Number theory | Calculus | Special functions
In number theory, the ruler function of an integer can be either of two closely-related functions. One of these functions counts the number of times can be evenly divided by two, which for the numbers 1, 2, 3, ... is 0, 1, 0, 2, 0, 1, 0, 3, 0, 1, 0, 2, 0, 1, 0, 4, ... (sequence in the OEIS). Alternatively, the ruler function can be defined as the same numbers plus one, which for the numbers 1, 2, 3, ... produces the sequence 1, 2, 1, 3, 1, 2, 1, 4, 1, 2, 1, 3, 1, 2, 1, 5, ... (sequence in the OEIS). As well as being related by adding one, these two sequences are related in a different way: the second one can be formed from the first one by removing all the zeros, and the first one can be formed from the second one by adding zeros at the start and between every pair of numbers. For either definition of the ruler function, the rising and falling patterns of the values of this function resemble the lengths of marks on rulers with traditional units such as inches. These functions should be distinguished from Thomae's function, a function on real numbers which behaves similarly to the ruler function when restricted to the dyadic rational numbers. In advanced mathematics, the 0-based ruler function is the 2-adic valuation of the number, and the lexicographically earliest infinite square-free word over the natural numbers. It also gives the position of the bit that changes at each step of the Gray code. In the Tower of Hanoi puzzle, with the disks of the puzzle numbered in order by their size, the 1-based ruler function gives the number of the disk to move at each step in an optimal solution to the puzzle. A simulation of the puzzle, in conjunction with other methods for generating its optimal sequence of moves, can be used in an algorithm for generating the sequence of values of the ruler function in constant time per value. (Wikipedia).
Using the vertical line test to determine if a graph is a function or not
π Learn how to determine whether relations such as equations, graphs, ordered pairs, mapping and tables represent a function. A function is defined as a rule which assigns an input to a unique output. Hence, one major requirement of a function is that the function yields one and only one r
From playlist What is the Domain and Range of the Function
Define an inverse function. Determine if a function as an inverse function. Determine inverse functions.
From playlist Determining Inverse Functions
(New Version Available) Inverse Functions
New Version: https://youtu.be/q6y0ToEhT1E Define an inverse function. Determine if a function as an inverse function. Determine inverse functions. http://mathispower4u.wordpress.com/
From playlist Exponential and Logarithmic Expressions and Equations
How to determine if an ordered pair is a function or not
π Learn how to determine whether relations such as equations, graphs, ordered pairs, mapping and tables represent a function. A function is defined as a rule which assigns an input to a unique output. Hence, one major requirement of a function is that the function yields one and only one r
From playlist What is the Domain and Range of the Function
Transcendental Functions 19 The Function a to the power x.mp4
The function a to the power x.
From playlist Transcendental Functions
Determine the domain, range and if a relation is a function
π Learn how to determine whether relations such as equations, graphs, ordered pairs, mapping and tables represent a function. A function is defined as a rule which assigns an input to a unique output. Hence, one major requirement of a function is that the function yields one and only one r
From playlist What is the Domain and Range of the Function
Determine if the equation represents a function
π Learn how to determine whether relations such as equations, graphs, ordered pairs, mapping and tables represent a function. A function is defined as a rule which assigns an input to a unique output. Hence, one major requirement of a function is that the function yields one and only one r
From playlist What is the Domain and Range of the Function
Functions of equations - IS IT A FUNCTION
π Learn how to determine whether relations such as equations, graphs, ordered pairs, mapping and tables represent a function. A function is defined as a rule which assigns an input to a unique output. Hence, one major requirement of a function is that the function yields one and only one r
From playlist What is the Domain and Range of the Function
Sigmoid functions for population growth and A.I.
