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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 By the early twentieth century, it had been superseded by "number theory".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.
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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.
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
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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.
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.
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Akshay Venkatesh (born 21 November 1981) is an Indian Australian mathematician. His research interests are in the fields of counting, equidistribution problems in automorphic forms and number theory, in particular representation theory, locally symmetric spaces and ergodic theory. He is the only Australian to have won medals at both the International Physics Olympiad and International Mathematics Olympiad, at the age of 12.
Raised in Perth, Western Australia, where he attended Scotch College, Venkatesh attended extracurricular training classes for gifted students in the state mathematical olympiad program. In 1993, whilst aged only 11, he competed at the 24th International Physics Olympiad in Williamsburg, Virginia, winning a bronze medal. The following year in 1994, he switched his attention to mathematics, and after placing second in the Australian Mathematical Olympiad, he won a silver medal in the 6th Asian Pacific Mathematics Olympiad, before winning a bronze medal in the International Mathematics Olympiad held in Hong Kong that year. He completed his secondary education that year, turning 13 at the end of the year. He entered the University of Western Australia the following year as the youngest ever student at the institution and was awarded First Class Honours in Pure mathematics in 1997, the youngest ever to achieve this feat, as well as being awarded the J. A. Woods Memorial Prize for being the leading graduating student of the year.[citation needed]
This page contains text from Wikipedia, the Free Encyclopedia -
http://en.wikipedia.org/wiki/Akshay_Venkatesh
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.
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.
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Introduction to Higher Mathematics - Lecture 10: Number Theory
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Introduction to Higher Mathematics - Lecture 10: Number Theory
- Duration: 32:33
- Updated: 05 Sep 2014
In this lecture we delve into number theory, one of the oldest branches of mathematics that still has unsolved problems to this day. http://www.polymathlectu...
http://wn.com/Introduction_to_Higher_Mathematics_-_Lecture_10_Number_Theory
In this lecture we delve into number theory, one of the oldest branches of mathematics that still has unsolved problems to this day. http://www.polymathlectu...
- published: 28 Feb 2013
- views: 22352
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http://wn.com/LMS_Popular_Lecture_Series_2013,_Addictive_Number_Theory
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- views: 317228
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Lec 4 | MIT 6.042J Mathematics for Computer Science, Fall 2010
- Duration: 80:25
- Updated: 05 Sep 2014
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- views: 21188
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From Quantum Physics to Number Theory
- Duration: 64:19
- Updated: 02 Sep 2014
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http://wn.com/From_Quantum_Physics_to_Number_Theory
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- Duration: 91:02
- Updated: 21 Aug 2014
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http://wn.com/Lecture_11_Number_Theory_for_PKC_Euclidean_Algorithm,_Euler's_Phi_Function_&_Euler's_Theorem
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- Updated: 23 Aug 2014
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http://wn.com/Number_Theory_-_Factors_Question_with_Explanation
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- views: 672
- author: 2IIM CAT Preparation
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- Updated: 09 Jul 2014
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- published: 17 May 2012
- views: 9278
- author: nptelhrd
An Introduction to Number Theory : College Math
- Duration: 1:45
- Updated: 11 Jun 2013
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http://wn.com/An_Introduction_to_Number_Theory_College_Math
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- published: 09 Nov 2012
- views: 342
- author: eHow
Recent Progress in Additive Prime Number Theory -- 2009 Moursund Lectures, Day 1
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- Updated: 03 Jan 2014
Terence Tao, 2006 Fields Medal Recipient University of California, Los Angeles Lecture one of a three part series Abstract: Additive prime number theory is t...
http://wn.com/Recent_Progress_in_Additive_Prime_Number_Theory_--_2009_Moursund_Lectures,_Day_1
Terence Tao, 2006 Fields Medal Recipient University of California, Los Angeles Lecture one of a three part series Abstract: Additive prime number theory is t...
- published: 14 Jul 2010
- views: 7346
- author: UOregon
Akshay Venkatesh - 1/4 Analytic number theory around torsion homology
- Duration: 63:38
- Updated: 10 Aug 2014
Akshay Venkatesh - Analytic number theory around torsion homology.
http://wn.com/Akshay_Venkatesh_-_1_4_Analytic_number_theory_around_torsion_homology
Akshay Venkatesh - Analytic number theory around torsion homology.
- published: 16 Jul 2014
- views: 372
- author: Institut des Hautes Études Scientifiques (IHÉS)
Elementary Number Theory - 1 - Introduction
- Duration: 5:02
- Updated: 25 Aug 2014
What's going on everybody! Welcome to today's tutorial on elementary number theory. Today we are talking about what's gonna be in this unit. Visit: http://ac...
http://wn.com/Elementary_Number_Theory_-_1_-_Introduction
What's going on everybody! Welcome to today's tutorial on elementary number theory. Today we are talking about what's gonna be in this unit. Visit: http://ac...
