The High Schooler Who Solved a Prime Number Theorem
In his senior year of high school, Daniel Larsen proved a key theorem about Carmichael numbers — strange entities that mimic the primes. “It would be a paper that any mathematician would be really proud to have written,” said one mathematician. Read more at Quanta Magazine: https://www.qua
From playlist Discoveries
Theory of numbers: Prime tests
This lecture is part of an online undergraduate course on the theory of numbers. We describe how to use Fermat's theorem as a test to see if numbers n are not prime, by checking to see if a^n=a mod n for various numbers a. We then given an example of a "Carmichael number": a composite num
From playlist Theory of numbers
Theory of numbers: Congruences: Euler's theorem
This lecture is part of an online undergraduate course on the theory of numbers. We prove Euler's theorem, a generalization of Fermat's theorem to non-prime moduli, by using Lagrange's theorem and group theory. As an application of Fermat's theorem we show there are infinitely many prim
From playlist Theory of numbers
The Campbell-Baker-Hausdorff and Dynkin formula and its finite nature
In this video explain, implement and numerically validate all the nice formulas popping up from math behind the theorem of Campbell, Baker, Hausdorff and Dynkin, usually a.k.a. Baker-Campbell-Hausdorff formula. Here's the TeX and python code: https://gist.github.com/Nikolaj-K/8e9a345e4c932
From playlist Algebra
Wilson's Theorem ← Number Theory
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 primality. (Though in practice there are far more efficient tests.) Subject: Elementary Number Theory Teacher: Michael Harrison Artist
From playlist Number Theory
Calculus - The Fundamental Theorem, Part 1
The Fundamental Theorem of Calculus. First video in a short series on the topic. The theorem is stated and two simple examples are worked.
From playlist Calculus - The Fundamental Theorem of Calculus
In this video, I present another example of Stokes theorem, this time using it to calculate the line integral of a vector field. It is a very useful theorem that arises a lot in physics, for example in Maxwell's equations. Other Stokes Example: https://youtu.be/-fYbBSiqvUw Yet another Sto
From playlist Vector Calculus
What is Stokes theorem? - Formula and examples
► My Vectors course: https://www.kristakingmath.com/vectors-course Where Green's theorem is a two-dimensional theorem that relates a line integral to the region it surrounds, Stokes theorem is a three-dimensional version relating a line integral to the surface it surrounds. For that reaso
From playlist Vectors
Fermat’s HUGE little theorem, pseudoprimes and Futurama
A LOT of people have heard about Andrew Wiles solving Fermat's last theorem after people trying in vain for over 350 years. Today's video is about Fermat's LITTLE theorem which is at least as pretty as its much more famous bigger brother, which has a super pretty accessible proof and which
From playlist Recent videos
The Prime Number Theorem, an introduction ← Number Theory
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 Kim Parkhurst, Katrina de Dios and Olga Reukova Written & Produced by Michael Harrison & Kimberly Hatch Harrison ♦♦♦♦♦♦♦♦♦♦ Ways t
From playlist Number Theory
Fermat's "Little" Theorem is great - but beware of Fermat Liars and tricky Carmichael Numbers. More links & stuff in full description below ↓↓↓ Continues at: http://youtu.be/HvMSRWTE2mI Featuring Dr James Grime - https://twitter.com/jamesgrime Support us on Patreon: http://www.patreon.c
From playlist Numberphile Videos
CTNT 2018 - "L-functions and the Riemann Hypothesis" (Lecture 4) by Keith Conrad
This is lecture 4 of a mini-course on "L-functions and the Riemann Hypothesis", taught by Keith Conrad, during CTNT 2018, the Connecticut Summer School in Number Theory. For more information about CTNT and other resources and notes, see https://ctnt-summer.math.uconn.edu/
From playlist CTNT 2018 - "L-functions and the Riemann Hypothesis" by Keith Conrad
Lecture 14 - Number Theory - Problem Discussion
This is Lecture 14 of the COMP300E (Programming Challenges) course taught by Professor Steven Skiena [http://www.cs.sunysb.edu/~skiena/] at Hong Kong University of Science and Technology in 2009. The lecture slides are available at: http://www.algorithm.cs.sunysb.edu/programmingchallenges
From playlist COMP300E - Programming Challenges - 2009 HKUST
Introduction to number theory lecture 16. More numerical calculation
This lecture is part of my Berkeley math 115 course "Introduction to number theory" For the other lectures in the course see https://www.youtube.com/playlist?list=PL8yHsr3EFj53L8sMbzIhhXSAOpuZ1Fov8 We give some more examples of numerical algorithms, such as as algorithm to find square roo
From playlist Introduction to number theory (Berkeley Math 115)
A presentation of fermat's little theorem for RSA Next video: https://youtu.be/WrVXuneadH8
From playlist RSA
34b: Numerical Algorithms I - Richard Buckland UNSW
Introduction to numerical algorithms Lecture 34 comp1927 "computing2"
From playlist CS2: Data Structures and Algorithms - Richard Buckland
The Fundamental Theorem of Calculus | Algebraic Calculus One | Wild Egg
In this video we lay out the Fundamental Theorem of Calculus --from the point of view of the Algebraic Calculus. This key result, presented here for the very first time (!), shows how to generalize the Fundamental Formula of the Calculus which we presented a few videos ago, incorporating t
From playlist Algebraic Calculus One
A History of Primes - Manindra Agrawal [2002]
2002 Annual Meeting Clay Math Institute Manindra Agrawal, American Academy of Arts and Sciences, October 2002
From playlist Number Theory