Number Theory

Introduction to Higher Mathematics - Lecture 10: Number Theory

Duration: 32:33
Updated: 17 Aug 2013

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

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Transcendental Numbers - Numberphile

Duration: 13:41
Updated: 19 Aug 2013

Numbers like e and Pi cannot be made using normal algebra. Featuring Australia's Numeracy Ambassador, Simon Pampena. Extra footage: http://youtu.be/dzerDfN2E...

http://wn.com/Transcendental_Numbers_-_Numberphile

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LMS Popular Lecture Series 2013, Addictive Number Theory

Duration: 55:48
Updated: 23 Apr 2014

Addictive Number Theory by Dr Vicky Neale Held at the Institute of Education in London

http://wn.com/LMS_Popular_Lecture_Series_2013,_Addictive_Number_Theory

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Intro to Number Theory Part 1

Duration: 9:59
Updated: 16 Aug 2013

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...

http://wn.com/Intro_to_Number_Theory_Part_1

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MathHistory3a: Greek number theory

Duration: 42:04
Updated: 13 Aug 2013

The ancient Greeks studied squares, triangular numbers, primes and perfect numbers. Euclid stated the Fundamental theorem of Arithmetic: that a natural numbe...

http://wn.com/MathHistory3a_Greek_number_theory

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MathHistory22: Algebraic number theory and rings I

Duration: 48:27
Updated: 19 May 2014

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 an abstract ring was born, through the more concrete examples of rings of algebraic integers in number fields. Key examples include the Gaussian integers, which are complex numbers with integer coefficients, and which are closed under addition, subtraction and multiplication. The properties under division mimic those of the integers, with primes, units and most notably unique factorization. However for other algebraic number rings, unique factorization proved more illusive, and had to be rescued by Kummer and Dedekind with the introduction of ideal elements, or just ideals. This interesting area of number theory does have some foundational difficulties, as in most current formulations it rests ultimately on transcendental results re complex numbers, notably the Fundamental theory of algebra. Sadly, this is not as solid as it is usually made out, and so very likely new purely algebraic techniques are needed to recast some of the ideas into a more solid framework.

http://wn.com/MathHistory22_Algebraic_number_theory_and_rings_I

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Lec 4 | MIT 6.042J Mathematics for Computer Science, Fall 2010

Duration: 80:25
Updated: 21 Jun 2014

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...

http://wn.com/Lec_4_|_MIT_6.042J_Mathematics_for_Computer_Science,_Fall_2010

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Fermat's Little Theorem

Duration: 10:35
Updated: 07 Aug 2013

Fermat's Little Theorem was observed by Fermat and proven by Euler, who generalized the theorem significantly. This theorem aids in dividing extremely large ...

http://wn.com/Fermat's_Little_Theorem

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Recent Progress in Additive Prime Number Theory -- 2009 Moursund Lectures, Day 1

Duration: 61:16
Updated: 31 Jul 2013

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

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From Quantum Physics to Number Theory

Duration: 64:19
Updated: 06 Aug 2013

Michael Atiyah.

http://wn.com/From_Quantum_Physics_to_Number_Theory

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Lecture 11: Number Theory for PKC: Euclidean Algorithm, Euler's Phi Function and Euler's Theorem

Duration: 91:02
Updated: 30 Jan 2014

http://wn.com/Lecture_11_Number_Theory_for_PKC_Euclidean_Algorithm,_Euler's_Phi_Function_and_Euler's_Theorem

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Number Theory Problem 6 - Perfect Square and Divisibility

Duration: 6:59
Updated: 13 Jul 2013

Please visit http://www.mathxpress.com for more math problem solving videos.

http://wn.com/Number_Theory_Problem_6_-_Perfect_Square_and_Divisibility

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Arithmetic Geometry - solving number theoretical problems using geometrical intuition

Duration: 3:34
Updated: 02 Aug 2013

In the Department of Mathematical Sciences at Keio University, the Bannai Group, led by Professor Kenichi Bannai, is conducting research in number theory. Nu...

http://wn.com/Arithmetic_Geometry_-_solving_number_theoretical_problems_using_geometrical_intuition

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Andrew Granville - 1/3 The pretentious approach to analytic number theory

Duration: 68:49
Updated: 14 Jul 2014

Andrew Granville - The pretentious approach to analytic number theory

http://wn.com/Andrew_Granville_-_1_3_The_pretentious_approach_to_analytic_number_theory

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An Introduction to Number Theory : College Math

Duration: 1:45
Updated: 11 Jun 2013

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 ...

http://wn.com/An_Introduction_to_Number_Theory_College_Math

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MathHistory22b: Algebraic number theory and rings II

Duration: 27:29
Updated: 19 May 2014

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 an abstract ring was born, through the more concrete examples of rings of algebraic integers in number fields. Key examples include the Gaussian integers, which are complex numbers with integer coefficients, and which are closed under addition, subtraction and multiplication. The properties under division mimic those of the integers, with primes, units and most notably unique factorization. However for other algebraic number rings, unique factorization proved more illusive, and had to be rescued by Kummer and Dedekind with the introduction of ideal elements, or just ideals. This interesting area of number theory does have some foundational difficulties, as in most current formulations it rests ultimately on transcendental results re complex numbers, notably the Fundamental theory of algebra. Sadly, this is not as solid as it is usually made out, and so very likely new purely algebraic techniques are needed to recast some of the ideas into a more solid framework.

http://wn.com/MathHistory22b_Algebraic_number_theory_and_rings_II

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MathHistory13: The number theory revival

Duration: 57:12
Updated: 14 Aug 2013

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

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MathHistory3b: Greek number theory (cont.)

