SOST 11315 - Basic Mathematics

Intended Learning Outcomes

At the completion of this course student will be able to

• Identify the scale and type of the data and basic concepts of the statistics
• Define the process of a research and select appropriate data collection method in a given situation
• Identify the method of organize and present the data
• Recognize and interpret measures of central tendency, dispersion, skewness, and kurtosis

Course Content

Algebra Operation
• Introduction to Algebra
• Define variables
• Numerical expressions and algebraic expressions
• Algebraic expression using the correct order of operations
• Algebraic expression (by adding, subtracting, dividing, multiplication)
• Transform factorize algebraic form into its factors, Factorization and Fractions

Index Numbers and Logarithms
• Describe the meaning of index numbers
• Laws of index numbers and their applications
• Explain logarithms and identify the laws of logarithms

Function and Graphs
• Find the intercept and the slope of a graph
• Find the absolute maximum/ minimum of a function using the equation and the graph
• Graph linear equations
• Find X, Y, intercept and slope for given simple linear equation

Solving Equations
• Solve Formulas and Simple Linear Equations for a specific variable
• Solve simultaneous equations and define them in algebraic and graphical methods

Basic Calculus
• Derivative in terms of a tangent line to the graph of the function
• Limit of the function using limit laws, Derivative at a point as a limit
• Compute algebraically the derivative function using limits
• Explain basic rules of differentiation and use them to find derivatives of products and quotients

Vector and Matrix
• Define the terminology of Vector and Matrix
• Describe geometric and algebraic properties of vectors to compute vector additions, subtractions and multiplication
• Compute the determinant of a square matrix (22) by using the definition and by using the properties of determinants
• Compute the inverse of a square matrix by using the definition and by using the properties of inverse
• Illustrate the transpose of the matrix, Solve simultaneous equations using matrices (22)

• Sancheti, D. C. & Kapoor, V. K. (2009). Business Mathematics. Sultan Chand and Sons: New Delhi
• Bradely, T. & Patlon, P. (1998). Essential Mathematics for Economics and Business. Jhone Wiley publication: New York
• Freund, J. (2001). Mathematics for Statistics. Prentice Hall of India
• Strauss, M. J., Bradley, G. L. & Smith, K. J. (2002). Calculus. Prentice Hall of India

SOST 12315 - Basic Statistics

Intended Learning Outcomes

At the completion of this course student will be able to

• Identify the scale and type of the data and basic concepts of the statistics
• Define the process of a research and select appropriate data collection method in a given situation
• Identify the method of organize and present the data
• Recognize and interpret measures of central tendency, dispersion, skewness, and kurtosis
• Describe indices theory and methods

Course Content

Introduction
• Meaning and Definition of Statistics
• Importance and Scope of Statistics
• Nature of Statistics problem and examples
• Introduction to descriptive and inferential statistics

Population and Sample

• Population and Census
• Finite and infinite population
• Sample and selecting a random sample
• Difference between parameters and statistics

Classification of Data

• Purpose of classification of data
• Advantages of classification of data
• Types of classification: Primary Data and Secondary Data
• Internal and External Data
• Qualitative and Quantitative Data
• Continuous and Discrete Data and etc.

Scales of Measurement
• Nominal, Ordinal, Interval, Ratio

Survey and Experiment
• Deference between survey and experiment
• Steps to be taken to conduct a research

Data Collection Methods
• Primary Data Collection Methods
• Secondary Data Collection Methods
• Define suitable data collection method in a given scenario
• Distinguish the procedure of each data collection methods

Organization of Data
• Concept of classification and tabulation
• Construct the frequency distribution
• Basic principles of tabulation
Presentation of Data
• Use of different types of data presentation methods (bar charts, pie charts, line graphs and etc.)

