An example of expanding a function in a Legendre-Fourier Series.
From playlist Mathematical Physics II Uploads
An introduction to Legendre Polynomials and the Legendre-Fourier Series.
From playlist Mathematical Physics II Uploads
Number Theory | When is 3 a perfect square mod p?
We use properties of the Legendre symbol and quadratic reciprocity to determine for which primes p, 3 is a quadratic residue. http://www.michael-penn.net http://www.randolphcollege.edu/mathematics/
From playlist Number Theory
Proof of Lemma and Lagrange's Theorem
Please Subscribe here, thank you!!! https://goo.gl/JQ8Nys Proof of Lemma and Lagrange's Theorem. This video starts by proving that any two right cosets have the same cardinality. Then we prove Lagrange's Theorem which says that if H is a subgroup of a finite group G then the order of H div
From playlist Abstract Algebra
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
Theory of numbers: Gauss's lemma
This lecture is part of an online undergraduate course on the theory of numbers. We describe Gauss's lemma which gives a useful criterion for whether a number n is a quadratic residue of a prime p. We work it out explicitly for n = -1, 2 and 3, and as an application prove some cases of Di
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
2023 Number Challenge: Find sum of four squares that is equal to 2023
#mathonshorts #shorts check out wiki page: https://en.wikipedia.org/wiki/Lagrange%27s_four-square_theorem Lagrange's four-square theorem, also known as Bachet's conjecture, states that every natural number can be represented as the sum of four integer squares.
From playlist Math Problems with Number 2023
Powered by https://www.numerise.com/ Square numbers
From playlist Indices, powers & roots
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
Quadratic Reciprocity Examples — Number Theory 24
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From playlist Number Theory
Quadratic Reciprocity Examples -- Number Theory 24
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From playlist Number Theory v2
Quadratic Residues — Number Theory 22
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From playlist Number Theory
Cellular legendrian contact homology by Michael G Sullivan
J-Holomorphic Curves and Gromov-Witten Invariants DATE:25 December 2017 to 04 January 2018 VENUE:Madhava Lecture Hall, ICTS, Bangalore Holomorphic curves are a central object of study in complex algebraic geometry. Such curves are meaningful even when the target has an almost complex stru
From playlist J-Holomorphic Curves and Gromov-Witten Invariants
Quadratic Reciprocity proof -- Number Theory 23
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From playlist Number Theory v2
Proving Quadratic Reciprocity — Number Theory 23
⭐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
Quadratic Residues -- Number Theory 22
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
Knot contact homology and related topics by Michael G Sullivan
J-Holomorphic Curves and Gromov-Witten Invariants DATE:25 December 2017 to 04 January 2018 VENUE:Madhava Lecture Hall, ICTS, Bangalore Holomorphic curves are a central object of study in complex algebraic geometry. Such curves are meaningful even when the target has an almost complex stru
From playlist J-Holomorphic Curves and Gromov-Witten Invariants
Olivier Benoist: Sums of three squares and Noether-Lefschetz loci
Abstract: It is a theorem of Hilbert that a real polynomial in two variables that is nonnegative is a sum of 4 squares of rational functions. Cassels, Ellison and Pfister have shown the existence of such polynomials that are not sums of 3 squares of rational functions. In this talk, we wil
From playlist Algebraic and Complex Geometry
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