In mathematics, what is a Galois field?
In mathematics, a finite field or Galois field (so-named in honor of Évariste Galois) is a field that contains a finite number of elements. As with any field, a finite field is a set on which the operations of multiplication, addition, subtraction and division are defined and satisfy certain basic rules.
Finite fields are fundamental in a number of areas of mathematics and computer science, including number theory, algebraic geometry, Galois theory, finite geometry, cryptography and coding theory.
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3 Comments
Ray Anderson
I did 5 years of maths at High school and did quite well at it but I have never heard of the term field associated with maths. Set I vaguely understand as I came across this in my kids homework. The subject has changed somewhat in the last 60 years. The one big change I did notice i my 20 years as a Trades College Teacher was that today's kids don't know their Times Tables and cannot do mental arithmetic at any level, which is a backward step in my view. I once asked "what is half of 2?" and most of the class got their calculators out to work it out!
Nicholas Miernicki
Someone please check on Carol! Based on this question, she's appears to have bumped her head or something.
John McLardie
Here was me thinking it was a cloud of cigarette smoke, lol. Oh wait, that's a 'Gaulois Field'. Typical CW bot question - from the sublime to the ridiculous.