Department of Statistics and Operations Research Undergraduate Programmes OPERATIONS RESEARCH YEAR LEVEL 2 INTRODUCTION TO LINEAR PROGRAMMING SSOA021 Linear Programming Model: Formulation of an LP model; Graphical solution to two variable problems; the Simplex Method; the Big-M-method; the two-phase method; Concept of duality and duality theorem. Transportation model: formulation; methods of determining an initial basic feasible sol solution; procedures to determine optimal solution. Assignment problems: formulation and solutions. Network problems: formulation and solutions. 6 1 1 0 Formulate a linear programming model for a given real-life problem Solve linear programming problems using the simplex algorithm and other related methods Formulate and solve transportation and assignment problems. Formative Min Formati.ve mark for exam admission 40% Weighting towards final mark 60% Weighting towards final mark 40% Min Final mark to pass (%) 50% Lecturer: Mr RP Dikgale GAME AND DECISION THEORY SSOA022 Game Theory: Rectangular games; Graphical solution procedure; Algebraic technique; Solution by LP method. Decision Theory: Decision rules; Decision making without probabilities; Decision making with Probabilities; Decision Analysis with additional information; Utility; Decision Trees. 6 1 1 0 To formulate game theory models To solve game theory problems
To understand decision theory rules and their application to real-life problems. Formative Min Formative mark for exam admission 40% Weighting towards final mark 60% Weighting towards final mark 40% Min Final mark to pass (%) 50% Lecturer: Mr RP Dikgale YEAR LEVEL 3 STATISTICAL QUALITY CONTROL SSOA031 Quality improvement in the modern era; Statistical methods useful in quality control; Inferences about process quality; Basic methods of statistical process control; control charts for variables; control charts for attributes; univariate and multivariate process monitoring and control. Apply statistical techniques to quality control problems Make inferences about process quality Distinguish between controls charts for variables and control charts for attributes Apply univariate and multivariate techniques to monitor and control quality processes. Formative Min Formative mark for exam admission 40% Weighting towards final mark 60% Weighting towards final mark 40% Min Final mark to pass (%) 50% Lecturer: Mr TB Darikwa ADVANCED LINEAR PROGRAMMING SSOB031 Review of Linear Programming Model; Algebra of the Simplex Method; Geometry of the Simplex Method; The two-phase method; Duality and sensitivity analysis; The Revised Simplex method; Case studies.
Formulate complex linear programming models Understand and apply duality and sensitivity analysis Apply linear programming algorithms to more complex problems and case studies Apply the revised simplex algorithm to solve linear programming problems. Min Formative mark for exam admission 40% Formative Weighting towards final mark 60% Weighting towards final mark 40% Min Final mark to pass (%) 50% Lecturer: Mr SS Nkwane INTEGER PROGRAMMING SSOA032 Pure and Mixed Integer Programming models; Problem formulation; Graphical Solutions / Lattice Points; Cutting Plane Algorithms; Branch-and-Bound Algorithms; Case Studies. To model integer programming problems To apply different integer programming algorithms real-life problems. Formative Min Formative mark for exam admission 40% Weighting towards final mark 60% Weighting towards final mark 40% Min Final mark to pass (%) 50% Lecturer: Mr SS Nkwane DYNAMIC PROGRAMMING SSOB032 The Stagecoach problem; Characteristics of a Dynamic Programming Problem; Deterministic and Probabilistic Dynamic Programming Problems; Case studies.