- published: 01 Nov 2013
- views: 1532
- author: Academy of One
Elementary Number Theory - 6 - Division Algorithm
- Duration: 3:51
- Updated: 03 Dec 2013
What's going on everybody! Welcome to today's video on elementary number theory. Today we are talking about the division algorithm. Have a great day! Visit: ...
http://wn.com/Elementary_Number_Theory_-_6_-_Division_Algorithm
What's going on everybody! Welcome to today's video on elementary number theory. Today we are talking about the division algorithm. Have a great day! Visit: ...
- published: 03 Dec 2013
- views: 382
- author: Academy of One
Online Workshop On Number Theory for CAT 13 Students
- Duration: 117:38
- Updated: 04 May 2014
Numerous CAT like questions solved in the simplest of the ways. 3 day intensive workshop covering all aspects of Number Theory relevant for CAT 13(2 hours a ...
http://wn.com/Online_Workshop_On_Number_Theory_for_CAT_13_Students
Numerous CAT like questions solved in the simplest of the ways. 3 day intensive workshop covering all aspects of Number Theory relevant for CAT 13(2 hours a ...
- published: 27 Aug 2013
- views: 1760
- author: VistaMindVideos
MathHistory13: The number theory revival
- Duration: 57:12
- Updated: 31 Aug 2014
After the work of Diophantus, there was something of a lapse in interest in pure number theory for quite some while. Around 1300 Gersonides developed the con...
http://wn.com/MathHistory13_The_number_theory_revival
After the work of Diophantus, there was something of a lapse in interest in pure number theory for quite some while. Around 1300 Gersonides developed the con...
- published: 30 Apr 2012
- views: 10328
- author: njwildberger
CA- CPT- QA-Index Number Theory-Part 1-by Navkar Institute
- Duration: 37:01
- Updated: 22 Aug 2014
Quantitative Aptitude Video lecture by Prof. Nirav Pandya. It contains a Chapter Index Number Especially designed By NAVKAR INSTITUTE as a part of online coa...
http://wn.com/CA-_CPT-_QA-Index_Number_Theory-Part_1-by_Navkar_Institute
Quantitative Aptitude Video lecture by Prof. Nirav Pandya. It contains a Chapter Index Number Especially designed By NAVKAR INSTITUTE as a part of online coa...
- published: 20 Jun 2014
- views: 226
- author: Navkar Institute
Number Theory Problem 6 - Perfect Square and Divisibility
- Duration: 6:59
- Updated: 15 Aug 2014
Please visit http://www.usamath.com for math problem solving classes.
http://wn.com/Number_Theory_Problem_6_-_Perfect_Square_and_Divisibility
Please visit http://www.usamath.com for math problem solving classes.
- published: 16 Mar 2012
- views: 1710
- author: MathXpress
- Playlist
- Chat
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
author: Bill Shillito
Introduction to Higher Mathematics - Lecture 10: Number Theory
Introduction to Higher Mathematics - Lecture 10: Number Theory
In this lecture we delve into number theory, one of the oldest branches of mathematics that still has unsolved problems to this day. http://www.polymathlectu...- published: 28 Feb 2013
- views: 22352
- author: Bill Shillito
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
author: London Mathematical Society
LMS Popular Lecture Series 2013, Addictive Number Theory
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
- views: 868
- author: London Mathematical Society
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
Intro to Number Theory Part 1
Intro to Number Theory Part 1
Introduction to Number Theory and the Fundamental theorem of arithmetic. Check out http://www.cscgtuts.com/home for more videos and resources Don't forget to...- published: 14 Oct 2011
- views: 24113
- author: cscgtuts
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
Andrew Granville - 1/3 The pretentious approach to analytic number theory
Andrew Granville - 1/3 The pretentious approach to analytic number theory
Andrew Granville - The pretentious approach to analytic number theory.- published: 14 Jul 2014
- views: 542
- author: Institut des Hautes Études Scientifiques (IHÉS)
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
Number Theory: Fermat's Little Theorem
Number Theory: Fermat's Little Theorem
Fermat's Little Theorem was observed by Fermat and proven by Euler, who generalized the theorem significantly. This theorem aids in dividing extremely large ...- published: 12 Jan 2012
- views: 34018
- author: Socratica
42:04
MathHistory3a: Greek number theory
The ancient Greeks studied squares, triangular numbers, primes and perfect numbers. Euclid...
published: 25 Mar 2011
author: njwildberger
MathHistory3a: Greek number theory
MathHistory3a: Greek number theory
The ancient Greeks studied squares, triangular numbers, primes and perfect numbers. Euclid stated the Fundamental theorem of Arithmetic: that a natural numbe...- published: 25 Mar 2011
- views: 16239
- author: njwildberger
13:41
Transcendental Numbers - Numberphile
Numbers like e and Pi cannot be made using normal algebra. Featuring Australia's Numeracy ...
