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Results tagged with galois-theory
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user 9550
Galois theory, named after Évariste Galois, provides a connection between field theory and group theory. Using Galois theory, certain problems in field theory can be reduced to group theory, which is, in some sense, simpler and better understood.
15
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2
answers
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Is there an algebraic number that cannot be expressed using only elementary functions?
(this is basically a repost of a question I asked at M.SE last year)
Is there an explicit real algebraic number (such that we can write its minimal polynomial and a rational isolating interval) that …
- 6,819
91
votes
2
answers
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Is it possible to express $\int\sqrt{x+\sqrt{x+\sqrt{x+1}}}dx$ in elementary functions?
I asked a question at Math.SE last year and later offered a bounty for it, but it remains unsolved even in the simplest case. So I finally decided to repost this case here:
Is it possible to express …
- 6,819
28
votes
0
answers
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On certain representations of algebraic numbers in terms of trigonometric functions
Let's say that a real number has a simple trigonometric representation, if it can be represented as a product of zero or more rational powers of positive integers and zero or more (positive or negativ …
- 6,819