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.polymathlectures.org/

Prerequisites: To follow this video, you will want to first learn the basics of congruences.

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You might like the other videos in our Number Theory Playlist:

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Subject: Number Theory

Teacher: Michael Harrison

Artist: Katrina de Dios]]>

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Number theory is actually a pretty intensive course that's in junior or senior levels of undergraduate college mathematics. Get an introduction to number theory with help from a longtime mathematics educator in this free video clip.

Expert: Jimmy Chang

Filmmaker: Christopher Rokosz

Series Description: Topics like number theory will start to come into play as your mathematics career advances towards the college level and beyond. Learn about the ins and outs of college math with help from a longtime mathematics educator in this free video series.

Held at the Institute of Education in London]]>

Narrated by Cissy Jones

Artwork by Kim Parkhurst, Katrina de Dios and Olga Reukova

Written & Produced by Michael Harrison & Kimberly Hatch Harrison]]>

Source: Wikipedia.org article, adapted under https://creativecommons.org/licenses/by-sa/3.0/ license.

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 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 By the early twentieth century, it had been superseded by "number theory".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.]]>

We also state Fermat's little theorem using the modular arithmetic language introduced by Gauss.

My research papers can be found at my Research Gate page, at https://www.researchgate.net/profile/.... I also have a blog at http://njwildberger.com/, where I will discuss lots of foundational issues, along with other things, and you can check out my webpages at http://web.maths.unsw.edu.au/~norman/. Of course if you want to support all these bold initiatives, become a Patron of this Channel at https://www.patreon.com/njwildberger?... .]]>

Date: December 1, 2010

Video taken from:

http://video.impa.br/index.php?page=solenidades-e-palestras-especiais]]>

My video got the attention of a math forum called www.cut-the-knot.org. The user Alexander Bogomolny, made an extended work about the process of the video. You can take a look at it here:

http://www.cut-the-knot.org/Curriculum/Arithmetic/PrimesFromTriangle.shtml

(IT'S NOT THE FIRST TIME THIS VIDEO IS UPLOADED TO YOUTUBE. I DID IT A YEAR AGO, IN A NOW DELETED ACCOUNT.)]]>

We also discuss the influence of probably the most important problem of the mathematical sciences from a historical point of view: understanding the motion of the night sky, in particular the planets. This motivated work in trigonometry, particularly spherical trigonometry, of both Indian and Arab mathematicians.

Prominent mathematicians whose work we discuss include Sun Zi, Aryabhata, Brahmagupta, Bhaskara I and II, al-Khwarizmi, al-Biruni and Omar Khayyam.

If you are interested in supporting my YouTube Channel: here is the link to my Patreon page:

https://www.patreon.com/njwildberger?ty=h You can sign up to be a Patron, and give a donation per view, up to a specified monthly maximum.]]>