Frequency Distribution
• Introduction
• Cumulative and Relative frequency distribution
• Grouped and Ungrouped frequency distribution
• Graphical representation of frequency distribution : histogram, frequency polygon, Less than ogive or More Ogive, Lawrence Curve

Measures of Central Tendency
• Uses of Central Tendency Measures
• Find and interpret the various measures of central tendency (Mean, Median, Mode)
• Merits and demerits of each type of measures

Measures of Relative Location
• Find and interpret the various measures of relative location (Quartiles, Deciles, Percentiles)

Measures of Dispersion
• Importance of measuring dispersion
• Measures of dispersion (Range, Mean deviation, Quartile Range, Variance, Standard deviation)
• Distinguish absolute and relative measures of dispersion
• Merits and demerits of each type of measures

Measures of Skewness and Kurtosis
• Symmetric and asymmetric distributions
• Skewness of distributions and interpret the nature of skewness
• Kurtosis of distributions
• Evaluate and interpret the types of kurtosis
• Calculate Skewness and Kurtosis

Indices
• Construct price, quantity, and value indices (Simple Relative Indices, Simple Aggregate Indices, Aggregate Indices, Laspeyre’s Index, Paaschey’s Index, Marshell Addedge Index, Fisher’s Index)
• Practically use of indices

• යතිස්ස, ඩබ්- ඒ- (1987)- මූලික සංඛ්‍යාන විද්‍යාව 1 - විස්තරාත්මක සංඛ්‍යානය.. කර්තෘ ප්‍රකාශන:නුගේගොඩ
• Arora, P.N., Arora, S., Arora, S. & Arora, A. (2007). Comprehensive Statistical Methods. Chand & Company Ltd: India
• Pillai, R.S.N. & Bagavathi. (2018). Statistics: Theory and Practice. S. Chand & Company Ltd, India
SOST 21312 - Probability Distribution

Intended Learning Outcomes

At the completion of this course student will be able to

• Explain sets theory and probability theory in decision making
• Construct calculation for the probability values of a given events
• Discuss probability distributions

Course Content

Set theory
• Introduction
• Terminology of set theory (Union, Intersection and complement)
• Venn Diagrams representing events and their probabilities
• Union and intersection of events
• Mutually exclusive events and independent events using Venn diagram.

Introduction to Probability
• Terminology of probability
• Basic rules of probability
• Random events
• Permutation and Combination
• Venn Diagrams representing events and their probabilities
• Union and intersection of events
• Mutually exclusive events and independent events
• Conditional probability of a given event
• Bayes’ Theorem

Random variables
• Identify random variables
• Discrete and continuous random variables
• Expected value and Variance of discrete random variable and continuous random variable.

Discrete Probability distribution
• Identify discrete probability distribution
• Probability mass function
• Uniform distribution
• Binomial distribution
• Poisson distribution
• Hyper geometric distribution

Continuous Probability distribution
• Identify continuous probability distribution
• Probability density function
• Uniform distribution
• Normal distribution
• Exponential distribution

• ජයතිස්ස, ඩබ්- ඒ- (1991). මූලික සංඛ්‍යාන විද්‍යාව 2 - සම්භාවිතාව සහ ව්‍යාප්ති න්‍යාය. කර්තෘ ප්‍රකාශන: නුගේගොඩ
• Kandasamy, P., Thilagavathi, K. & Gunavathi, K. (2005). Probability Statistics and Queueing Theory. Chand & Company Ltd, India.
• Ross, S.  (2019). A First Course in Probability. (10th Edition). Pearson Education
SOST 22312 - Statistical Inference

Intended Learning Outcomes

At the completion of this course student will be able to

• Discuss basic concepts of the statistical inference procedure and various methods of point estimators and their characteristics
• Construct interval estimates, confidence intervals and confidence limit
• Explain the various concepts related to the testing of hypothesis

Course Content

Statistical Inference Procedure
• Introduction to Statistical Inference
• Type of Estimation (point estimation, interval estimation)
• Properties of a good point estimation

Point Estimation
• Population mean
• Population proportion
• Population variance and standard deviation

Interval estimation
• Confidence interval (population mean, difference between two population means, population proportion, difference between two population proportions, population variance, difference between two population variances, population standard deviation, difference between two population standard deviation)
• Determination of sample size

