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- W2332512658 abstract "Dick and Jane are students in an advanced undergraduate modern algebra course. They are studying Galois theory. To help them we write down a family of polynomials {ff(x): n > 1) where f,(x) has degree i. We then show them how to check, using standard methods that they have used before, that the polynomials f (x) for primes p have Galois group the symmetric group on p letters. Let's see how. Dick and Jane are fortunate to have had a good high school background in mathematics. They have learned about prime factorization of integers since grade school. They know that a polynomial f(x) = Enc xi of degree n with rational coefficients has a rational root a if and only if the polynomial (x a) is a factor of p(x); that is, f(a) = 0 -=*f(x) = (x a)g(x) for some polynomial g(x) with rational coefficients. They also know that if f(x) is a nonconstant polynomial with integer coefficients, then any rational root P of f(x), where p and q are relatively prime" @default.
- W2332512658 created "2016-06-24" @default.
- W2332512658 creator A5039248585 @default.
- W2332512658 date "1999-06-01" @default.
- W2332512658 modified "2023-10-16" @default.
- W2332512658 title "Nice Polynomials for Introductory Galois Theory" @default.
- W2332512658 cites W1510478584 @default.
- W2332512658 doi "https://doi.org/10.1080/0025570x.1999.11996733" @default.
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