Mathematics

Distributions of random variables, conditional probability and agreement independence, probability distributions, distribution of associations of random variables, queue theory, reliability theory, efficient control and sample acceptance, information theory and computing.

Introduction to probability, discrete and continuous random variables, probability and distributional coupling, mathematical expectation, descriptive statistics, random sample, median estimation, point estimation and confidence interval, hypothesis testing, regression and correlation

Field functions, operations on functions, drawing functions, trigonometric functions, inverse function, exponential and logarithmic functions, inverse trigonometric functions, limits and connection, derivation, chain rule, implicit derivation, differentials, Rolle's theorem, mean value theorem, increasing and decreasing functions, concavity, minimum and maximum values, functions, drawing fractional functions, Infinite integration, the basic theorem of calculus, the area between a curve and the horizontal axis

Measurements, motion in one direction, vectors, motion in two directions, laws of motion, work and energy, potential energy and conservation of energy, collision and linear torque, rotation, simple harmonic motion

Classification, solution of ordinary differential equations of the first degree, second degree and higher degrees, mechanical and physical applications, solution using series, power series and individual normal and non-normal points, Laplace transform method, linear and non-linear equations, homogeneous and non-homogeneous equations.

Real numbers, order, absolute value, definite subsets, completeness property, smallest upper term and largest lower term, sequences, limits, Cauchy sequence, regressive sequence, increasing and decreasing sequences, functions, limits and connection at a point, continuity over an interval, regular continuity, differentiability, the relationship between continuity and differentiation, Rolle's theorem, mean value theorem, applications to the mean value theorem.

Vector differential calculus, gradient, divergence, rotation, vector calculus, linear integration, surface integral, Green's theorem, Stokes's theorem, divergence theorem, inverse and implicit coupling theorem, Leibniz's theorem, calculating function change in a variable.

Solutions to linear systems, matrices and operations on them, homogeneous and inhomogeneous systems, Gaussian reductions, primitive matrices and methods for finding inverse matrices, determinants, Euclidean space, linear transformations and their properties, general space, subspace, basis, dimensions, row space, column space, null space, rank and null, internal product spaces, feature values, diagonals.

Point estimate, confidence interval. Cramer and Rowe's inequality, hypothesis testing, UMP test, proportional likelihood test, chi-square test, SPRT, non-parametric methods, adequate statistics and its properties, family of complete statistical foundations, Fisher information, information theory