Hypothesis Testing
• Procedure for hypothesis testing
• Type I and II errors
• One tailed and Two tailed test
• Hypothesis test for large sample (Population Mean, Difference between two population mean, Population Proportion, Difference between two population Proportion, Population Variance, Difference between two populations variance)
• Hypothesis tests for small sample
• Paired Sample t test

• ජයතිස්ස, ඩබ්- ඒ- (1991). මූලික සංඛ්‍යාන විද්‍යාව 3 - අනුමිතික සංඛ්‍යානය. කර්තෘ ප්‍රකාශන: නුගේගොඩ
• Arora, P.N., Arora, S., Arora, S. & Arora, A. (2007). Comprehensive Statistical Methods. Chand & Company Ltd: India
• Anderson, D. R., Sweeney, D. J., Williams, T. A., Camm, J. D., Fry, M. J., Cochran, J. J. & Ohlmann, J. W. (2014). Statistics for Business and Economics. Cengage Learning India Private Limited:Delhi, India
SOST 21322 - Sampling Techniques

Intended Learning Outcomes

At the completion of this course student will be able to

• Explain the sampling techniques in field of Social Sciences
• Discuss the Sampling methods.
• Differentiate the basic principles and methods underlying sample surveys

Course Content

Introduction to Sampling Methods
• Introduction, Terminology, Sampling Survey, Methods of Sampling

Probability Sampling Techniques
• Simple Random sampling
• Stratified random sampling
• Systematic sampling
• Cluster sampling (Introduction, Merits and Demerits, Calculations)

Non-probability Sampling Techniques
• Quota sampling
• Convenience sampling
• Judgmental sampling
• Purposive sampling
• Snowball sampling (Introduction, merits and demerits)

Applications
• Practical applications of the sampling methods

• ජයතිස්ස, ඩබ්- ඒ- (1991). මූලික සංඛ්‍යාන විද්‍යාව 3 - අනුමිතික සංඛ්‍යානය. කර්තෘ ප්‍රකාශන: නුගේගොඩ
• Ardilly, P. and Tille, Y. (2006). Sampling Methods: Exercise and Solutions. Springer: Verlag, New York
• Thompson, S.K. (2002). Sampling. Wiley Series in Probability and Statistics
SOST 22322 - Nonparametric Techniques

Intended Learning Outcomes

At the completion of this course student will be able to

• Discuss the situations where nonparametric tests are used
• Construct appropriate Non-Parametric Tests

Course Content

Introduction to Non-Parametric Tests

Types of Non-Parametric Methods
• The Sign test for Paired data
• One Sample Sign Test
• Rank Sum Test
• Mann-Whitney U Test and Kruskal-Wallis Test (H Test)
• One Sample Runs Test
• Median Test for Randomness (Runs above and below the median)
• Spearman’s Rank Correlation Test
• Testing hypothesis about Rank Correlation
• Kolmogorov-Smirnov Test
• Kendall Test of Concordance
• Median Test for Two Independent Samples
• Wilcoxon’s Signed Rank Test
• The matched pairs Sign Test
• Chi-Square test (Introduction, Chi-Square defined, Conditions for applying Chi-Square Test, Yate’s corrections, uses of Chi-Square test: independence, goodness of fit, homogeneity, Misuses of chi-square test, limitations of chi-square test)

• Arora, P.N., Arora, S., Arora, S. & Arora, A. (2007). Comprehensive Statistical Methods. Chand & Company Ltd: India
• Anderson, D. R., Sweeney, D. J., Williams, T. A., Camm, J. D., Fry, M. J., Cochran, J. J. & Ohlmann, J. W. (2014). Statistics for Business and Economics. Cengage Learning India Private Limited:Delhi, India
• Levin, R. I., Rubin, D. S., Siddiqui, M. H. & Rastogi, S. (2017). Statistics for Management. (8th Edition). Pearson India Education Service Pvt Ltd: India
SOST 31314 - Correlation and Regression

Intended Learning Outcomes:

At the completion of this course student will be able to

• Clarify dependent and independent variables and the pattern of raw data.
• Calculate correlation between dependent variable and one or more independent variables.
• Compute the regression mode
• Use Statistical software to do statistical analysis

