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 ...more

Number Theory Books

An Introduction to the Theory of Numbers

A Classical Introduction to Modern Number Theory (Graduate Texts in Mathematics, 84)

The Higher Arithmetic: An Introduction to the Theory of Numbers

Rational Points on Elliptic Curves (Undergraduate Texts in Mathematics)

Number Theory (Dover Books on Mathematics)

A Concise Introduction to the Theory of Numbers (Volume 0)

Prime Numbers and the Riemann Hypothesis

Elements of Number Theory (Undergraduate Texts in Mathematics)

A Friendly Introduction to Number Theory

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Lists

A First Course in Geometry by Edward T. Walsh

History of the Theory of Numbers, Volume II by Leonard Eugene Dickson

Mathematics

20 books — 1 voter

An Introduction To The Theory Of Numbers by G.H. Hardy

A classical introduction to modern number theory by Kenneth F. Ireland

Rational Points on Elliptic Curves by Joseph H. Silverman

A Course in Arithmetic by Jean-Pierre Serre

The Higher Arithmetic by Harold Davenport

Number Theory (MMath)

50 books — 8 voters

Real and Complex Analysis by Walter Rudin

Visual Complex Analysis by Tristan Needham

The Math of Neural Networks by Michael Taylor

Not Pop-Science - Mathematics

111 books — 10 voters

Tensor Methods in Statistics by Peter McCullagh.

Introduction to Analysis by Maxwell Rosenlicht

Vector Spaces and Matrices by Robert M. Thrall

Tensor and Vector Analysis by C.E. Springer

Influential Monographs in Modern Mathematics

101 books — 2 voters

Introduction to Quantum Mechanics by David J. Griffiths

The Elements of Statistical Learning by Trevor Hastie

Modern Quantum Mechanics by J.J. Sakurai

Options, Futures and Other Derivatives by John C. Hull

Classical Mechanics by Charles P. Poole Jr.

Mathematics Part II (University of Cambridge)

175 books — 16 voters

Related Genres

Mathematics
Numbers
Arithmetic

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Quotes Tagged “Number Theory”

“ Mathematicians call it “the arithmetic of congruences.” You can think of it as clock arithmetic. Temporarily replace the 12 on a clock face with 0. The 12 hours of the clock now read 0, 1, 2, 3, … up to 11. If the time is eight o’clock, and you add 9 hours, what do you get? Well, you get five o’clock. So in this arithmetic, 8 + 9 = 5; or, as mathematicians say, 8 + 9 ≡ 5 (mod 12), pronounced “eight plus nine is congruent to five, modulo twelve. ”
― John Derbyshire, Prime Obsession: Bernhard Riemann and the Greatest Unsolved Problem in Mathematics

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“ [W]e can transfer the study of any formal system—in fact the study of [all] formal systems—into number theory. ”
― Douglas R. Hofstadter, Godel, Escher, Bach: An Eternal Golden Braid

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