Modular arithmetic | Pseudorandom number generators
A linear congruential generator (LCG) is an algorithm that yields a sequence of pseudo-randomized numbers calculated with a discontinuous piecewise linear equation. The method represents one of the oldest and best-known pseudorandom number generator algorithms. The theory behind them is relatively easy to understand, and they are easily implemented and fast, especially on computer hardware which can provide modular arithmetic by storage-bit truncation. The generator is defined by the recurrence relation: where is the sequence of pseudo-random values, and — the "modulus" — the "multiplier" — the "increment" — the "seed" or "start value" are integer constants that specify the generator. If c = 0, the generator is often called a multiplicative congruential generator (MCG), or Lehmer RNG. If c ≠ 0, the method is called a mixed congruential generator. When c ≠ 0, a mathematician would call the recurrence an affine transformation, not a linear one, but the misnomer is well-established in computer science. (Wikipedia).
Number Theory | Linear Congruences Proposition 2
We give the proof of a proposition regarding the number of solutions of a linear congruence. http://www.michael-penn.net
From playlist Modular Arithmetic and Linear Congruences
Number Theory | When does a linear congruence have a solution??
We give the proof of a proposition regarding linear congruences and their solvability. http://www.michael-penn.net
From playlist Modular Arithmetic and Linear Congruences
Stanford Seminar - PCG: A Family of Better Random Number Generators
"PCG: A Family of Better Random Number Generators" - Melissa O'Neill of Harvey Mudd College Colloquium on Computer Systems Seminar Series (EE380) presents the current research in design, implementation, analysis, and use of computer systems. Topics range from integrated circuits to operat
From playlist Engineering
What is the parent function of a linear graph
👉 Learn about graphing linear equations. A linear equation is an equation whose highest exponent on its variable(s) is 1. i.e. linear equations has no exponents on their variables. The graph of a linear equation is a straight line. To graph a linear equation, we identify two values (x-valu
From playlist ⚡️Graph Linear Equations | Learn About
In this video we continue discussing congruences and, in particular, we discuss solutions of linear congruences. The content of this video corresponds to Section 4.4 of my book "Number Theory and Geometry" which you can find here: https://alozano.clas.uconn.edu/number-theory-and-geometry/
From playlist Number Theory and Geometry
Summary for graph an equation in Standard form
👉 Learn about graphing linear equations. A linear equation is an equation whose highest exponent on its variable(s) is 1. i.e. linear equations has no exponents on their variables. The graph of a linear equation is a straight line. To graph a linear equation, we identify two values (x-valu
From playlist ⚡️Graph Linear Equations | Learn About
How to determine if an equation is a linear relation
👉 Learn how to determine if an equation is a linear equation. A linear equation is an equation whose highest exponent on its variable(s) is 1. The variables do not have negative or fractional, or exponents other than one. Variables must not be in the denominator of any rational term and c
From playlist Write Linear Equations
Lecture 9 - Random Walk Models
This is Lecture 9 of the COMP510 (Computational Finance) course taught by Professor Steven Skiena [http://www.cs.sunysb.edu/~skiena/] at Hong Kong University of Science and Technology in 2008. The lecture slides are available at: http://www.algorithm.cs.sunysb.edu/computationalfinance/pdf
From playlist COMP510 - Computational Finance - 2007 HKUST
👉 Learn about graphing linear equations. A linear equation is an equation whose highest exponent on its variable(s) is 1. i.e. linear equations has no exponents on their variables. The graph of a linear equation is a straight line. To graph a linear equation, we identify two values (x-valu
From playlist ⚡️Graph Linear Equations | Learn About
Science & Technology Q&A for Kids (and others) [Part 55]
Stephen Wolfram hosts a live and unscripted Ask Me Anything about science and technology for all ages. Find the playlist of Q&A's here: https://wolfr.am/youtube-sw-qa Originally livestreamed at: https://twitch.tv/stephen_wolfram Outline of Q&A 0:00 Stream starts 2:25 Stephen begins the s
From playlist Stephen Wolfram Ask Me Anything About Science & Technology
How Do Computers Produce Random Numbers?
The first in a series of videos on noise; in this premiere we tackle the idea of white noise and pseudo-random number generators. Twitter: https://twitter.com/Acerola_t Twitch: https://www.twitch.tv/acerola_t Discord: https://discord.gg/FxGQvbfm6Y Code: https://github.com/GarrettGunnell/L
From playlist Noise
Applications of thin orbits - Alex Kontorovich
Members' Seminar Topic: Applications of thin orbits Speaker:Alex Kontorovich Date: Monday, April 11 We will discuss some natural problems in arithmetic that can be reformulated in terms of orbits of certain "thin" (semi)groups of integer matrix groups. For more videos, visit http://v
From playlist Mathematics
👉 Learn about graphing linear equations. A linear equation is an equation whose highest exponent on its variable(s) is 1. i.e. linear equations has no exponents on their variables. The graph of a linear equation is a straight line. To graph a linear equation, we identify two values (x-valu
From playlist ⚡️Graph Linear Equations | Learn About
Discrete Structures: Random number generators, checksums, hashing
Learn about random number generators, checksums, and hashing. We'll start with the von Neumann random number generator and the contemporary linear congruential generator. Then we'll go over the Luhn algorithm used for credit card number validation and then introduce hash functions such as
From playlist Discrete Structures, Spring 2022
How do you graph an equation using the intercept method
👉 Learn about graphing linear equations. A linear equation is an equation whose highest exponent on its variable(s) is 1. i.e. linear equations has no exponents on their variables. The graph of a linear equation is a straight line. To graph a linear equation, we identify two values (x-valu
From playlist ⚡️Graph Linear Equations | Learn About
Alex Kontorovich: Local-Global in Thin Orbits and Applications
The lecture was held within the framework of the Hausdorff Trimester Program: Harmonic Analysis and Partial Differential Equations and the Workshop: Analytic Number Theory of the Hausdorff Center for Mathematics 17.07.2014 This video was created and edited with kind support from eCampus
From playlist HIM Lectures: Trimester Program "Harmonic Analysis and Partial Differential Equations"
Giray Ökten: Number sequences for simulation - lecture 1
After an overview of some approaches to define random sequences, we will discuss pseudorandom sequences and low-discrepancy sequences. Applications to numerical integration, Koksma-Hlawka inequality, and Niederreiter’s uniform point sets will be discussed. We will then present randomized q
From playlist Probability and Statistics
What do I need to know to graph an equation in slope intercept form
👉 Learn about graphing linear equations. A linear equation is an equation whose highest exponent on its variable(s) is 1. i.e. linear equations has no exponents on their variables. The graph of a linear equation is a straight line. To graph a linear equation, we identify two values (x-valu
From playlist ⚡️Graph Linear Equations | Learn About
Periodic Random Function Generation using Matplotlib and Python
In signal processing, for certain applications, periodic random signals might be needed. In this micro-tutorial we show how such a periodic random function can be generated. This is achieved by looping a 2d random noise onto itself to create a 1 dimensional random noise. The algorithm is i
From playlist Engineering Animations