Number theory Full Course [A to Z]
Number theory (or arithmetic or higher arithmetic in older usage) is a branch of pure #mathematics devoted primarily to the study of the integers and integer-valued functions. Number theorists study prime numbers as well as the properties of objects made out of integers (for example, ratio
From playlist Number Theory
Prove that there is a prime number between n and n!
A simple number theory proof problem regarding prime number distribution: Prove that there is a prime number between n and n! Please Like, Share and Subscribe!
From playlist Elementary Number Theory
A crash course in Algebraic Number Theory
A quick proof of the Prime Ideal Theorem (algebraic analog of the Prime Number Theorem) is presented. In algebraic number theory, the prime ideal theorem is the number field generalization of the prime number theorem. It provides an asymptotic formula for counting the number of prime idea
From playlist Number Theory
Abundant, Deficient, and Perfect Numbers ← number theory ← axioms
Integers vary wildly in how "divisible" they are. One way to measure divisibility is to add all the divisors. This leads to 3 categories of whole numbers: abundant, deficient, and perfect numbers. We show there are an infinite number of abundant and deficient numbers, and then talk abou
From playlist Number Theory
Why Are There Infinitely Many Prime Numbers?
Here's why there are infinitely many prime numbers!
From playlist Summer of Math Exposition Youtube Videos
Noam Elkies, Supersingular reductions of elliptic curves
VaNTAGe seminar, October 26, 2021 License: CC-BY-NC-SA
From playlist Complex multiplication and reduction of curves and abelian varieties
Steven Galbraith, Isogeny graphs, computational problems, and applications to cryptography
VaNTAGe Seminar, September 20, 2022 License: CC-BY-NC-SA Some of the papers mentioned in this talk: Ducas, Pierrot 2019: https://link.springer.com/article/10.1007/s10623-018- 0573-3 (https://rdcu.be/cVYrC) Kohel 1996: http://iml.univ-mrs.fr/~kohel/pub/thesis.pdf Fouquet, Morain 2002: ht
From playlist New developments in isogeny-based cryptography
Introduction to Number Theory, Part 6: The infinitude of primes & their factorization
In this video we recall the definition of prime numbers, prove there are infinitely many, and that every natural number larger than 1, has a unique decomposition as a product of primes. (Up to re-ordering)
From playlist Introduction to Number Theory
Kritin Lauter, Supersingular isogeny graphs in cryptography
VaNTAGe Seminar, September 20, 2022 License: CC-BY-NC-SA Some of the papers mentioned in this talk: Charles, Goren, Lauter 2007: https://doi.org/10.1007/s00145-007-9002-x Mackenzie 2008: https://doi.org/10.1126/science.319.5869.1481 Pizer 1990: https://doi.org/10.1090/S0273-0979-1990-15
From playlist New developments in isogeny-based cryptography
Wouter Castryck, An efficient key recovery attack on supersingular isogeny Diffie-Hellman
VaNTAGe Seminar, October 18, 2022 License: CC-BY-NC-SA Links to some of the papers mentioned in this talk: Rostovstev-Stolbunov: https://eprint.iacr.org/2006/145 Charles-Goren-Lauter: https://eprint.iacr.org/2006/021 Jao-De Feo: https://eprint.iacr.org/2011/506 Castryck-Decru: https://e
From playlist New developments in isogeny-based cryptography
Valentijn Karemaker, Mass formulae for supersingular abelian varieties
VaNTAGe seminar, Jan 18, 2022 License: CC-BY-NC-SA Links to some of the papers mentioned in this talk: Oort: https://link.springer.com/chapter/10.1007/978-3-0348-8303-0_13 Honda: https://doi.org/10.2969/jmsj/02010083 Tate: https://link.springer.com/article/10.1007/BF01404549 Tate: https
From playlist Curves and abelian varieties over finite fields
Tomoyoshi Ibukiyama: Survey on quaternion hermitian lattices and its application to supersingular...
CIRM HYBRID EVENT The theme of the survey is how arithmetic theory of quatenion hermitian lattices can be applied to the theory of supersingular abelian varieties. Here the following geometric objects will be explained by arithmetics. Principal polarizations of superspecial abelian varieti
From playlist Number Theory
Kirsten Eisenträger: Computing endomorphism rings of supersingular elliptic curves
CIRM HYBRID EVENT Computing endomorphism rings of supersingular elliptic curves is an important problem in computational number theory, and it is also closely connected to the security of some of the recently proposed isogeny-based cryptosystems. In this talk we give a new algorithm for co
From playlist Number Theory
Ananth Shankar, Picard ranks of K3 surfaces and the Hecke orbit conjecture
VaNTAGe Seminar, November 23, 2021
From playlist Complex multiplication and reduction of curves and abelian varieties
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
Interesting Facts About the Last Digits of Prime Numbers
This video explains some interesting facts about the last digits of prime numbers.
From playlist Mathematics General Interest
Edgar Costa, From counting points to rational curves on K3 surfaces
VaNTAGe Seminar, Jan 26, 2021
From playlist Arithmetic of K3 Surfaces
Number Theory | Infinitely many primes of the form 4n+3.
We prove that there are infinitely many primes of the form 4n+3. http://www.michael-penn.net http://www.randolphcollege.edu/mathematics/
From playlist Number Theory
Algebra - Ch. 6: Factoring (4 of 55) What is a Prime Number?
Visit http://ilectureonline.com for more math and science lectures! In this video I will explain what is a prime number. A prime number is a positive integer that can only be written as a product of one and itself. Its factors are “1” and itself. To donate: http://www.ilectureonline.com/
From playlist ALGEBRA CH 6 FACTORING
Luca De Feo, Proving knowledge of isogenies, quaternions and signatures
VaNTAGe Seminar, November 15, 2022 License: CC-BY-NC-SA Links to some of the papers and cites mentioned in the talk: Couveignes (2006): https://eprint.iacr.org/2006/291 Fiat-Shamir (1986): https://doi.org/10.1007/3-540-47721-7_12 De Feo-Jao-Plût (2011): https://eprint.iacr.org/2011/506 B
From playlist New developments in isogeny-based cryptography