Concepts In Number Theory

Number theory is a branch of pure mathematics devoted primarily to the study of the integers. Number theorists study prime numbers as well as the properties of objects made out of integers (such as rational numbers) or defined as generalizations of the integers. Integers can be 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 (e.g., the Riemann zeta function) that encode properties of the integers, primes or other number-theoretic objects in some fashion (analytic number theory). One may also study real numbers in relation to rational numbers, e.g., as approximated by the latter (diophantine approximation). The older term for number theory is arithmetic. By the early twentieth century, it had been superseded by “number theory”. The use of the term arithmetic for number theory regained some ground in the second half of the 20th century, arguably in part due to French influence. The book is replete with features which enable the building of a firm foundation of the underlying principles of the subject and also provide adequate scope for testing the comprehension acquired by the students.