Mathematical & Statistical Techniques for Data Analysis

 Introduction to Sets, Sets and their Representation, Tabular or Roster Method, Rule Method or Set Builder, Empty or Void or Null Set, Finite sets and Infinite sets, Proper Subset Improper Subset, Power Set, Universal Set, Open Interval, Closed Interval, Semi-Open or Semi Closed intervals, Infinite Intervals, Venn Diagrams, Operations on Sets, Union, Intersection of Sets, Disjoint Sets, Difference of Sets, Symmetric Difference of Sets, Complement of a Set Laws of Algebra of Sets. 

 Definition of a Matrix, Addition & Subtraction of Matrices Multiplication of Matrices, Transpose of a Matrix, Determinants, Determinants of order one and more, Properties of Determinants, Multiplication of two Determinants, Minors and Cofactors System of linear equations, Gauss elimination method, Inverse of a Matrix, Cramer's rule for solution of linear equations, Adjoint of a Matrix, Rank of a Matrix.  

 Vectors, Types of Vectors, Operations on Vectors, Addition of Vectors Properties of Operation of Addition, Subtraction, Properties of Operation of Subtraction Multiplication by a scalar, , Product of Two Vectors, Scalar Product or Dot Product of Two Vectors, Properties of Scalar Product, Vector Product or Cross Product, Properties of Vector Product.

 Introduction to Statistics, Scale of Measurement, Nominal, Ordinal, Interval & Ratio. Frequency Distribution, Histogram, Frequency Polygon, Ogive, Measure of Central Tendency: Mean, Median & Mode, Properties, Advantages and Disadvantages. Measure of Dispersion: Range, Interquartile Range, Standard Deviation, Quartiles, Deciles, Percentiles.

 Introduction to Probability, Types of probability ,Random Experiment, Event, Compound Event, Independent and Dependent Events, Mutually Exclusive Events, Equally Likely Events, Marginal, Union, Joint, Conditional Probability, General Rule of Addition, General Rule of Multiplication, Concept of Baye's Theorem.