Field Definition (expanded) - Abstract Algebra
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.
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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
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Teaching Assistant: Liliana de Castro
Written & Directed by Michael Harrison
Produced by Kimberly Hatch Harrison
Видео Field Definition (expanded) - Abstract Algebra канала Socratica
**************
To help us continue making advanced math videos, you can support Socratica at:
Patreon:
https://www.patreon.com/socratica
Socratica Paypal:
https://www.paypal.me/socratica
We also accept Bitcoin! :)
Our address is: 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
**************
You can also follow Socratica on:
- Twitter: @socratica
- Instagram: @SocraticaStudios
- Facebook: @SocraticaStudios
********
Teaching Assistant: Liliana de Castro
Written & Directed by Michael Harrison
Produced by Kimberly Hatch Harrison
Видео Field Definition (expanded) - Abstract Algebra канала Socratica
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