing students with a greater depth of understanding about standard inferential tools - confidence intervals, hypothesis testing, and parameter estimation - that were covered in earlier courses.

This course is an introduction to the study of Operations Research and explores some of the fundamental quantitative techniques in the Operations Research armamentarium. The course is intended for students in the applied statistics stream but may be taken as an elective by students in the mathematical statistics stream. The course is divided into four major sections: Mathematical programming (linear and non-linear programming to find optimal solutions to objectives subject to a series of constraints), Computer Simulation (mimicking the operation of real world systems as they evolve over time), Decision-making under uncertainty (exploration of decision rules and tools) and Forecasting using time series. The course is a very fun and practical one and exposes students in statistics to other practical applications of mathematics.

## Contact Us

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University of Cape Town