### 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

##### Application of matrices: statistical modelling, Markov analysis, inputoutput analysis and general applications

##### Application of mathematical functions in solving business problems

### 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

##### 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

##### 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

##### 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

##### 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

##### 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

##### 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)

##### 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

##### 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

##### 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

##### 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

##### 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

##### 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

##### 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