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
  • Interpolation

Basic Concepts of Set Theory: Definitions, Inclusion, Equality of Sets, Cartesian product, The Power Set, Some operations on Sets, Venn Diagrams, Some Basic Set Identities
Definition, Statements & Notation, Truth Values, Connectives, Statement Formulas & Truth Tables, Well-formed Formulas, Tautologies, Equivalence of Formulas, Duality Law, Tautological Implications, Examples Predicate Logic: Definition of Predicates; Statement functions, Variables, Quantifiers, Predicate Formulas, Free & Bound Variables; The Universe of Discourse, Examples, Valid Formulas & Equivalences, Examples
Definition, Binary Relation, Representation, Domain, Range, Universal Relation, Void Relation, Union, Intersection, and Complement Operations on Relations, Properties of Binary Relations in a Set: Reflexive, Symmetric, Transitive, Anti-symmetric Relations, Relation Matrix and Graph of a Relation; Partition and Covering of a Set, Equivalence Relation, Equivalence Classes, Compatibility Relation, Maximum Compatibility Block, Composite Relation, Converse of a Relation, Transitive Closure of a Relation R in Set X Partial Ordering: Definition, Examples, Simple or Linear Ordering, Totally Ordered Set (Chain), Frequently Used Partially Ordered Relations, Representation of Partially Ordered Sets, Hesse Diagrams, Least & Greatest Members, Minimal & Maximal Members, Least Upper Bound (Supremum), Greatest Lower Bound (infimum), Wellordered Partially Ordered Sets (Posets). Lattice as Posets, complete, distributive
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