Course Content

Correlation
• Identify dependent variable and the independent variable
• Draw scatter plot
• Identify the patterns and outliers from the scatter plot
• Calculate and Interpret Correlation coefficients (Pearson correlation, Partial correlation, Spearman correlation, Correlation coefficient by Two-way tables)
• Define the merits and demerits of different types of Correlation Coefficients
• Practical applications of the correlation coefficient

Simple Linear Regression Analysis
• Introduction to Simple Linear Regression
• Assumptions of the linear regression
• Regression coefficients using OLS method
• Interpret OLS regression coefficients
• Calculate and interpret R square
• Test the significance of the parameters and the overall significance of the model
• Construct and interpret a confidence interval for the parameters

Multiple linear Regression analysis
• Describe the relationship between two or more independent variables with dependent variable
• Compute and interpret the multiple regression coefficients
• Calculate and interpret R square
• Determine the significance of regression coefficients
• Overall significance of the model
• Violation of the Assumptions of the Basic Model: Multicolinearity (Identification, Effect and Treatments)
• Autocorrelation (Identification, Effect and Treatments), Heteroscedasticity (Identification, Effect and Treatments)

Statistical software

• Use the Statistical software for data analysis

• සේමසිංහ, ඩබ්. එම්.,  (2015). ආර්ථිකමිතිය න්‍යාය හා භාවිතය. සරසවි ප්‍රකාශකයෝ: නුගේගොඩ
• Gujarati, D. N. (2004). Basic Econometrics. (4th Edition). Tata McGraw-Hill Publishing Company Limited: New-Delhi, India
• Maddala, G. S. (2005). Introduction to Econometrics. (3rd Edition). John Wiley & Sons Ltd. New York
• Koutsoyiannis, A. (2005). Theory of Econometrics. (2nd Edition). Palgrave: New York
SOST 32314 - Operational Research

Intended Learning Outcomes

At the completion of this course student will be able to

• Clarify the background of Operational Research
• Compute linear programming problems in different methods
• Use Transportation problems and assignment problems in different method
• Apply methodologies for analyzing networks of different ways

Course Content

Introduction to Operational Research
• The historical development of operational research
• Operational research techniques
• Limitations of applications of operational research
• Methodology of operational research

Linear programming
• Introduction to linear programing
• Formulate linear programming problems
• General statement of linear programming problems
• Assumptions of linear programming
• Solutions using graphical method
• Special cases in graphical method (multiple optimal solutions, infeasibility and unboundedness)
• Introduction to simplex method
• Solutions using simplex methods
• Big-M method, Two-phase method
• Special cases in simplex method (multiple optimal solutions, infeasibility unboundedness and degeneracy problem)
• Duality in linear programming
• Dual Simplex method
• Sensitivity analysis in linear programing

Transportation Problems

• Introduction to transportation problems
• Types of transportation problems
• Finding the basic feasible solution (North-West corner method
• Least Cost method
• Vogel’s approximation method)
• Finding the optimal feasible solution (Stepping Stone method, Modified distribution method)
• Special cases in transportation problem (Unbalanced transportation problem
• Multiple Solutions transportation problems
• Degeneracy problem, maximization problem, restrictions of routes)
• Solutions to the transportation problems using linear programming
• Sensitivity analysis in transportation problem

Assignment Problem

• Introduction to Assignment Problem
• Hungarian Assignment method
• Solutions to the Assignment problems using linear programming
• Special cases in Assignment problem (Unbalanced Assignment problems
• Constrained Assignment problems, Multiple Optimal Solutions, Maximization Case)

Network Analysis
• Introduction Network Problems
• Critical Path Method (CPM)
• Network Analysis (Scheduling the activities, Earliest and Latest time, Determining the critical path, Calculation of Floats)
• Resource analysis and allocation (Crashing, Resource Levelling)
• Programme Evaluation and Review Technique (PERT)
• Difference between PERT and CPM
• Shortest route problem
• Maximum flow problem
• Minimum Spanning Tree Problem