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
Elementary Number Theory
A Classical Introduction to Modern Number Theory (Graduate Texts in Mathematics, 84)
Fermat's Enigma
An Introduction to the Theory of Numbers
Introduction to Analytic Number Theory
Rational Points on Elliptic Curves (Undergraduate Texts in Mathematics)
The Higher Arithmetic: An Introduction to the Theory of Numbers
A Concise Introduction to the Theory of Numbers
Prime Numbers and the Riemann Hypothesis
Elements of Number Theory (Undergraduate Texts in Mathematics)
On Numbers and Games
The Music of the Primes
104 Number Theory Problems: From the Training of the USA IMO Team
Number Theory (Dover Books on Mathematics)
Machine Learning by Samuel HackReal and Complex Analysis by Walter RudinVisual Complex Analysis by Tristan NeedhamGreek Mathematical Works, Volume I by Ivor  ThomasThe Math of Neural Networks by Michael Taylor
Not Pop-Science - Mathematics
108 books — 9 voters
An Introduction To The Theory Of Numbers by G.H. HardyA classical introduction to modern number theory by Kenneth F. IrelandRational Points on Elliptic Curves by Joseph H. SilvermanThe Higher Arithmetic by Harold DavenportA Course in Arithmetic by Jean-Pierre Serre
Number Theory (MMath)
50 books — 8 voters



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

It is shown that the golden ratio plays a prominent role in the dimensions of all objects which exhibit five-fold symmetry. It is also showed that among the irrational numbers, the golden ratio is the most irrational and, as a result, has unique applications in number theory, search algorithms, the minimization of functions, network theory, the atomic structure of certain materials and the growth of biological organisms.
Richard A. Dunlap, GOLDEN RATIO AND FIBONACCI NUMBERS, THE

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