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32:33
Introduction to Higher Mathematics - Lecture 10: Number Theory
In this lecture we delve into number theory, one of the oldest branches of mathematics tha...
published: 28 Feb 2013
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55:48
LMS Popular Lecture Series 2013, Addictive Number Theory
Addictive Number Theory by Dr Vicky Neale Held at the Institute of Education in London....
published: 23 Apr 2014
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9:59
Intro to Number Theory Part 1
Introduction to Number Theory and the Fundamental theorem of arithmetic. Check out http://...
published: 14 Oct 2011
author: cscgtuts
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10:35
Number Theory: Fermat's Little Theorem
Fermat's Little Theorem was observed by Fermat and proven by Euler, who generalized the th...
published: 12 Jan 2012
author: Socratica
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13:41
Transcendental Numbers - Numberphile
Numbers like e and Pi cannot be made using normal algebra. Featuring Australia's Numeracy...
published: 12 Jun 2013
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68:49
Andrew Granville - 1/3 The pretentious approach to analytic number theory
Andrew Granville - The pretentious approach to analytic number theory....
published: 14 Jul 2014
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48:27
MathHistory22: Algebraic number theory and rings I
In the 19th century, algebraists started to look at extension fields of the rational numbe...
published: 19 May 2014
author: njwildberger
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80:25
Lec 4 | MIT 6.042J Mathematics for Computer Science, Fall 2010
Lecture 4: Number Theory I Instructor: Marten van Dijk View the complete course: http://oc...
published: 31 Dec 2012
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91:02
Lecture 11: Number Theory for PKC: Euclidean Algorithm, Euler's Phi Function & Euler's Theorem
For slides, a problem set and more on learning cryptography, visit www.crypto-textbook.com...
published: 30 Jan 2014
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69:14
Progress in Prime Number Theory (Roger Heath-Brown)
Abstract: This lecture will discuss prime numbers and their history, along with some of th...
published: 10 Nov 2014
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2:35
Number theory - geometrical connection (part 1)
This is a work i made long time ago, about the prime numbers. It became a wider study. ...
published: 27 Dec 2007
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42:04
MathHistory3a: Greek number theory
The ancient Greeks studied squares, triangular numbers, primes and perfect numbers. Euclid...
published: 25 Mar 2011
author: njwildberger
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2:01
Number Theory: The Prime Number Theorem, an introduction
An introduction to the meaning and history of the prime number theorem - a fundamental res...
published: 02 May 2013
author: Socratica
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7:01
Number Theory - Factors Question with Explanation
The sum of factors of a number is 124. What is the number? Explanation provided by Rajesh ...
published: 04 Mar 2014
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Number Theory: Wilson's Theorem
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Number theory (or arithmetic) 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 (such as, for example, 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 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 word "arithmetic" is used by the general public to mean "elementary calculations"; it has also acquired other meanings in mathematical logic, as in Peano arithmetic, and computer science, as in floating point arithmetic.) 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. In particular, arithmetical is preferred as an adjective to number-theoretic.




This page contains text from Wikipedia, the Free Encyclopedia - http://en.wikipedia.org/wiki/Number_theory

This article is licensed under the Creative Commons Attribution-ShareAlike 3.0 Unported License, which means that you can copy and modify it as long as the entire work (including additions) remains under this license.


Listen to Andrew Granville interviews

Andrew James Granville (born 1962) is a British mathematician, working in the field of number theory.

He has been a faculty member at the Université de Montréal since 2002. Before moving to Montreal he was a mathematics professor at University of Georgia (UGA) from 1991 until 2002. He was a section speaker in the 1994 International Congress of Mathematicians together with Carl Pomerance from UGA.

Granville received his Bachelor of Arts (Honours) (1983) and his Certificate of Advanced Studies (Distinction) (1984) from Trinity College, Cambridge University. He received his Ph.D. from Queen's University in 1987 and was inducted into the Royal Society of Canada in 2006.

Granville's work is mainly in number theory, in particular analytic number theory. Along with Carl Pomerance and W. R. (Red) Alford he proved the infinitude of Carmichael numbers in 1994. This proof was based on a conjecture given by Paul Erdős.

In 2008, he won the Chauvenet Prize from the Mathematical Association of America for his paper "It is easy to determine whether a given integer is prime".




This page contains text from Wikipedia, the Free Encyclopedia - http://en.wikipedia.org/wiki/Andrew_Granville

This article is licensed under the Creative Commons Attribution-ShareAlike 3.0 Unported License, which means that you can copy and modify it as long as the entire work (including additions) remains under this license.