About Course
What Will You Learn?
- A candidate who passes this paper should be able to:
- Use mathematical techniques in solving business problems
- Apply set theory in business decision making
- Apply operation research techniques in decision making
- Apply simulation techniques in analysing business situations.
Course Content
Mathematical Techniques: Functions
Mathematical techniques:Functions
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Functions, equations and graphs: Linear, quadratic, cubic, exponential and logarithmic
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Application of mathematical functions in solving business problems
Basic Mathematical Techniques :Matrix Algebra
Basic mathematical techniques :Matrix algebra
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Types and operations (addition, subtraction, multiplication, transposition, and inversion)
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Types and operations (addition, subtraction, multiplication, transposition, and inversion)
Calculus:Differentiation
Calculus:Differentiation
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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
Calculus:Integration
Calculus:Integration
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Rules of integration
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Applications of integration to business problems
Probability :Set Theory
Probability :Set theory
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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 diagram
Probability Theory and Distribution Probability Theory
Probability theory and distribution Probability theory
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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 – Baye’s Theorem
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Bayes Theorem
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Probability trees
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Expected value, variance, standard deviation and coefficient of variation using frequency and probability
Probability Distributions
Probability distributions
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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
Hypothesis Testing and Estimation
Hypothesis testing and estimation
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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
Correlation Analysis
Correlation analysis
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Scatter diagrams
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Measures of correlation -product moment and rank correlation coefficients (Pearson and Spearman)
Regression Analysis
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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Simple and multiple linear regression analysis
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Analysis of Variances (ANOVA)
Time Series
Time series
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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
Linear Programming
Linear programming
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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
Decision Theory
Decision theory
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Decision process
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Decision making environment – deterministic situation (certainty), analytical hierarchical approach (AHA), risk and uncertainty, stochastic situations (risk), situations of uncertainty
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Decision making under uncertainty – maximin, maximax, minimax regret, Hurwicz decision rule, Laplace decision rule
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Decision making under risk – expected monetary value, expected opportunity loss, minimising 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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Limitations of expected monetary value criteria
Game Theory
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
Network Planning and Analysis
Network planning and analysis
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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 (levelling) and Gantt charts
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Limitations and advantages of CPA and PERT
Queuing Theory
Queuing theory
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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
Simulation
Simulation
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Types of simulation
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Variables in 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