Number Theory

By IntroBooks Team

In old times, number theory was also known as arithmetic.
However, now arithmetic and number theory are considered as
separate branches from each other's, it was not same in old
times. Number theory is one of the many important branches
of pure mathematics. This branch is mainly dedicated and
includes study about integers. This theory describes many
fundamental and basic concepts of mathematics that were used
to develop modern concepts. Thus, number theory is often
referred as "Queen of Mathematics". In number theory,
following concepts are described:
Concept of prime numbers
Properties of objects that are derived through integers
Generalization of integers
Rational numbers and algebraic integers are significant concepts
that are included in number theory. In number theory, integers
are considered as a solution to a particular problem. This
concept is known as Riemann Zeta Function. However, it is not
necessary to consider them as solution only; they can also be
considered in themselves. Study of analytical objects helps to
understand questions in number theory. Properties of integers,
prime numbers and number-theoretic objects are described in
Riemann Zeta Function. These properties can be studied
descriptively in a separated branch named analytic number
theory. In Diophantine approximation, real numbers are learnt
in ration to relational number.
In older terms, arithmetic was used to refer number theory.
However, it was separated in early 20
th century. Arithmetic
word is now used to refer to general elementary calculations.
Term arithmetic is now used in many fields such as:
Mathematical logic
Peano arithmetic
Computer science
Floating point arithmetic
In late 20
th century, French theorists leaved a noticeable
impact on number theory. Due to their influence, they again
related tern arithmetic with number theory. However, many
theorists argued upon this and denied to accept this as it was
already proven false in past time. However, term arithmetical is
now considered as adjective to number-theoretic. Early 20th
century was a golden time for development of number theory,
especially the time span of 1930s and 1940s. Many important
results were acquired in that period. Later on, 1970s was
proven an important period as well with the development of
computational complexity theory.
Number theory is an important branch of pure mathematics
since it contains many basic concepts that are used to build up
complex concepts of pure mathematics. One who is looking for
a breakthrough in broad term mathematics is suggested to start
from this theory. It will clear up basic concepts so it will be
surprisingly easy to understand complex concepts. This short
book describes all the basic concepts without going in too deep.
So, one can use this basic knowledge to understand complex
concepts easily and effectively.

• Language: English
• Publisher: IntroBooks
• Release date: Nov 21, 2019
• ISBN: 9781393327592

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Number Theory

IntroBooks #241

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Copyright © 2016 Can Akdeniz

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Preface

In old times, number theory was also known as arithmetic. However, now arithmetic and number theory are considered as separate branches from each other’s, it was not same in old times. Number theory is one of the many important branches of pure mathematics. This branch is mainly dedicated and includes study about integers. This theory describes many fundamental and basic concepts of mathematics that were used to develop modern concepts. Thus, number theory is often referred as Queen of Mathematics. In number theory, following concepts are described:

Concept of prime numbers

Properties of objects that are derived through integers

Generalization of integers

Rational numbers and algebraic integers are significant concepts that are included in number theory. In number theory, integers are considered as a solution to a particular problem. This concept is known as Riemann Zeta Function. However, it is not necessary to consider them as solution only; they can also be considered in themselves. Study of analytical objects helps to understand questions in number theory. Properties of integers, prime numbers and number-theoretic objects are described in Riemann Zeta Function. These properties can be studied descriptively in a separated branch named analytic number theory. In Diophantine approximation, real numbers are learnt in ration to relational number.

In older terms, arithmetic was used to refer number theory. However, it was separated in early 20th century. Arithmetic word is now used to refer to general elementary calculations. Term arithmetic is now used in many fields such as:

Mathematical logic

Peano arithmetic

Computer science

Floating point arithmetic

In late 20th century, French theorists leaved a