Number Theory

Number theory or, in older usage, arithmetic is a branch of pure mathematics devoted primarily to the study of the integers. It is sometimes called "The Queen of Mathematics" because of its foundational place in the discipline. Number theorists study prime numbers as well as the properties of objects made out of integers (e.g., rational numbers) or defined as generalizations of the integers (e.g., algebraic 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 anal
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An Introduction to the Theory of Numbers
Fermat's Enigma
Elementary Number Theory
A Classical Introduction to Modern Number Theory (Graduate Texts in Mathematics) (v. 84)
An Introduction to the Theory of Numbers
The Higher Arithmetic: An Introduction to the Theory of Numbers
Introduction to Analytic Number Theory
An Illustrated Theory of Numbers
A Pathway Into Number Theory
A Computational Introduction to Number Theory and Algebra
Number Theory
A Concise Introduction to the Theory of Numbers
Prime Numbers and the Riemann Hypothesis
Elements Of Number Theory (Undergraduate Texts In Mathematics)
The Book of Numbers
Real and Complex Analysis by Walter RudinMachine Learning by Samuel HackVisual Complex Analysis by Tristan NeedhamIntroductory Functional Analysis with Applications by Erwin KreyszigInside Interesting Integrals by Paul J. Nahin
Not Pop-Science - Mathematics
126 books — 10 voters

An Introduction to the Theory of Numbers by G.H. HardyA Classical Introduction to Modern Number Theory by Kenneth F. IrelandNumber Theory, Volume 1 by Henri CohenThe Higher Arithmetic by H. DavenportA Course in Arithmetic by Jean-Pierre Serre
Number Theory (MMath)
50 books — 6 voters


Adrien-Marie Legendre
It is a matter for considerable regret that Fermat, who cultivated the theory of numbers with so much success, did not leave us with the proofs of the theorems he discovered. In truth, Messrs Euler and Lagrange, who have not disdained this kind of research, have proved most of these theorems, and have even substituted extensive theories for the isolated propositions of Fermat. But there are several proofs which have resisted their efforts. ...more
Adrien-Marie Legendre

No part of mathematics is ever, in the long run, "useless." Most of number theory has very few "practical" applications. That does not reduce its importance, and if anything it enhances its fascination. No one can predict when what seems to be a most obscure theorem may suddenly be called upon to play some vital and hitherto unsuspected role. ...more
C. Stanley Ogilvy, Excursions in Number Theory

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