Set theory, set operations, cardinality, solved examples on set operations. Function, Domain and codomain of functions, image and preimages of functions, range of function, even function, odd function, equal functions, one-one, on-to and bijective functions.
• ## Set theory and Functions (BBA & BCA)

Matrix definition, row matrix, column matrix, square matrix, scalar matrix, identity matrix, symmetric matrix, skew-symmetric matrix, addition of matrices, subtraction of matrices, multiplication of matrices, detrminants, operation of determinants, Cramer’s rule for solving system Ax=B.
• ## Matrices and Determinants (BBA, BCA, BE)

Algebraic and transcedental equations, Bisection method, Regula-falsi method, Secant metod, Newton-Raphson method, Fixed Point Iteration or Iteration method,
• ## Numerical Solutions

Basic concepts of probability, definition of probability, event, random experiment, outcomes, Exhaustive event, Independent events, Sample Spaces, mutually exclusive events, Axioms of probability, compliment event, Conditional probability, Baye’s theorem, Random variables, Discrete Random Variables, Probability Mass Function, Discrete Distribution Function, Continuous Random variables, Probability Density Function, Properties of probability density function, Continuous Distribution Function, Two Dimensional Discrete Random Variable, Joint probability mass function, Cumulative Distribution Function , Conditional Probability Function, Marginal probability function, Two Dimensional Continuous Random Variable, Cumulative distribution function, Marginal probability function,
• ## Basic Probability

Measure of central tendency, mean, median, mod. Moments, Expectation, dispersion, skewness, kurtosis, expected value of two dimensional random variable, Linear Correlation, correlation coefficient, rank correlation coefficient, Regression, Bounds on probability, Chebyshev‘s Inequality
• ## Basic Statistics

Binomial distribution, Poisson distribution, Poisson approximation to the binomial distribution, Normal, Exponential and Gamma densities, Evaluation of statistical parameters for these distributions.
• ## Some special Probability Distributions

Finite Differences, Forward, Backward and Central operators, Interpolation by polynomials: Newton’s forward ,Backward interpolation formulae, Newton’s divided formulae and Lagrange’s interpolation formulae for unequal intervals

## Relations and POSET (Discrete Mathematics unit 3)

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