In which course should we teach solving general cubic and quartic equations?
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I am guessing solving general cubic and quartic equations should be taught in a course somewhere between precalculus and Galois theory, though personally I do not recall learning this topic ever in any course.
When should we teach students (mainly ones majoring in mathematics) how to solve general cubic and quartic equations? Or solving general cubic and quartic equations is so unimportant that it does not even deserve to be taught to even undergraduates majoring in mathematics?
undergraduate-education solving-polynomials
asked 2 hours ago
Zuriel
679513
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up vote
1
down vote
favorite
I am guessing solving general cubic and quartic equations should be taught in a course somewhere between precalculus and Galois theory, though personally I do not recall learning this topic ever in any course.
When should we teach students (mainly ones majoring in mathematics) how to solve general cubic and quartic equations? Or solving general cubic and quartic equations is so unimportant that it does not even deserve to be taught to even undergraduates majoring in mathematics?
undergraduate-education solving-polynomials
asked 2 hours ago
Zuriel
679513
1
My answer. Numerical solution in calculus. Solution in radicals should not be taught before Galois theory. And even in Galois theory maybe you do only the proof that solution in radicals is possible for cubic and quartic, but do not waste time carrying out all the cases.
– Gerald Edgar
1 hour ago
I don't remember learning them also. Jacobson put them after groups, rings and modules but before polynomials. Here's the ToC: 1, 2 and 3.
– BPP
1 hour ago
add a comment |
up vote
1
down vote
favorite
up vote
1
down vote
favorite
I am guessing solving general cubic and quartic equations should be taught in a course somewhere between precalculus and Galois theory, though personally I do not recall learning this topic ever in any course.
When should we teach students (mainly ones majoring in mathematics) how to solve general cubic and quartic equations? Or solving general cubic and quartic equations is so unimportant that it does not even deserve to be taught to even undergraduates majoring in mathematics?
undergraduate-education solving-polynomials
asked 2 hours ago
Zuriel
679513
I am guessing solving general cubic and quartic equations should be taught in a course somewhere between precalculus and Galois theory, though personally I do not recall learning this topic ever in any course.
When should we teach students (mainly ones majoring in mathematics) how to solve general cubic and quartic equations? Or solving general cubic and quartic equations is so unimportant that it does not even deserve to be taught to even undergraduates majoring in mathematics?
undergraduate-education solving-polynomials
undergraduate-education solving-polynomials
asked 2 hours ago
Zuriel
679513
asked 2 hours ago
Zuriel
679513
asked 2 hours ago
Zuriel
679513
asked 2 hours ago
Zuriel
679513
asked 2 hours ago
Zuriel
679513
679513
1
My answer. Numerical solution in calculus. Solution in radicals should not be taught before Galois theory. And even in Galois theory maybe you do only the proof that solution in radicals is possible for cubic and quartic, but do not waste time carrying out all the cases.
– Gerald Edgar
1 hour ago
I don't remember learning them also. Jacobson put them after groups, rings and modules but before polynomials. Here's the ToC: 1, 2 and 3.
– BPP
1 hour ago
add a comment |
1
My answer. Numerical solution in calculus. Solution in radicals should not be taught before Galois theory. And even in Galois theory maybe you do only the proof that solution in radicals is possible for cubic and quartic, but do not waste time carrying out all the cases.
– Gerald Edgar
1 hour ago
I don't remember learning them also. Jacobson put them after groups, rings and modules but before polynomials. Here's the ToC: 1, 2 and 3.
– BPP
1 hour ago
1
1
My answer. Numerical solution in calculus. Solution in radicals should not be taught before Galois theory. And even in Galois theory maybe you do only the proof that solution in radicals is possible for cubic and quartic, but do not waste time carrying out all the cases.
– Gerald Edgar
1 hour ago
My answer. Numerical solution in calculus. Solution in radicals should not be taught before Galois theory. And even in Galois theory maybe you do only the proof that solution in radicals is possible for cubic and quartic, but do not waste time carrying out all the cases.
