Analytic number theory | Integer sequences
In number theory, an n-smooth (or n-friable) number is an integer whose prime factors are all less than or equal to n. For example, a 7-smooth number is a number whose every prime factor is at most 7, so 49 = 72 and 15750 = 2 × 32 × 53 × 7 are both 7-smooth, while 11 and 702 = 2 × 33 × 13 are not 7-smooth. The term seems to have been coined by Leonard Adleman. Smooth numbers are especially important in cryptography, which relies on factorization of integers. The 2-smooth numbers are just the powers of 2, while 5-smooth numbers are known as regular numbers. (Wikipedia).
Smooth Transition Function in One Dimension | Smooth Transition Function Part 1
#SoME2 This video gives a detailed construction of transition function for various levels of smoothness. Sketch of proofs for 4 theorems regarding smoothness: https://kaba.hilvi.org/homepage/blog/differentiable.htm Faà di Bruno's formula: https://en.wikipedia.org/wiki/Fa%C3%A0_di_Bruno%2
From playlist Summer of Math Exposition 2 videos
A Zero-Density Approach to Smooth Numbers - Adam Harper
Adam Harper University of Montreal March 27, 2013 A number is said to be yy-smooth if all of its prime factors are less than yy. Such numbers appear in many places throughout analytic and combinatorial number theory, and much work has been done to investigate their distribution. I will try
From playlist Mathematics
Linear equations in smooth numbers - Lilian Matthiesen
Special Year Research Seminar Topic: Linear equations in smooth numbers Speaker: Lilian Matthiesen Affiliation: KTH Royal Institute of Technology Date: October 18, 2022 A number is called y-smooth if all of its prime factors are bounded above by y. The set of y-smooth numbers below x for
From playlist Mathematics
This came as a surprise. Although it looks like an example with smooth time-stepping, it is not. It is with original, simple time-stepping. I'm not exactly sure what this means. Maybe my smooth time-stepping method is superfluous.
From playlist SmoothLife
In this video, I define the concept of a winding number of a curve around a point, which intuitively measures how many times a curve loops around a point. For example, for a circle (or any simple closed curve), the winding number should be 1, but for the curve in the thumbnail, the winding
From playlist Multivariable Calculus
Dividing Complex Numbers Example
Dividing Complex Numbers Example Please Subscribe here, thank you!!! https://goo.gl/JQ8Nys
From playlist Complex Numbers
Ex: Determine a Number that is Less Than and Greater than Using a Specific Place Value
This video provides examples of how to find a number that is less than and greater than a given number using a specific place value. Search Video Library at http://www.mathispower4u.wordpress.com
From playlist Whole Numbers: Place Value and Writing Numbers
Finding Critical Numbers Example 1
Please Subscribe here, thank you!!! https://goo.gl/JQ8Nys Finding Critical Numbers Example 1. We find the critical numbers of f(x) = sin^2x + cosx on (0, 2pi).
From playlist Calculus
Calculus 2: Complex Numbers & Functions (1 of 28) What is a Complex Number?
Visit http://ilectureonline.com for more math and science lectures! In this video I will explain what is, graphically and mathematically, a complex number; and how it's used in electric circuits, Fourier transforms, and Euler formula. Next video in the series can be seen at: https://yout
From playlist CALCULUS 2 CH 11 COMPLEX NUMBERS
Tropical Geometry - Lecture 8 - Surfaces | Bernd Sturmfels
Twelve lectures on Tropical Geometry by Bernd Sturmfels (Max Planck Institute for Mathematics in the Sciences | Leipzig, Germany) We recommend supplementing these lectures by reading the book "Introduction to Tropical Geometry" (Maclagan, Sturmfels - 2015 - American Mathematical Society)
From playlist Twelve Lectures on Tropical Geometry by Bernd Sturmfels
CTNT 2018 - "Factoring with Elliptic Curves" by Jeremy Teitelbaum
This is lecture on "Factoring with Elliptic Curves", by Jeremy Teitelbaum, 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 - Guest Lectures
This lecture was held by Abel Laureate John Milnor at The University of Oslo, May 25, 2011 and was part of the Abel Prize Lectures in connection with the Abel Prize Week celebrations. Program for the Abel Lectures 2011 1. "Spheres" by Abel Laureate John Milnor, Institute for Mathematical
From playlist Abel Lectures
Factoring with Elliptic Curves - Jeremy Teitelbaum [2018]
May 30: Jeremy Teitelbaum (UConn) Title: Factoring with elliptic curves. Abstract: Lenstra’s elliptic curve algorithm ([1]) for factoring is a standard piece of the toolkit for computational number theory. I will give a brief introduction to this algorithm. [1] H. Lenstra, Factoring integ
From playlist Number Theory
Elisa Lorenzo Garcia : On smooth plane models for modular curves of Shimura type
CONFERENCE Recording during the thematic meeting : "COUNT, COmputations and their Uses in Number Theory" the February 27, 2023 at the Centre International de Rencontres Mathématiques (Marseille, France) Filmmaker: Jean Petit Find this video and other talks given by worldwide mathematici
From playlist Algebraic and Complex Geometry
On Singularities With Rational Homology Disk Smoothings - Andras Stipsicz
Andras Stipsicz Renyi Institute of Mathematics; Institute for Advanced Study September 30, 2011 For more videos, visit http://video.ias.edu
From playlist Mathematics
Unexpected fillings, singularities, and plane curve arrangements - Laura Starkston
Joint IAS/Princeton/Montreal/Paris/Tel-Aviv Symplectic Geometry Topic: Unexpected fillings, singularities, and plane curve arrangements Speaker: Laura Starkston Affiliation: University of California, Davis Date: May 07, 2021 For more video please visit http://video.ias.edu
From playlist Mathematics
Determine Probability from a Venn Diagram (Basis, And, Or, Complement)
This video explains how to determine probability from a Venn diagrams that gives the cardinality of sets. http://mathispower4u.com
From playlist Probability
2023 Number Challenge: Estimate the 2023rd Harmonic Number
Check out other 2023 Number Challenges from this list. Share with your friends!! https://www.youtube.com/playlist?list=PLXpXgWDr4HM7KKeX7CaQIu4tfPRJ2HiUM Find integer part of the Harmonic Number H_2023 H_2023 = 1 + 1/2 + 1/3 + .... + 1/2023 check out more properties of Harmonic Series
From playlist Math Problems with Number 2023