Duration: 24:41
Updated: 25 Jul 2013

The ancient Greeks studied squares, triangular numbers, primes and perfect numbers. Euclid stated the Fundamental theorem of Arithmetic: that a natural numbe...

http://wn.com/MathHistory3b_Greek_number_theory_(cont.)

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Number theory - geometrical connection (part 1)

Duration: 2:35
Updated: 14 Aug 2013

This is a work i made long time ago, about the prime numbers. It became a wider study. My video got the attention of a math forum called www.cut-the-knot.org...

http://wn.com/Number_theory_-_geometrical_connection_(part_1)

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Wilson's Theorem

Duration: 3:09
Updated: 19 Jun 2013

A proof of Wilson's Theorem, a basic result from elementary number theory. The theorem can be strengthened into an iff result, thereby giving a test for prim...

http://wn.com/Wilson's_Theorem

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Number Theory: Prime Numbers, Factors, Counting Factors, D-Function (1/3)

Duration: 9:48
Updated: 29 Jul 2013

Part 1/3 The following lesson covers: -Prime Numbers -Factors (and Unique Factorization Theorem/Fundamental Theorem of Arithmetic) -Factors -Counting Factors...

http://wn.com/Number_Theory_Prime_Numbers,_Factors,_Counting_Factors,_D-Function_(1_3)

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July 29 Office Hours - Number Theory

Duration: 87:36
Updated: 30 Jul 2014

July 29 Office Hours - Number Theory

http://wn.com/July_29_Office_Hours_-_Number_Theory

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MathHistory5a: Number theory and algebra in Asia

Duration: 49:46
Updated: 03 Aug 2013

After the later Alexandrian mathematicians Ptolemy and Diophantus, Greek mathematics went into decline and the focus shifted eastward. This lecture discusses...

http://wn.com/MathHistory5a_Number_theory_and_algebra_in_Asia

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Branches of Mathematics

Pure mathematics

Applied mathematics

Related Topics

Introduction to Higher Mathematics - Lecture 10: Number Theory

Transcendental Numbers - Numberphile

LMS Popular Lecture Series 2013, Addictive Number Theory

Intro to Number Theory Part 1

MathHistory3a: Greek number theory

MathHistory22: Algebraic number theory and rings I

Lec 4 | MIT 6.042J Mathematics for Computer Science, Fall 2010

Fermat's Little Theorem

Recent Progress in Additive Prime Number Theory -- 2009 Moursund Lectures, Day 1

From Quantum Physics to Number Theory

Lecture 11: Number Theory for PKC: Euclidean Algorithm, Euler's Phi Function and Euler's Theorem

Number Theory Problem 6 - Perfect Square and Divisibility

Arithmetic Geometry - solving number theoretical problems using geometrical intuition

Andrew Granville - 1/3 The pretentious approach to analytic number theory

Introduction to Higher Mathematics - Lecture 10: Number Theory

Transcendental Numbers - Numberphile

LMS Popular Lecture Series 2013, Addictive Number Theory

Intro to Number Theory Part 1

MathHistory3a: Greek number theory

MathHistory22: Algebraic number theory and rings I

Lec 4 | MIT 6.042J Mathematics for Computer Science, Fall 2010

Fermat's Little Theorem

Recent Progress in Additive Prime Number Theory -- 2009 Moursund Lectures, Day 1

From Quantum Physics to Number Theory

Lecture 11: Number Theory for PKC: Euclidean Algorithm, Euler's Phi Function and Euler's Theorem

Number Theory Problem 6 - Perfect Square and Divisibility

Arithmetic Geometry - solving number theoretical problems using geometrical intuition

Andrew Granville - 1/3 The pretentious approach to analytic number theory

An Introduction to Number Theory : College Math

MathHistory22b: Algebraic number theory and rings II

MathHistory13: The number theory revival

MathHistory3b: Greek number theory (cont.)

Number theory - geometrical connection (part 1)

Wilson's Theorem

Number Theory: Prime Numbers, Factors, Counting Factors, D-Function (1/3)

July 29 Office Hours - Number Theory

MathHistory5a: Number theory and algebra in Asia

Introduction to Higher Mathematics - Lecture 10: Number Theory

Transcendental Numbers - Numberphile

LMS Popular Lecture Series 2013, Addictive Number Theory

Intro to Number Theory Part 1

MathHistory3a: Greek number theory

MathHistory22: Algebraic number theory and rings I

Lec 4 | MIT 6.042J Mathematics for Computer Science, Fall 2010

Fermat's Little Theorem

Recent Progress in Additive Prime Number Theory -- 2009 Moursund Lectures, Day 1

From Quantum Physics to Number Theory

Lecture 11: Number Theory for PKC: Euclidean Algorithm, Euler's Phi Function and Euler's Theorem

Number Theory Problem 6 - Perfect Square and Divisibility

Arithmetic Geometry - solving number theoretical problems using geometrical intuition

Andrew Granville - 1/3 The pretentious approach to analytic number theory

An Introduction to Number Theory : College Math

MathHistory22b: Algebraic number theory and rings II

MathHistory13: The number theory revival

MathHistory3b: Greek number theory (cont.)