In mathematics, more specifically in computational algebra, a straight-line program (SLP) for a finite group G = ⟨S⟩ is a finite sequence L of elements of G such that every element of L either belongs to S, is the inverse of a preceding element, or the product of two preceding elements. An SLP L is said to compute a group element g ∈ G if g ∈ L, where g is encoded by a word in S and its inverses. Intuitively, an SLP computing some g ∈ G is an efficient way of storing g as a group word over S; observe that if g is constructed in i steps, the word length of g may be exponential in i, but the length of the corresponding SLP is linear in i. This has important applications in computational group theory, by using SLPs to efficiently encode group elements as words over a given generating set. Straight-line programs were introduced by Babai and Szemerédi in 1984 as a tool for studying the computational complexity of certain matrix group properties. Babai and Szemerédi prove that every element of a finite group G has an SLP of length O(log2|G|) in every generating set. An efficient solution to the constructive membership problem is crucial to many group-theoretic algorithms. It can be stated in terms of SLPs as follows. Given a finite group G = ⟨S⟩ and g ∈ G, find a straight-line program computing g over S. The constructive membership problem is often studied in the setting of black box groups. The elements are encoded by bit strings of a fixed length. Three oracles are provided for the group-theoretic functions of multiplication, inversion, and checking for equality with the identity. A black box algorithm is one which uses only these oracles. Hence, straight-line programs for black box groups are black box algorithms. Explicit straight-line programs are given for a wealth of finite simple groups in the online ATLAS of Finite Groups. (Wikipedia).
Vector Calculus 5: Vector Equation of a Straight Line
https://bit.ly/PavelPatreon https://lem.ma/LA - Linear Algebra on Lemma http://bit.ly/ITCYTNew - Dr. Grinfeld's Tensor Calculus textbook https://lem.ma/prep - Complete SAT Math Prep
From playlist Vector Calculus
This video states the perpendicular line postulate and shows how to construct a perpendicular line. http://mathispower4u.wordpress.com/
From playlist Parallel and Perpendicular Lines
Lines as linear functions -- Elementary Linear Algebra
This lecture is on Elementary Linear Algebra. For more see http://calculus123.com.
From playlist Elementary Linear Algebra
Linear Equations from the Graph of the Line, No. 1
Shows how to write the equation of a line in the slope intercept from from the graph of the line. You can link to all my videos at my website: https://www.stepbystepscience.com
From playlist Algebra; Linear Equations
Powered by https://www.numerise.com/ Straight line graphs 1
From playlist Linear sequences & straight lines
Parallel and Perpendicular Lines and Planes
http://mathispower4u.wordpress.com/
From playlist Parallel and Perpendicular Lines
Perpendicular Lines, Slope, Rays, and Segments | Geometry
This geometry video tutorial provides a basic introduction into perpendicular lines, slope, rays, line segments and right angles. Perpendicular lines have slopes that are negative reciprocals of each other. Perpendicular Lines, Rays, and Line Segments intersect each other at right angles
From playlist Geometry Video Playlist
Straight line graphs (alternative way to define)
Powered by https://www.numerise.com/ Straight line graphs (alternative way to define)
From playlist Linear sequences & straight lines
Lego Mindstorms EV3 Robotics Lesson 16 - Drawing a distance vs. time graph of the robot as it moves
In this lesson we talk about how to use the data logging block in the programming interface so you can program your robot to do other things (e.g. moving around) as it is logging data.
From playlist Lego Robotics
Powered by https://www.numerise.com/ Linear Programming (3)
From playlist Linear Programming - Decision Maths 1
Lec 4 | MIT Introduction to Bioengineering, Spring 2006
Biological Computing - Prof. Drew Endy View the complete course: http://ocw.mit.edu/20-010JS06 License: Creative Commons BY-NC-SA More information at http://ocw.mit.edu/terms More courses at http://ocw.mit.edu
From playlist MIT 20.010J Introduction to Bioengineering, Spring 2006
Robot Navigation Using VEX Encoders and Simulink
Perform obstacle detection tasks with your robot using the ultrasonic sensor block in the ARM Cortex-based VEX Support Package. Additional Resources: Getting Started with Simulink for VEX https://goo.gl/mO4QeT Other examples in documentation https://goo.gl/4yHbZy Simulink Quick Start V
From playlist Robotics Education: MATLAB and Simulink Robotics Arena
V2-04. Linear programming, Blending model, graphic solutions
Math 484: Linear programming, Blending model, graphic solutions. Wen Shen, 2020, Penn State University
From playlist Math484 Linear Programming Short Videos, summer 2020
Scratch Game Programming for Young Adults - Lesson 6
Free online course in Scratch: https://www.udemy.com/scratch-game-programming/?couponCode=GET_SCRATCHING Lesson 6 covers using the Paint Editor and it's drawing tools. This video comes from the Udemy course "Scratch Game Programming for Young Adults".
From playlist Scratch Game Programming for Young Adults
Powered by https://www.numerise.com/ Linear Programming (6)
From playlist Linear Programming - Decision Maths 1
Calculus lesson 1 - Instantaneous rate of change
In this lesson we talk about how the gradient of the tangent line to a curve is the same as gradient of the curve at the point of contact.
From playlist Maths B / Methods Course, Grade 11/12, High School, Queensland, Australia.
Tangent Line of Curve Parallel to A Line Calculus 1 AB
I work through an example to explain how to find tangent lines to a function that are parallel to a given line. Find free review test, useful notes and more at http://www.mathplane.com If you'd like to make a donation to support my efforts look for the "Tip the Teacher" button on my channe
From playlist Calculus
Vintage 1968 - 1970: Hewlett-Packard's 9100 Computer (Calculator) teaching, learning aids
1968 - Hewlett-Packard's HP-9100 was a desktop computer and calculator. Announced in 1968, this transistorized, programmable machine sold for $4,900, performed complex arithmetic, logarithmic, trigonometric, hyperbolic, and other complex operations; Sold in two models, the 91001A and 9100
From playlist Computers of the 1960's