In elementary number theory, a highly powerful number is a positive integer that satisfies a property introduced by the Indo-Canadian mathematician Mathukumalli V. Subbarao. The set of highly powerful numbers is a proper subset of the set of powerful numbers. Define prodex(1) = 1. Let be a positive integer, such that , where are distinct primes in increasing order and is a positive integer for . Define . (sequence in the OEIS) The positive integer is defined to be a highly powerful number if and only if, for every positive integer implies that The first 25 highly powerful numbers are: 1, 4, 8, 16, 32, 64, 128, 144, 216, 288, 432, 864, 1296, 1728, 2592, 3456, 5184, 7776, 10368, 15552, 20736, 31104, 41472, 62208, 86400. (sequence in the OEIS) (Wikipedia).
Why are complex numbers awesome? What are they and how are they useful? Free ebook http://bookboon.com/en/introduction-to-complex-numbers-ebook Test your understanding via a short quiz http://goo.gl/forms/3T2ZqTfgrL Make learning "complex" numbers easy through an interactive, fun and
From playlist Intro to Complex Numbers
How big are complex numbers? We discuss a way of measuring them via the modulus. The ideas use Pythagorus' theorem. Free ebook http://bookboon.com/en/introduction-to-complex-numbers-ebook
From playlist Intro to Complex Numbers
Exploring an amazing pattern that forms when we multiply numbers built only with the one digit
From playlist Number Patterns
Solving Higher Degree Trigonometric Equations (2 of 3: Combining results into proof)
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From playlist Using Complex Numbers
There are a lot more numbers than I thought there were - MegaFavNumbers
A short video detailing my favorite number larger than 1 million! There are so many numbers out there it was hard to choose from, but I’m glad I could participate in the #MegaFavNumbers series
From playlist MegaFavNumbers
#MegaFavNumbers The biggest known prime
From playlist MegaFavNumbers
"Understand power notation and calculate simple powers, e.g. squares, cubes."
From playlist Number: Powers, Roots & Laws of Indices
Seven Factor MegaFavoriteNumber
I might be a bit late to the #megafavnumbers party, but I decided to make this video to show an interesting idea I came up with. It took some months of insomnia to come up with this concept. I consider whether a certain string of numbers, characterized by the number of their factors, c
From playlist MegaFavNumbers
5040 and other Anti-Prime Numbers - Numberphile
Audible: http://www.audible.com/numberphile (free trial) Dr James Grime discusses highly composite numbers. More links & stuff in full description below ↓↓↓ Continues and extra footage: https://youtu.be/PF2GtiApF3E Prime numbers (more videos): http://bit.ly/primevids http://www.antiprim
From playlist Prime Numbers on Numberphile
MegaFavNumbers - superior highly composite numbers and roundness
this is my contribution to the #MegaFavNumbers crossover event within math youtube. for those of you who are subscribed for my language videos, don't worry, Conlang Critic: Viossa is on its way. check out the MegaFavNumbers playlist: https://www.youtube.com/playlist?list=PLar4u0v66vIodqt3
From playlist MegaFavNumbers
Closing Keynote: Quantum Computing: Reality vs. Hype - John Preskill - 6/27/2019
AstroInformatics 2019 Conference: Methodology Transfer, Quantum Computing, and Looking Ahead http://astroinformatics2019.org/
From playlist AstroInformatics 2019 Conference
Quantum Interference with Cold Rydberg Atoms by Sanjukta Roy
DISCUSSION MEETING STRUCTURED LIGHT AND SPIN-ORBIT PHOTONICS ORGANIZERS: Bimalendu Deb (IACS Kolkata, India), Tarak Nath Dey (IIT Guwahati, India), Subhasish Dutta Gupta (UOH, TIFR Hyderabad, India) and Nirmalya Ghosh (IISER Kolkata, India) DATE: 29 November 2022 to 02 December 2022 VE
From playlist Structured Light and Spin-Orbit Photonics - Edited
CSE 519 -- Lecture 19, Fall 2020
From playlist CSE 519 -- Fall 2020
How does LIGO detect gravitational waves?
Overview of the math behind the core optical technologies in the Advanced LIGO gravitational wave detectors, including Michelson and Fabry-Perot interferometers. Intro 0:00 Gravitational waves interaction with spacetime 2:28 Basics of laser beams and mirror 5:18 Fabry Perot interferometer
From playlist Summer of Math Exposition Youtube Videos
Citation networks as a window to science: a case study by Remco van der Hofstad
PROGRAM: ADVANCES IN APPLIED PROBABILITY ORGANIZERS: Vivek Borkar, Sandeep Juneja, Kavita Ramanan, Devavrat Shah, and Piyush Srivastava DATE & TIME: 05 August 2019 to 17 August 2019 VENUE: Ramanujan Lecture Hall, ICTS Bangalore Applied probability has seen a revolutionary growth in resear
From playlist Advances in Applied Probability 2019
Bruno Olshausen: "From Natural Scene Statistics to Models of Neural Coding & Representation, Pt. 1"
Graduate Summer School 2012: Deep Learning, Feature Learning "From Natural Scene Statistics to Models of Neural Coding & Representation, Pt. 1" Bruno Olshausen, UC Berkeley Institute for Pure and Applied Mathematics, UCLA July 24, 2012 For more information: https://www.ipam.ucla.edu/pro
From playlist GSS2012: Deep Learning, Feature Learning
Polymers in Turbulence: Stretching Statistics and the Role of Extreme Strain...by Dario Vincenzi
PROGRAM TURBULENCE: PROBLEMS AT THE INTERFACE OF MATHEMATICS AND PHYSICS ORGANIZERS Uriel Frisch (Observatoire de la Côte d'Azur and CNRS, France), Konstantin Khanin (University of Toronto, Canada) and Rahul Pandit (IISc, India) DATE & TIME 16 January 2023 to 27 January 2023 VENUE Ramanuj
From playlist Turbulence: Problems at the Interface of Mathematics and Physics 2023
Complex Numbers Question (Finding the greatest value of |z| if |z-4/z|=2)
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From playlist Introduction to Complex Numbers
Jean Écalle - Resurgence’s two Main Types and Their Signature Complications...
Resurgence’s two Main Types and Their Signature Complications: Tessellation, Isography, Autarchy Quite specific challenges attend the move from equational resurgence (i.e. resurgence in a singular variable –the main type in frequency and importance) to coequational re
From playlist Resurgence in Mathematics and Physics