Some elaborations on sigmoid functions. https://en.wikipedia.org/wiki/Sigmoid_function https://www.learnopencv.com/understanding-activation-functions-in-deep-learning/ If you have any questions of want to contribute to code or videos, feel free to write me a message on youtube or get my co
From playlist Analysis
Order Within Chaos: How this game creates a fractal | Summer of Math Exposition #1
How does a seemingly random universe create something seemingly concrete and certain? In this video, we will unpack the reasoning behind this phenomena, while exploring the field of fractals. Chapters: 0:00 Introduction 0:25 The Chaos Game 1:44 Sierpinski's Triangle 3:14 Self-simil
From playlist Summer of Math Exposition Youtube Videos
Gerber Variable Scale Review / HowTo
The Gerber Variable Scale, made in the 1950s by Gerber Scientific Instruments. It's a stretchy ruler! This is episode 44 of my series about antique calculating devices. Chris Staecker webarea: http://cstaecker.fairfield.edu/~cstaecker/index.html End song inspired by "Hotter Than a M
From playlist Calculating Devices Review / HowTos
Algebra II: Functions and Probability
70-75, functions and probability
From playlist California Standards Test: Algebra II
Questo Limite viene solo se ROMPIAMO l'insieme dei Reali!
πππ PER I MIEI ISCRITTI: πππ Ciao! Siamo arrivati a piΓΉ di 1000 iscritti! Non ho parole, veramente! ππππ Per ringraziarvi nel miglior modo che conosco (a parte darvi dei soldi), ho preparato per voi un video decisamente piΓΉ di qualitΓ del solito. Sapevate che certi limiti di funzione esist
From playlist Summer of Math Exposition 2 videos
Classical Latin Named Entity Recognition (NER for DH 10.01)
In this video, I walk you through from beginning to end solving a domain-specific NER problem where the domain language is dead and highly inflected. In this video, we work with Classical Latin. Even if you do not read Latin, I encourage you to watch this video if you are interested in non
From playlist Latin Natural Language Processing (NLP)
Differentiating Trigonometric Functions (2 of 5: Taking gradient measurements)
More resources available at www.misterwootube.com
From playlist Differential Calculus
Adam Savage's Favorite Tools: Folding Rulers!
One of the best places to find beautiful vintage tools is at antique malls, and Adam shares some of his favorite tools he's picked up from his travels. One such tool is an elegant folding ruler--the kind that craftspeople used to carry around all the time. That classic design is renewed wi
From playlist Adam Savage's Favorite Tools
Newton's Infinitesimal Calculus (3): Algebraic Curves and Puiseux Series
We talk about how Newton is able to work with algebraic curves (polynomials in the variables x and y set equal to 0, which he calls "affected equations") by expanding the dependent variable as a power series in the independent variable. Apparently, the technical name for this power series
From playlist Math
Loci & Construction - GCSE Maths Exam Questions
GCSE Loci and Construction maths exam question practice taken from past papers and practice papers. This video is suitable for both Foundation and Higher tier. Keywords: Loci, locus, construction, angle bisector, perpendicular bisector, right angle, arc, compass, compasses, ruler, straigh
From playlist GCSE Maths Exam Question Compilations
The Replica-dynamic Correspondence in Finite Dimensions by Jorge Kurchan
DISCUSSION MEETING : CELEBRATING THE SCIENCE OF GIORGIO PARISI (ONLINE) ORGANIZERS : Chandan Dasgupta (ICTS-TIFR, India), Abhishek Dhar (ICTS-TIFR, India), Smarajit Karmakar (TIFR-Hyderabad, India) and Samriddhi Sankar Ray (ICTS-TIFR, India) DATE : 15 December 2021 to 17 December 2021 VE
From playlist Celebrating the Science of Giorgio Parisi (ONLINE)
What are bounded functions and how do you determine the boundness
π Learn about the characteristics of a function. Given a function, we can determine the characteristics of the function's graph. We can determine the end behavior of the graph of the function (rises or falls left and rises or falls right). We can determine the number of zeros of the functi
From playlist Characteristics of Functions