Number Theory - E-book - ePub

In old times, number theory was also known as arithmetic. However, now arithmetic and number theory are considered asseparate branches from each other's, it was not same in oldtimes. Number theory is one of the many important branchesof pure mathematics. This branch is mainly dedicated andincludes study about integers. This theory describes manyfundamental and basic concepts of mathematics that were usedto develop modern concepts.
Thus, number theory is oftenreferred as "Queen of Mathematics". In number theory, following concepts are described:Concept of prime numbersProperties of objects that are derived through integersGeneralization of integersRational numbers and algebraic integers are significant conceptsthat are included in number theory. In number theory, integersare considered as a solution to a particular problem. Thisconcept is known as Riemann Zeta Function.
However, it is notnecessary to consider them as solution only; they can also beconsidered in themselves. Study of analytical objects helps tounderstand questions in number theory. Properties of integers, prime numbers and number-theoretic objects are described inRiemann Zeta Function. These properties can be studieddescriptively in a separated branch named analytic numbertheory. In Diophantine approximation, real numbers are learntin ration to relational number.
In older terms, arithmetic was used to refer number theory. However, it was separated in early 20th century. Arithmeticword is now used to refer to general elementary calculations. Term arithmetic is now used in many fields such as:Mathematical logicPeano arithmeticComputer scienceFloating point arithmeticIn late 20th century, French theorists leaved a noticeableimpact on number theory. Due to their influence, they againrelated tern arithmetic with number theory.
However, manytheorists argued upon this and denied to accept this as it wasalready proven false in past time. However, term arithmetical isnow considered as adjective to number-theoretic. Early 20thcentury was a golden time for development of number theory, especially the time span of 1930s and 1940s. Many importantresults were acquired in that period. Later on, 1970s wasproven an important period as well with the development ofcomputational complexity theory.
Number theory is an important branch of pure mathematicssince it contains many basic concepts that are used to build upcomplex concepts of pure mathematics. One who is looking fora breakthrough in broad term mathematics is suggested to startfrom this theory. It will clear up basic concepts so it will besurprisingly easy to understand complex concepts. This shortbook describes all the basic concepts without going in too deep.
So, one can use this basic knowledge to understand complexconcepts easily and effectively.