Identify characteristics of a dynamic programming model Apply dynamic programming techniques to operations research problems. Min Formative mark for exam admission 40% Formative Weighting towards final mark 60% Weighting towards final mark 40% Min Final mark to pass (%) 50% Lecturer: Mr SS Nkwane QUEUING MODELS SSOC032 Basic Structure of Queuing Models; Examples of Real Queuing Systems; The Role of Exponential Distribution; The Birth and Death Process; The M/M/S Model and its Variations; Queuing Models Involving Non-Exponential Distributions. Identify basic structures of a queuing model. Apply queuing models to real-life problems. Formative Min Formative mark for exam admission 40% Weighting towards final mark 60% Weighting towards final mark 40% Min Final mark to pass (%) 50% Lecturer: Mr TB Darikwa
STATISTICS YEAR LEVEL 1 DESCRIPTIVE STATISTICS SSTS000 Definitions and concepts. Sources and types of data. Organizing and summarizing data; Descriptive statistics. Elementary probability theory. Counting techniques: Permutations and combinations. Random variables and probability distributions: Bernoulli, Binomial, Poisson and Normal distributions. 4 1 1 0 Students will be assessed on: Different types of data The ability to summarize the characteristics of a data or a collection of data and construct charts, graphs, tables and interpret The basic skills and knowledge of descriptive statistics The basic knowledge of sampling methods. The concepts of probability distributions Formative Min Formative mark for exam admission 40% Weighting towards final mark 60% Weighting towards final mark 40% Min Final mark to pass (%) 50% Lecturer: Mr P Moleko INTRODUCTION TO STATISTICAL INFERENCE SSTB000 Sampling distributions: t, F and Chi-square distributions. Central Limit Theorem. Estimation: point and interval; Confidence Interval for the mean, proportion and variance. Test of hypotheses: Tests for the mean, proportion and variance. Inferences about differences in two means and two proportions; One-way ANOVA. Chi-square tests. Simple linear regression and correlation. Time series analysis. Index numbers. 4 1 1 0 The students will be assessed on: The knowledge of inferential statistics procedures The estimation of parameters and interpreting test of hypothesis. The statistical problem-solving process using suitable statistical methods and drawing simple conclusions that are relevant to their original question. 5
Fitting simple linear model and check the validity of the model. Plotting a time series data, decompose into components and draw a simple conclusion Calculating different indices and interpreting index numbers. Formative Min Formative mark for exam admission 40% Weighting towards final mark 60% Weighting towards final mark 40% Min Final mark to pass (%) 50% Lecturer: Mr N Yibas INTRODUCTION TO STATISTICS SSTS011 Definitions and concepts. Sources and types of data. Organizing and summarizing data; Descriptive statistics. Elementary probability theory. Counting techniques: Permutations and combinations. Random variables and probability distributions: Bernoulli, Binomial, Poisson and Normal distributions. 4 1 1 0 Distinguish the different types of data; Organize and summarize data by using tabular and graphical methods; Compute values of different descriptive statistics; Evaluate probabilities of events; Use elementary probability distribution functions. Formative Min Formative mark for exam admission 40% Weighting towards final mark 60% Weighting towards final mark 40% Min Final mark to pass (%) 50% Lecturer: Ms A Ramalata INTRODUCTION TO STATISTICAL INFERENCE SSTS012 Sampling distributions: t, F and Chi-square distributions. Central Limit Theorem. Estimation: point and interval; Confidence Interval for the mean, proportion and variance. Test of hypotheses: Tests for the mean, proportion and variance. Inferences about differences in two means and two proportions; One-way ANOVA. Chi-square tests. Simple linear regression and correlation. Time series analysis. Index numbers. 6
