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VTU NOTES
Subject code
21MATCS41
Semester
4th

## Module - 1

Fundamentals of Logic: Basic connectives and truth tables, Logical equivalence – The laws of Logic, Logical implication – Rules of Inference. Fundamentals of Logic contd.: The Use of Quantifiers, Quantifiers, Definitions, and the Proofs of Theorems.

## Module - 2

Relations and Functions: Cartesian Products and Relations, Functions – Plain and One-to- One, Onto Functions. Function Composition, and Inverse Functions. Relations: Properties of Relations, Computer Recognition – Zero-One Matrices and Directed Graphs, Partial Orders – Hasse Diagrams, Equivalence Relations and Partitions. Introduction to Graph Theory: Definitions and Examples, Subgraphs, Complements, and Graph Isomorphism, Vertex Degree. Euler Trails and Circuits

## Module - 3

Statistical Methods: Correlation and regression- Karl Person’s coefficient of correlation and rank correlation problems. Regression analysis- lines of regression -problems. Curve Fitting: Curve fitting by the method of least squares- fitting the curves

## Module - 4

Probability Distributions: Review of basic probability theory. Random variables (discrete and continuous), probability mass and density functions. Mathematical expectation, mean and variance. Binomial, Poison and normal distributions- problems (derivations for mean and standard deviation for Binomial and Poison distributions onlv)-Illustrative examples

## Module - 5

Joint probability distribution: Joint Probability distribution for two discrete random variables, expectation, covariance and correlation. Sampling Theory: Introduction to sampling distributions, standard error, Type-I and Type-II errors. Test of hypothesis for means, student’s t-distribution, Chi-square distribution as a test of goodness of fit