Ring Definition (expanded) - Abstract Algebra @Socratica

Uploaded May 2019 | Updated September 2026, 2 weeks ago

A ring is a commutative group under addition that has a second operation: multiplication. These generalize a wide variety of mathematical objects like the integers, polynomials, matrices, modular arithmetic, and more. In this video we will take an in depth look at the definition of a ring.

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We recommend the following textbooks:
Dummit & Foote, Abstract Algebra 3rd Edition
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Milne, Algebra Course Notes (available free online)
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Teaching Assistant: Liliana de Castro
Written & Directed by Michael Harrison
Produced by Kimberly Hatch Harrison

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Ring Definition (expanded) - Abstract Algebra

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$Bag of Words - Feature Extraction in Natural Language Processing (BoW in NLP) Mathematica Essentials - the first PRO COURSE from Socratica Buy here: https://www.socratica.com/courses/mathematica-essentials Learn along with free Mathematica notebooks available on github: https://github.com/socratica/wolfram 𝙒𝘼𝙉𝙏 𝙈𝙊𝙍𝙀? https://snu.socratica.com/mathematica To be notified about updates to our first Pro Course Mathematica Essentials,, join our mailing list at: https://snu.socratica.com/mathematica Natural Language Processing (NLP) is a specialized field within machine learning, focused on interpreting and processing HUMAN language, or natural language. This is crucial, as only a fraction of the population knows a computer language. In this video, we explore the Bag of Words (or BoW) technique, which is a way to transform docs from something qualitative (text) into something quantitative (word frequencies, etc.). Well discuss the math terminology used in this area, including sets and multisets, creating a vector (embedding in feature space), normalization, and more. Well use the Wolfram Language to work these examples. In a future lesson, we will explore these concepts using Python as well. BTW—Socratica offers a pro course, Mathematica Essentials, providing key concepts for mastering Wolfram products: https://www.socratica.com/courses/mathematica-essentials You can jump to sections of the video here: 0:00 Intro & Conceptual Definition 0:48 Making text quantitative (word frequencies) 1:53 Feature Extraction 2:16 Example: The Foundation 3:34 Word Frequencies and repeats 4:03 Math terminology: Set and Multiset 5:06 Create a vector (embedding in feature space) 7:03 Example: War & Peace (Normalization) Thank you to our VIP Patreon Members who helped make this video possible! KW, M Andrews, Jim Woodworth, Massimiliano Pala, Marcos Silveira, Christopher Kemsley, Eric Eccleston, Jeremy Shimanek, Michael Shebanow, Alvin Khaled, Kevin B, John Krawiec, Umar Khan, and Tracy Karin Prell — we are so happy to have you on our team! — Thank you kind friends! 💜🦉 ✷✷✷ We recommend the following (affiliate links): The Wolfram Language https://amzn.to/3D4jqvz The Mythical Man Month - Essays on Software Engineering & Project Management http://amzn.to/2tYdNeP Innumeracy: Mathematical Illiteracy and Its Consequences http://amzn.to/2ri1nf7 Mindset by Carol Dweck https://amzn.to/2q9y8Nj How to Be a Great Student (our first book!) ebook: https://amzn.to/2Lh3XSP Paperback: https://amzn.to/3t5jeH3 Kindle Unlimited: https://amzn.to/3atr8TJ ✷✷✷ If you find our work at Socratica valuable, please consider becoming our Patron on Patreon! https://www.patreon.com/socratica If you would prefer to make a one-time donation, you can also use Socratica Paypal https://www.paypal.me/socratica ✷✷✷ Written & Produced by Michael Harrison & Kimberly Hatch Harrison Edited by Megi Shuke About our Instructors: Michael earned his BS in Math from Caltech, and did his graduate work in Math at UC Berkeley and University of Washington, specializing in Number Theory. A self-taught programmer, Michael taught both Math and Computer Programming at the college level. He applied this knowledge as a financial analyst (quant) and as a programmer at Google. Kimberly earned her BS in Biology and another BS in English at Caltech. She did her graduate work in Molecular Biology at Princeton, specializing in Immunology and Neurobiology. Kimberly spent 16+ years as a research scientist and a dozen years as a biology and chemistry instructor. Michael and Kimberly Harrison co-founded Socratica. Their mission? To create the education of the future. ✷✷✷ Welcome to Socratica! We make SMART videos focusing on STEM - science, math, programming. Subscribe here: http://bit.ly/SocraticaSubscribe PLAYLISTS Study Tips http://bit.ly/StudyTipsPlaylist Python programming http://bit.ly/PythonSocratica SQL programming http://bit.ly/SQL_Socratica Chemistry http://bit.ly/Chemistry_Playlist Abstract Algebra http://bit.ly/AbstractAlgebra Astronomy http://bit.ly/AstronomySocratica Biology http://bit.ly/BiologySocratica Calculus http://bit.ly/CalculusSocratica Geometry https://bit.ly/GeometrySocratica Mathematica http://bit.ly/SocraticaMathematica #NaturalLanguageProcessing #BagOfWords #Mathematica$

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