### MATHEMATICAL TECHNIQUES – FUNCTIONS?

- Functions, equations and graphs: Linear, quadratic, cubic, exponential and logarithmic - Application of mathematical functions in solving business problems

### MATHEMATICAL TECHNIQUES – MATRIX ALGEBRA?

- Types and operations (addition, subtraction, multiplication, transposition and inversion) - Application of matrices: statistical modelling, Markov analysis, inputoutput analysis and general applications

### CALCULUS – DIFFERENTIATION?

- Rules of differentiation (general rule, chain, product, quotient) - Differentiation of exponential and logarithmic functions - Higher order derivatives: turning points (maxima and minima) - Ordinary derivatives and their applications - Partial derivatives and their applications - Constrained optimisation; lagrangian multiplier

### CALCULUS INTEGRATION?

- Rules of integration - Applications of integration to business problems

### PROBABILITY-SET THEORY?

- Types of sets - Set description: enumeration and descriptive properties of sets - Operations of sets: union, intersection, complement and difference - Venn diagrams

### PROBABILITY THEORY?

- Definitions: event, outcome, experiment, sample space - Types of events: elementary, compound, dependent, independent, mutually exclusive, exhaustive, mutually inclusive - Laws of probability: additive and multiplicative rules - Baye’s Theorem - Probability trees - Expected value, variance, standard deviation and coefficient of variation using frequency and probability

### PROBABILITY DISTRIBUTION?

- Discrete and continuous probability distributions (uniform, normal, binomial, poisson and exponential) - Application of probability to business problems

### HYPOTHESIS TESTING AND ESTIMATION?

- Hypothesis tests on the mean (when population standard deviation is unknown) - Hypothesis tests on proportions - Hypothesis tests on the difference between means (independent samples) - Hypothesis tests on the difference between means (matched pairs) - Hypothesis tests on the difference between two proportions

### CORRELATION AND REGRESSION ANALYSIS?

- Scatter diagrams - Measures of correlation –product moment and rank correlation coefficients (Pearson and Spearman) - Regression analysis - Simple and multiple linear regression analysis - Assumptions of linear regression analysis - Coefficient of determination, standard error of the estimate, standard error of the slope, t and F statistics - Computer output of linear regression - T-ratios and confidence interval of the coefficients - Analysis of Variances (ANOVA)

### TIME SERIES?

- Definition of time series - Components of time series (circular, seasonal, cyclical, irregular/ random, trend) - Application of time series - Methods of fitting trend: free hand, semi-averages, moving averages, least squares methods - Models - additive and multiplicative models - Measurement of seasonal variation using additive and multiplicative models - Forecasting time series value using moving averages, ordinary least squares method and exponential smoothing - Comparison and application of forecasts for different techniques - Trend projection methods: linear, quadratic and exponential

### LINEAR PROGRAMMING?

- Definition of decision variables, objective function and constraints - Assumptions of linear programming - Solving linear programming using graphical method - Solving linear programming using simplex method - Sensitivity analysis and economic meaning of shadow prices in business situations - Interpretation of computer assisted solutions - Transportation and assignment problems

### DECISION THEORY?

- Decision making process - Decision making environment: deterministic situation (certainty) - Decision making under risk - expected monetary value, expected opportunity loss, risk using coefficient of variation, expected value of perfect information - Decision trees - sequential decision, expected value of sample information - Decision making under uncertainty - maximin, maximax, minimax regret, Hurwicz decision rule, Laplace decision rule

### GAME THEORY?

- Assumptions of game theory - Zero sum games - Pure strategy games (saddle point) - Mixed strategy games (joint probability approach) - Dominance, graphical reduction of a game - Value of the game - Non zero sum games - Limitations of game theory

### NETWORK PLANNING AND ANALYSIS?

- Basic concepts – network, activity, event - Activity sequencing and network diagram - Critical path analysis (CPA) - Float and its importance - Crashing of activity/project completion time - Project evaluation and review technique (PERT) - Resource scheduling (leveling) and Gantt charts - Advantages and limitations of CPA and PERT

### QUEUING THEORY?

- Components/elements of a queue: arrival rate, service rate, departure, customer behaviour, service discipline, finite and infinite queues, traffic intensity - Elementary single server queuing systems - Finite capacity queuing systems - Multiple server queues

### SIMULATION?

- Types of simulation - Variables in a simulation model - Construction of a simulation model - Monte Carlo simulation - Random numbers selection - Simple queuing simulation: single server, single channel “first come first served” (FCFS) model - Application of simulation models

### EMERGING ISSUES AND TRENDS

Application of mathematical functions in solving business problems
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