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| Name | Field Definition (expanded) - Abstract Algebra |
| Video Uploader | Video From Socratica |
| Upload Date | This Video Uploaded At 13-07-2018 19:02:42 |
| Video Discription | The field is one of the key objects you will learn about in abstract algebra. Fields generalize the real numbers and complex numbers. They are sets with two operations that come with all the features you could wish for: commutativity, inverses, identities, associativity, and more. They give you a lot of freedom to do mathematics similar to regular algebra. Today we motivate the definition of a field by looking at 6 different groups, give the formal definition, and talk about the characteristic of the field and the starting point for all fields - prime fields. Be sure to subscribe so you don't miss new lessons from Socratica: http://bit.ly/1ixuu9W ♦♦♦♦♦♦♦♦♦♦ Ways to support our channel: ► Join our Patreon : https://www.patreon.com/socratica ► Make a one-time PayPal donation: https://www.paypal.me/socratica ► We also accept Bitcoin @ 1EttYyGwJmpy9bLY2UcmEqMJuBfaZ1HdG9 Thank you! ♦♦♦♦♦♦♦♦♦♦ We recommend the following textbooks: Dummit & Foote, Abstract Algebra 3rd Edition http://amzn.to/2oOBd5S Milne, Algebra Course Notes (available free online) http://www.jmilne.org/math/CourseNotes/index.html ♦♦♦♦♦♦♦♦♦♦ Connect with us! Facebook: https://www.facebook.com/SocraticaStudios/ Instagram: https://www.instagram.com/SocraticaStudios/ Twitter: https://twitter.com/Socratica ♦♦♦♦♦♦♦♦♦♦ Teaching Assistant: Liliana de Castro Written & Directed by Michael Harrison Produced by Kimberly Hatch Harrison ♦♦♦♦♦♦♦♦♦♦ |
| Category | Education |
| Tags | Socratica | SocraticaMath | math | maths | mathematics | abstract algebra | field | fields | finite fields | definition of a field | what is a field | field definition | operation | closure | associative | associativity | multiplication | inverse | inverses | prime field | prime fields | characteristic | characteristic of a field |
