In mathematics, the Iverson bracket, named after Kenneth E. Iverson, is a notation that generalises the Kronecker delta, which is the Iverson bracket of the statement x = y. It maps any statement to a function of the free variables in that statement. This function is defined to take the value 1 for the values of the variables for which the statement is true, and takes the value 0 otherwise. It is generally denoted by putting the statement inside square brackets: In other words, the Iverson bracket of a statement is the indicator function of the set of values for which the statement is true. The Iverson bracket allows using capital-sigma notation without summation index. That is, for any property of the integer , By convention, does not need to be defined for the values of k for which the Iverson bracket equals 0; that is, a summand must evaluate to 0 regardless of whether is defined.Likewise for products: The notation was originally introduced by Kenneth E. Iverson in his programming language APL, though restricted to single relational operators enclosed in parentheses, while the generalisation to arbitrary statements, notational restriction to square brackets, and applications to summation, was advocated by Donald Knuth to avoid ambiguity in parenthesized logical expressions. (Wikipedia).
What is a Module? (Abstract Algebra)
A module is a generalization of a vector space. You can think of it as a group of vectors with scalars from a ring instead of a field. In this lesson, we introduce the module, give a variety of examples, and talk about the ways in which modules and vector spaces are different from one an
From playlist Abstract Algebra
About these sessions: https://forums.fast.ai/t/live-coding-aka-walk-thrus/96617. Playlist: https://www.youtube.com/playlist?list=PLfYUBJiXbdtSLBPJ1GMx-sQWf6iNhb8mM.
From playlist fast.ai live coding & tutorials
Calculus, 11 9 #13 a, Power Series Representation
Calculus, Algebra and more at www.blackpenredpen.com Differential equation, factoring, linear equation, quadratic equation, derivatives, integrals, stewart calculus 7th edition, algebra.
From playlist Calculus, Sect 11.9, Power Series Representations of Functions
Abstract Algebra: The definition of a Ring
Learn the definition of a ring, one of the central objects in abstract algebra. We give several examples to illustrate this concept including matrices and polynomials. Be sure to subscribe so you don't miss new lessons from Socratica: http://bit.ly/1ixuu9W ♦♦♦♦♦♦♦♦♦♦ We recommend th
From playlist Abstract Algebra
History of Science and Technology Q&A (Apr. 7, 2021)
Stephen Wolfram hosts a live and unscripted Ask Me Anything about the history of science and technology for all ages. Originally livestreamed at: https://twitch.tv/stephen_wolfram/ Outline of Q&A 0:00 Stream starts 2:28 Stephen begins the stream 3:00 History of Lisp 40:40 What was ctrl+en
From playlist Stephen Wolfram Ask Me Anything About Science & Technology
How Boxing Championship Belts Are Made | How It's Made
When professional boxers win a title, they’re crowned the champ and rewarded with a belt to be worn around the waist. Stream Full Episodes of How It's Made: https://www.sciencechannel.com/tv-shows/how-its-made/ Subscribe to Science Channel: http://bit.ly/SubscribeScience Like us on Face
From playlist How It's Made
Will Iverson interviewed at Fluent 2013
http://fluentconf.com Will Iverson from Dynacron Group interviewed by Mike Hendrickson of O'Reilly Media.
From playlist Fluent Conference 2013
Linear Algebra: Continuing with function properties of linear transformations, we recall the definition of an onto function and give a rule for onto linear transformations.
From playlist MathDoctorBob: Linear Algebra I: From Linear Equations to Eigenspaces | CosmoLearning.org Mathematics
Polymer Chemistry: Crash Course Organic Chemistry #35
So far in this series we’ve focused on molecules with tens of atoms in them, but in organic chemistry molecules can get way bigger! Polymers are molecules that contain hundreds, thousands, or even millions of identical subunits. In this episode of Crash Course Organic Chemistry, we’ll look
From playlist Organic Chemistry
Did you know that you can define the factorial A! of a matrix A? If not, then definitely check out this video! Functional Analysis Overview: https://youtu.be/pTUo1g3kYMw Linear Algebra Playlist: https://www.youtube.com/playlist?list=PLJb1qAQIrmmCM0HdpHbhWcKdM-oVXPPRI Eigenvalues Playlist
From playlist Eigenvalues
Part 9 of the APL study group. Details here: https://forums.fast.ai/t/apl-array-programming/97188 Discuss this session here: https://forums.fast.ai/t/fast-ai-apl-study-session-9/97510
From playlist fast.ai APL Study Group
An identity matrix under matrix multiplication serves a similar role to the number 1, when it comes to integer multiplication, i.e. any number times 1, remains that number. You can learn more about Mathematica on my Udemy course at https://www.udemy.com/mathematica/ PS! Wait until Udemy
From playlist Introducing linear algebra
Part 7 of the APL study group. Details here: https://forums.fast.ai/t/apl-array-programming/97188 Discuss this session here: https://forums.fast.ai/t/fast-ai-apl-study-session-7/97417
From playlist fast.ai APL Study Group
Batch Normalization - EXPLAINED!
What is Batch Normalization? Why is it important in Neural networks? We get into math details too. Code in references. Follow me on M E D I U M: https://towardsdatascience.com/likelihood-probability-and-the-math-you-should-know-9bf66db5241b REFERENCES [1] 2015 paper that introduced Batch
From playlist Deep Learning 101
Stephen Wolfram answers questions live about his favorite Cellular Automata and the Wolfram Rule 30 Prizes. More information about the prizes can be found here: https://www.rule30prize.org/
From playlist Stephen Wolfram Livestreams
Center of a group in abstract algebra
After the previous video where we saw that two of the elements in the dihedral group in six elements commute with all the elements in the group, we finally get to define the center of a group. The center of a group is a subgroup and in this video we also go through the proof to show this.
From playlist Abstract algebra
Ring Examples (Abstract Algebra)
Rings are one of the key structures in Abstract Algebra. In this video we give lots of examples of rings: infinite rings, finite rings, commutative rings, noncommutative rings and more! Be sure to subscribe so you don't miss new lessons from Socratica: http://bit.ly/1ixuu9W ♦♦♦♦♦♦♦♦♦
From playlist Abstract Algebra
Lesson 10: Deep Learning Foundations to Stable Diffusion, 2022
(All lesson resources are available at http://course.fast.ai.) This lesson creates a complete Diffusers pipeline from the underlying components: the VAE, unet, scheduler, and tokeniser. By putting them together manually, this gives you the flexibility to fully customise every aspect of the
From playlist Practical Deep Learning 2022 Part 2
Calculus, 11 9 #3, Power Series Representation
Calculus, Algebra and more at www.blackpenredpen.com Differential equation, factoring, linear equation, quadratic equation, derivatives, integrals, stewart calculus 7th edition, algebra.
From playlist Calculus, Sect 11.9, Power Series Representations of Functions
Part 4 of the APL study group. Details here: https://forums.fast.ai/t/apl-array-programming/97188 Discuss this session here: https://forums.fast.ai/t/apl-study-session-4/97324
From playlist fast.ai APL Study Group