Legendre Symbol Definition and Example
Intro to quadratic residues: https://youtu.be/M6gDsFhQugM The Legendre symbol is a useful notation for describing whether a number is a quadratic residue mod p. Here we explain what the Legendre symbol is and do a practice example with quadratic residues mod 5. Quadratic Residues playli
From playlist Quadratic Residues
Theory of numbers: Jacobi symbol
This lecture is part of an online undergraduate course on the theory of numbers. We define the Jacobi symbol as an extension of the Legendre symbol, and show how to use it to calculate the Legendre symbol fast. We also briefly mention the Kronecker symbol. For the other lectures in t
From playlist Theory of numbers
Number Theory | Some properties of the Legendre symbol.
We present some properties of the Legendre symbol. http://www.michael-penn.net http://www.randolphcollege.edu/mathematics/
From playlist Number Theory
An introduction to Legendre Polynomials and the Legendre-Fourier Series.
From playlist Mathematical Physics II Uploads
In this video I derive three series representations for Legendre Polynomials. For more videos on this topic, visit: https://www.youtube.com/playlist?list=PL2uXHjNuf12bnpcGIOY2ZOsF-kl2Fh55F
From playlist Fourier
Proof of Multiplication Rule for Legendre Symbol
Proof that quadratic residues always have even index: https://youtu.be/zs0ZtQzVBSE Intro to indices: https://youtu.be/jLeNX2jYuUs One of the most important properties of the Legendre symbol is that we can split up the Legendre symbol of a product. Using the power of indices, we can easi
From playlist Quadratic Residues
In this video I briefly introduce Legendre Polynomials via the Rodrigues formula. For more videos on this topic, visit: https://www.youtube.com/playlist?list=PL2uXHjNuf12bnpcGIOY2ZOsF-kl2Fh55F
From playlist Fourier
Number Theory | The Legendre Symbol and Euler's Criterion
We present a definition of the Legendre symbol and Euler's criterion to calculate it quickly. http://www.michael-penn.net http://www.randolphcollege.edu/mathematics/
From playlist Mathematics named after Leonhard Euler
An example of expanding a function in a Legendre-Fourier Series.
From playlist Mathematical Physics II Uploads
Why did they prove this amazing theorem in 200 different ways? Quadratic Reciprocity MASTERCLASS
The longest Mathologer video ever, just shy of an hour (eventually it's going to happen :) One video I've been meaning to make for a long, long time. A Mathologerization of the Law of Quadratic Reciprocity. This is another one of my MASTERCLASS videos. The slide show consists of 550 slides
From playlist Recent videos
Cryptography and Network Security by Prof. D. Mukhopadhyay, Department of Computer Science and Engineering, IIT Kharagpur. For more details on NPTEL visit http://nptel.iitm.ac.in
From playlist Computer - Cryptography and Network Security
Square roots mod p -- Number Theory 25
Suggest a problem: https://forms.gle/ea7Pw7HcKePGB4my5 Please Subscribe: https://www.youtube.com/michaelpennmath?sub_confirmation=1 Patreon: https://www.patreon.com/michaelpennmath Merch: https://teespring.com/stores/michael-penn-math Personal Website: http://www.michael-penn.net Randolp
From playlist Number Theory v2
Square Roots Modulo P — Number Theory 25
⭐Support the channel⭐ Patreon: https://www.patreon.com/michaelpennmath Merch: https://teespring.com/stores/michael-penn-math My amazon shop: https://www.amazon.com/shop/michaelpenn ⭐my other channels⭐ Main Channel: https://www.youtube.com/michaelpennmath non-math podcast: http
From playlist Number Theory
Introduction to number theory lecture 35 Jacobi symbol
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 define the Jacobi symbol and prove its basic properties, and show how to calculate it fa
From playlist Introduction to number theory (Berkeley Math 115)
Quadratic Reciprocity Examples — Number Theory 24
⭐Support the channel⭐ Patreon: https://www.patreon.com/michaelpennmath Merch: https://teespring.com/stores/michael-penn-math My amazon shop: https://www.amazon.com/shop/michaelpenn ⭐my other channels⭐ Main Channel: https://www.youtube.com/michaelpennmath non-math podcast: http
From playlist Number Theory
Introduction to number theory lecture 32. Calculation of the Legendre symbol
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 use Gauss's lemma to find out when -2, 3, 5, are quadratic residues of a prime and give
From playlist Introduction to number theory (Berkeley Math 115)
Quadratic Reciprocity Examples -- Number Theory 24
Suggest a problem: https://forms.gle/ea7Pw7HcKePGB4my5 Please Subscribe: https://www.youtube.com/michaelpennmath?sub_confirmation=1 Patreon: https://www.patreon.com/michaelpennmath Merch: https://teespring.com/stores/michael-penn-math Personal Website: http://www.michael-penn.net Randolp
From playlist Number Theory v2