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MATHEMATICAL TECHNIQUES – FUNCTIONS?

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

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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

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

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Application of mathematical functions in solving business problems

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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

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Rules of differentiation (general rule, chain, product, quotient)

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Differentiation of exponential and logarithmic functions

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Higher order derivatives: turning points (maxima and minima)

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Ordinary derivatives and their applications

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Partial derivatives and their applications

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Constrained optimisation; lagrangian multiplier

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CALCULUS INTEGRATION?

- Rules of integration
- Applications of integration to business problems

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Rules of integration

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Applications of integration to business problems

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PROBABILITY-SET THEORY?

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

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Types of sets

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Set description: enumeration and descriptive properties of sets

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Operations of sets: union, intersection, complement and difference

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Venn diagrams

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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

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Definitions: event, outcome, experiment, sample space

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Types of events: elementary, compound, dependent, independent, mutually exclusive, exhaustive, mutually inclusive

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Laws of probability: additive and multiplicative rules

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Baye’s Theorem

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Probability trees

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Expected value, variance, standard deviation and coefficient of variation using frequency and probability

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PROBABILITY DISTRIBUTION?

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

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Discrete and continuous probability distributions (uniform, normal, binomial, poisson and exponential)

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Application of probability to business problems

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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

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Hypothesis tests on the mean (when population standard deviation is unknown)

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Hypothesis tests on proportions

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Hypothesis tests on the difference between means (independent samples)

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Hypothesis tests on the difference between means (matched pairs)

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Hypothesis tests on the difference between two proportions

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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)

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Scatter diagrams

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Measures of correlation –product moment and rank correlation coefficients (Pearson and Spearman)

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Regression analysis

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Simple and multiple linear regression analysis

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Assumptions of linear regression analysis

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Coefficient of determination, standard error of the estimate, standard error of the slope, t and F statistics

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Computer output of linear regression

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T-ratios and confidence interval of the coefficients

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Analysis of Variances (ANOVA)

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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

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Definition of time series

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Components of time series (circular, seasonal, cyclical, irregular/ random, trend)

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Application of time series

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Methods of fitting trend: free hand, semi-averages, moving averages, least squares methods

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Models – additive and multiplicative models

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Measurement of seasonal variation using additive and multiplicative models

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Forecasting time series value using moving averages, ordinary least squares method and exponential smoothing

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Comparison and application of forecasts for different techniques

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Trend projection methods: linear, quadratic and exponential

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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

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Definition of decision variables, objective function and constraints

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Assumptions of linear programming

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Solving linear programming using graphical method

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Solving linear programming using simplex method

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Sensitivity analysis and economic meaning of shadow prices in business situations

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Interpretation of computer assisted solutions

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Transportation and assignment problems

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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

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Decision making process

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Decision making environment: deterministic situation (certainty)

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Decision making under risk – expected monetary value, expected opportunity loss, risk using coefficient of variation, expected value of perfect information

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Decision trees – sequential decision, expected value of sample information

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Decision making under uncertainty – maximin, maximax, minimax regret, Hurwicz decision rule, Laplace decision rule

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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

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Assumptions of game theory

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Zero sum games

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Pure strategy games (saddle point)

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Mixed strategy games (joint probability approach)

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Dominance, graphical reduction of a game

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Value of the game

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Non-zero sum games

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Limitations of game theory

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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

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Basic concepts – network, activity, event

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Activity sequencing and network diagram

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Critical path analysis (CPA)

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Float and its importance

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Crashing of activity/project completion time

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Project evaluation and review technique (PERT)

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Resource scheduling (leveling) and Gantt charts

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Advantages and limitations of CPA and PERT

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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

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Components/elements of a queue: arrival rate, service rate, departure, customer behaviour, service discipline, finite and infinite queues, traffic intensity

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Elementary single server queuing systems

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Finite capacity queuing systems

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Multiple server queues

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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

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Types of simulation

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Variables in a simulation model

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Construction of a simulation model

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Monte Carlo simulation

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Random numbers selection

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Simple queuing simulation: single server, single channel “first come first served” (FCFS) model

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Application of simulation models

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EMERGING ISSUES AND TRENDS