Number Theory Hand Written Note By P Kalika

Here, We provide to Number Theory Hand Written Note By P Kalika. Number theory (or mathematic or higher mathematic in older usage) may be a branch of 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 THEORY HAND WRITTEN NOTENumber 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 know the properties of integer systems in spite of their apparent complexity.

Integers are often considered either in themselves or as solutions to equations (Diophantine geometry). Questions in number theory are often best understood through the study of analytical objects (for example, the Riemann zeta function) that encode properties of the integers, primes or other number-theoretic objects in some fashion (analytic number theory). One can also study real numbers in reference to rational numbers, for instance, as approximated by the latter (Diophantine approximation).

The older term for number theory is arithmetic. By the first twentieth century, it had been superseded by “number theory”. (The word “mathematic” is employed by the overall public to mean “elementary calculations”; it’s also acquired other meanings in mathematical logic, as in Peano mathematic, and computer science, as in floating-point mathematic.) The use of the term arithmetic for number theory regained some ground in the last half of the 20th century, arguably partially thanks to French influence. Especially, mathematical is preferred as an adjective to number-theoretic.




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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”.

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.

In this book, the author solves the matter of maintaining the interest of scholars at both levels by offering a combinatorial approach to elementary number theory. Of particular importance during this text is that the author’s emphasis on the worth of numerical examples in number theory and therefore the role of computers in obtaining such examples.


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