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Number theory is a branch of pure mathematics devoted primarily to the study of the integers and integer-valued functions. German mathematician Carl Friedrich Gauss (1777–1855) said, “Mathematics is the queen of the sciences—and number theory is the queen of mathematics. Number theorists study prime numbers as well as the properties of objects made out of integers (for example, rational numbers) or defined as generalizations of the integers (for example, algebraic integers). Number theory seeks to understand the properties of integer systems in spite of their apparent complexity. Free download PDF CSIR NET Solution Of NT, NA, LPP, And DS By P Kalika.
Number theory may be a branch of mathematics dedicated to the study of the natural numbers and therefore the integers. It is the study of the set of positive whole numbers which are usually called the set of natural numbers. As it holds the foundational place within the discipline, Number theory is additionally called “The Queen of Mathematics”. Free download PDF CSIR NET Solution Of NT, NA, LPP, And DS By P Kalika.
Although mathematics majors are usually conversant with number theory by the time they need to be completed a course in abstract algebra, other undergraduates, especially those in education and therefore the humanistic discipline, often need a more basic introduction to the subject.
Numerical analysis is the study of algorithms that use numerical approximation (as opposed to symbolic manipulations) for the problems of mathematical analysis. Numerical analysis naturally finds application in all fields of engineering and the physical sciences, but in the 21st century also the life sciences, social sciences, medicine, business, and even the arts have adopted elements of scientific computations.
The growth in computing power has revolutionized the use of realistic mathematical models in science and engineering, and subtle numerical analysis is required to implement these detailed models of the world. For example, ordinary differential equations appear in celestial mechanics; numerical linear algebra is important for data analysis; stochastic differential equations and Markov chains are essential in simulating living cells for medicine and biology. Free download PDF CSIR NET Solution Of NT, NA, LPP, And DS By P Kalika.
Numerical analysis continues this long tradition: rather than exact symbolic answers, which can only be applied to real-world measurements by a translation into digits, it gives approximate solutions within specified error bounds. Free download PDF CSIR NET Solution Of NT, NA, LPP, And DS By P Kalika.
BOOK NAME – CSIR NET SOLUTION OF NT, NA, LPP, AND DS
AUTHOR – P KALIKA
YEAR – DECEMBER-2014 TO 2019
SIZE – 27.1MB
PAGES – 88
Linear Programming Problems:
In Mathematics, linear programming is a method of optimizing operations with some constraints. The main objective of linear programming is to maximize or minimize the numerical value. It consists of linear functions that are subjected to the constraints in the form of linear equations or in the form of inequalities.
Linear Programming is widely used in Mathematics and some other fields such as economics, business, telecommunication, and manufacturing fields. In this article, let us discuss the definition of linear programming, its components, a simplex method with linear programming problems. Free download PDF CSIR NET Solution Of NT, NA, LPP, And DS By P Kalika.
Linear programming (LP) or Linear Optimisation may be defined as the problem of maximizing or minimizing a linear function that is subjected to linear constraints. The constraints may be equalities or inequalities. The optimization problems involve the calculation of profit and loss. Linear programming problems are an important class of optimization problems, that helps to find the feasible region and optimize the solution in order to have the highest or lowest value of the function.
Linear programming is the method of considering different inequalities relevant to a situation and calculating the best value that is required to be obtained in those conditions. Free download PDF CSIR NET Solution Of NT, NA, LPP, And DS By P Kalika.
Dynamical systems theory is an area of mathematics used to describe the behavior of the complex dynamical systems, usually by employing differential equations or difference equations. When differential equations are employed, the theory is called continuous dynamical systems. From a physical point of view, continuous dynamical systems are a generalization of classical mechanics, a generalization where the equations of motion are postulated directly and are not constrained to be Euler–Lagrange equations of the least action principle. Free download PDF CSIR NET Solution Of NT, NA, LPP, And DS By P Kalika.
When difference equations are employed, the theory is called discrete dynamical systems. When the time variable runs over a set that is discrete over some intervals and continuous over other intervals or is any arbitrary time-set such as a cantor set, one gets dynamic equations on time scales. Some situations may also be modeled by mixed operators, such as differential-difference equations. Free download PDF CSIR NET Solution Of NT, NA, LPP, And DS By P Kalika.
Dynamical systems theory deals with the long-term qualitative behavior of dynamical systems, and studies the nature of, and when possible the solutions of, the equations of motion of systems that are often primarily mechanical or otherwise physical in nature, such as planetary orbits and the behavior of electronic circuits, as well as systems that arise in biology, economics, and elsewhere. Much of modern research is focused on the study of chaotic systems.
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