## 21MATCS41 Mathematical Foundations for Computing, Probability and Statistics | Syllabus

**MODULE- 1 (Fundamentals of Logics)**- Basic Connectives and Truth Tables, Logical equivalences: The laws of Logic, Logical Implication: Rules of Inference,
- The use of Quantifiers, Quantifiers, Definitions and the proofs of Theorems
**MODULE-2 (Relations, functions and Graph Theory)**- Cartesian products and Relations, Functions: Plain and One-to-One, Onto functions, Function Composition and Inverse Functions
- 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, Compliments and Graph Isomorphism, Vertex Degree, Euler trails and Circuits
**MODULE-3 (Statistical Methods)**- Correlation and regression-Karl Pearson’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 of the forms 𝑦 = 𝑎𝑥 + 𝑏, 𝑦 = 𝑎𝑥 𝑏 𝑎𝑛𝑑 𝑦 = 𝑎𝑥 2 + 𝑏𝑥 + c
**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, Poisson and normal distributions- problems (derivations for mean and standard deviation for Binomial and Poisson distributions only)- Illustrative example
**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 tdistribution, Chi-square distribution as a test of goodness of fit.

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