4 1 1 0 Find point and interval estimates of the mean, proportion and variance; Test hypotheses on the mean, proportion and variance; Compare several means and proportions; Fit a simple linear regression model and calculate the correlation coefficient; Analyse a time series data; Calculate different indices. Min Formative mark for exam admission 40% Formative Weighting towards final mark 60% Weighting towards final mark 40% Min Final mark to pass (%) 50% Lecturer: Ms A Ramalata YEAR LEVEL 2 THEORY OF DISTRIBUTIONS SSTA021 Basic probability concepts. Theory of discrete and continuous probability distributions. Expected values and MGF. Special discrete and continuous probability distributions: Bernoulli, Binomial, Hypergeometric, Geometric, Poisson and Negative Binomial, Uniform, Gamma, Exponential, Weibull, Pareto and Normal distributions. Theory of multivariate discrete and continuous distributions, marginal and conditional distributions. Covariance and correlation. Theory of conditional expectation and conditional variance. Distributions of random functions: distribution function, transformation and MGF techniques. 6 1 1 0 Know the basic concepts of probability. Identify the important distribution functions. Derive distributions of random functions. Formative Min Formative mark for exam admission 40% Weighting towards final mark 60% Weighting towards final mark 40% Min Final mark to pass (%) 50% Lecturer: Mr MM Nemukula 7
STATISTICAL INFERENCE SSTA022 Sampling distributions: t, F and Chi-square distributions. Central Limit Theorem. Estimation: point and interval; Confidence Interval for the mean, proportion and variance. Test of hypotheses: Tests for the mean, proportion and variance. Inferences about differences in two means and two proportions; One-way ANOVA. Chi-square tests. Simple linear regression and correlation. Time series analysis. Index numbers. 6 1 1 0 Know the important sampling distributions. Estimate parameters. Conduct statistical tests. Formative Min Formative mark for exam admission 40% Weighting towards final mark 60% Weighting towards final mark 40% Min Final mark to pass (%) 50% Lecturer: Mr MM Nemukula YEAR LEVEL 3 TIME SERIES ANALYSIS SSTA031 The classical approach to time series analysis: Decomposition of time series. Smoothing methods. Forecasting. Properties of stochastic time series models. stationary series. Autocorrelation and partial autocorrelation functions. Purely random, moving average and autoregressive processes. The Box-Jenkins approach: ARMA and ARIMA models. Case studies. Understand basic time series concepts and terminology. Select time series methods appropriate for the situation. Summarize results of the analysis in writing. Formative Min Formative mark for exam admission 40% Weighting towards final mark 60% 8
Weighting towards final mark 40% Min Final mark to pass (%) 50% Lecturer: Mr N Maswanganyi APPLIED LINEAR REGRESSION SSTB031 Simple Linear Regression: Fitting the model, Model assumptions, Estimation and tests, Regression through the origin. Review of Matrix Algebra: Matrices, Operations on matrices. Multiple Linear Regression: Fitting the model, Estimation and tests, Prediction, Multicollinearity. Model Adequacy Checking: Residual analysis, Detecting unequal variances, Checking the normality assumption, Detecting outliers. Variable Selection and Model Building: Subset regression models, All possible regressions, Stepwise procedures. Fit simple and multiple regression models. Select appropriate models. Test for adequacy of models. Formative Min Formative mark for exam admission 40% Weighting towards final mark 60% Weighting towards final mark 40% Min Final mark to pass (%) 50% Lecturer: Mr Maluleke H DESIGN AND ANALYSIS OF EXPERIMENTS SSTA032 Definitions of basic terminologies; Design of experiments. Design and analysis of: Completely randomized, Randomized block, Latin square and Factorial designs. Multiple comparisons of treatment means. Analysis of covariance. Design and analyze experiments with and without blocking. Design and analyze factorial experiments. Perform multiple comparisons. 9
Perform analysis of covariance. Formative Min Formative mark for exam admission 40% Weighting towards final mark 60% Weighting towards final mark 40% Min Final mark to pass (%) 50% Lecturer: Mr Maluleke H MULTIVARIATE STATISTICAL METHODS SSTB032 Review of matrix theory. Multivariate distributions: Multivariate normal distribution and its properties; Inference about multivariate means; Hotelling s T2. Multivariate analysis of variance and regression. Introduction to data reduction. Understand multivariate methods and what they do. Know when to apply the different multivariate methods. Analyze a multivariate data set and write a report. Formative Min Formative mark for exam admission 40% Weighting towards final mark 60% Weighting towards final mark 40% Min Final mark to pass (%) 50% Lecturer: Mr KD Moloi SAMPLING THEORY SSTC032 Elements of Sampling, Questionnaire Design, Simple Random Sampling, Stratified Random Sampling, Ratio Estimation, Difference and Regression Estimators, Systematic Sampling. Design a questionnaire Design a sample survey Estimate the parameters and standard errors 10
Write a report. Formative Min Formative mark for exam admission 40% Weighting towards final mark 60% Weighting towards final mark 40% Min Final mark to pass (%) 50% Lecturer: Mr N Maswaganyi 11