published: 12 Jun 2013
author: Numberphile
Transcendental Numbers - Numberphile
Transcendental Numbers - Numberphile
Numbers like e and Pi cannot be made using normal algebra. Featuring Australia's Numeracy Ambassador, Simon Pampena. Extra footage: http://youtu.be/dzerDfN2E...- published: 12 Jun 2013
- views: 317228
- author: Numberphile
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
MathHistory22: Algebraic number theory and rings I
MathHistory22: Algebraic number theory and rings I
In the 19th century, algebraists started to look at extension fields of the rational numbers as new domains for doing arithmetic. In this way the notion of a...- published: 19 May 2014
- views: 3574
- author: njwildberger
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
author: MIT OpenCourseWare
Lec 4 | MIT 6.042J Mathematics for Computer Science, Fall 2010
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://ocw.mit.edu/6-042JF10 License: Creative Commons BY-NC-SA More informa...- published: 31 Dec 2012
- views: 21188
- author: MIT OpenCourseWare
64:19
From Quantum Physics to Number Theory
Michael Atiyah....
published: 18 Sep 2012
author: Cristiano Cavalcanti
From Quantum Physics to Number Theory
From Quantum Physics to Number Theory
Michael Atiyah.- published: 18 Sep 2012
- views: 7509
- author: Cristiano Cavalcanti
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
Lecture 11: Number Theory for PKC: Euclidean Algorithm, Euler's Phi Function & Euler's Theorem
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
- views: 4382
- author: Introduction to Cryptography by Christof Paar
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
author: 2IIM CAT Preparation
Number Theory - Factors Question with Explanation
Number Theory - Factors Question with Explanation
The sum of factors of a number is 124. What is the number? Explanation provided by Rajesh Balasubramanian (IITM, IIMB) 100%iler in CAT 2011 and 2012.- published: 04 Mar 2014
- views: 672
- author: 2IIM CAT Preparation
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
Number Theory: The Prime Number Theorem, an introduction
Number Theory: The Prime Number Theorem, an introduction
An introduction to the meaning and history of the prime number theorem - a fundamental result from analytic number theory. Narrated by Cissy Jones Artwork by...- published: 02 May 2013
- views: 2265
- author: Socratica
63:30
Mod-01 Lec-03 Introduction to Number Theory
Cryptography and Network Security by Prof. D. Mukhopadhyay, Department of Computer Science...
published: 17 May 2012
author: nptelhrd
Mod-01 Lec-03 Introduction to Number Theory
Mod-01 Lec-03 Introduction to Number Theory
Cryptography and Network Security by Prof. D. Mukhopadhyay, Department of Computer Science and Engineering, IIT Kharagpur. For more details on NPTEL visit ht...- published: 17 May 2012
- views: 9278
- author: nptelhrd
Youtube results:
1:45
An Introduction to Number Theory : College Math
Subscribe Now: http://www.youtube.com/subscription_center?add_user=Ehow Watch More: http:/...
published: 09 Nov 2012
author: eHow
An Introduction to Number Theory : College Math
An Introduction to Number Theory : College Math
Subscribe Now: http://www.youtube.com/subscription_center?add_user=Ehow Watch More: http://www.youtube.com/Ehow Number theory is actually a pretty intensive ...- published: 09 Nov 2012
- views: 342
- author: eHow
61:16
Recent Progress in Additive Prime Number Theory -- 2009 Moursund Lectures, Day 1
Terence Tao, 2006 Fields Medal Recipient University of California, Los Angeles Lecture one...
published: 14 Jul 2010
author: UOregon
Recent Progress in Additive Prime Number Theory -- 2009 Moursund Lectures, Day 1
Recent Progress in Additive Prime Number Theory -- 2009 Moursund Lectures, Day 1
Terence Tao, 2006 Fields Medal Recipient University of California, Los Angeles Lecture one of a three part series Abstract: Additive prime number theory is t...- published: 14 Jul 2010
- views: 7346
- author: UOregon
63:38
Akshay Venkatesh - 1/4 Analytic number theory around torsion homology
Akshay Venkatesh - Analytic number theory around torsion homology....
published: 16 Jul 2014
Akshay Venkatesh - 1/4 Analytic number theory around torsion homology
Akshay Venkatesh - 1/4 Analytic number theory around torsion homology
Akshay Venkatesh - Analytic number theory around torsion homology.- published: 16 Jul 2014
- views: 372
- author: Institut des Hautes Études Scientifiques (IHÉS)
5:02
Elementary Number Theory - 1 - Introduction
What's going on everybody! Welcome to today's tutorial on elementary number theory. Today ...
published: 01 Nov 2013
author: Academy of One
Elementary Number Theory - 1 - Introduction
Elementary Number Theory - 1 - Introduction
What's going on everybody! Welcome to today's tutorial on elementary number theory. Today we are talking about what's gonna be in this unit. Visit: http://ac...- published: 01 Nov 2013
- views: 1532
- author: Academy of One
