Statistical Mathematics
The complete syllabus for Statistical Mathematics (MCA-102), the first-semester mathematics course for the Master of Computer Applications (MCA) programme at RGPV and Madhya Pradesh universities — matrices and eigenvalue problems, calculus, testing of hypothesis, probability distributions, and discrete mathematics.
Statistical Mathematics (MCA) · English
by Dr. D.C. Agarwal & Dr. Pradeep K. Joshi · ₹360 — covers this full syllabus.
Course contents — unit by unit
Unit 1 · Matrices & Eigenvalue Problems
Rank of a matrix, consistency of a system of linear equations, solution of the matrix equation, row-reduced echelon form, eigenvalues and eigenvectors and their properties, Cayley-Hamilton theorem, inverse of a matrix.
Unit 2 · Calculus
Functions of a single variable — limit, continuity, differentiability, mean-value theorems, indeterminate forms and L'Hospital's rule, maxima and minima, product and chain rule, Beta and Gamma functions; functions of several variables — limit, continuity, partial derivatives.
Unit 3 · Testing of Hypothesis
Sampling distributions; tests based on small and large samples — Normal, Student's t, Chi-square and F distributions for testing mean, variance and proportion, and the difference of means, variances and proportions; tests for independence of attributes and goodness of fit.
Unit 4 · Probability & Probability Distributions
Probability and its axioms, conditional probability, addition and multiplication laws of probability; probability mass function and probability density function and their properties; Binomial, Poisson and Normal distributions and their properties.
Unit 5 · Discrete Mathematics
Sets, subsets, power sets, counting functions, countability; basic proof techniques — induction and proof by contradiction; inductive, deductive and propositional logic; basic data structures — stacks, queues, graphs, arrays, hash tables, trees; graph properties — connected components, degree, maximum-flow/minimum-cut concepts, graph colouring.