– Gerald Edgar
1 hour ago
I don't remember learning them also. Jacobson put them after groups, rings and modules but before polynomials. Here's the ToC: 1, 2 and 3.
– BPP
1 hour ago
I don't remember learning them also. Jacobson put them after groups, rings and modules but before polynomials. Here's the ToC: 1, 2 and 3.
– BPP
1 hour ago
add a comment |
1 Answer
1
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up vote
2
down vote
The place I’ve seen this is usually in a History of Math class. This makes the most sense to me since
- solving polynomial equations (and the methods of reducing one type to another) plays an important role throughout the ages, but especially in 16th century mathematics.
- students of the sciences certainly don’t need this info for practical reasons, so there’s little motivation to include it in Precalculus or the Calculus sequence.
- that there is a general solution is enough to know for most upper level math classes, the actual methods and solutions being less important.
answered 1 hour ago
Aeryk
3,769631
1
In particular, history of math class should deal with how Tartaglia/Cardano introduced the notion of imaginary numbers in order to get real solutions of the cubic.
– Adam
38 mins ago
add a comment |
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1 Answer
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active
oldest
votes
1 Answer
1
active
oldest
votes
active
oldest
votes
active
oldest
votes
up vote
2
down vote
The place I’ve seen this is usually in a History of Math class. This makes the most sense to me since
- solving polynomial equations (and the methods of reducing one type to another) plays an important role throughout the ages, but especially in 16th century mathematics.
- students of the sciences certainly don’t need this info for practical reasons, so there’s little motivation to include it in Precalculus or the Calculus sequence.
- that there is a general solution is enough to know for most upper level math classes, the actual methods and solutions being less important.
answered 1 hour ago
Aeryk
3,769631
1
In particular, history of math class should deal with how Tartaglia/Cardano introduced the notion of imaginary numbers in order to get real solutions of the cubic.
– Adam
38 mins ago
add a comment |
up vote
2
down vote
The place I’ve seen this is usually in a History of Math class. This makes the most sense to me since
- solving polynomial equations (and the methods of reducing one type to another) plays an important role throughout the ages, but especially in 16th century mathematics.
- students of the sciences certainly don’t need this info for practical reasons, so there’s little motivation to include it in Precalculus or the Calculus sequence.
- that there is a general solution is enough to know for most upper level math classes, the actual methods and solutions being less important.
answered 1 hour ago
Aeryk
3,769631
1
In particular, history of math class should deal with how Tartaglia/Cardano introduced the notion of imaginary numbers in order to get real solutions of the cubic.
– Adam
38 mins ago
add a comment |
up vote
2
down vote
up vote
2
down vote
The place I’ve seen this is usually in a History of Math class. This makes the most sense to me since
- solving polynomial equations (and the methods of reducing one type to another) plays an important role throughout the ages, but especially in 16th century mathematics.
- students of the sciences certainly don’t need this info for practical reasons, so there’s little motivation to include it in Precalculus or the Calculus sequence.
- that there is a general solution is enough to know for most upper level math classes, the actual methods and solutions being less important.
answered 1 hour ago
Aeryk
3,769631
The place I’ve seen this is usually in a History of Math class. This makes the most sense to me since
- solving polynomial equations (and the methods of reducing one type to another) plays an important role throughout the ages, but especially in 16th century mathematics.
- students of the sciences certainly don’t need this info for practical reasons, so there’s little motivation to include it in Precalculus or the Calculus sequence.
- that there is a general solution is enough to know for most upper level math classes, the actual methods and solutions being less important.
answered 1 hour ago
Aeryk
3,769631
answered 1 hour ago
Aeryk
3,769631
answered 1 hour ago
Aeryk
3,769631
answered 1 hour ago
Aeryk
3,769631
3,769631
1
In particular, history of math class should deal with how Tartaglia/Cardano introduced the notion of imaginary numbers in order to get real solutions of the cubic.
– Adam
38 mins ago
add a comment |
1
In particular, history of math class should deal with how Tartaglia/Cardano introduced the notion of imaginary numbers in order to get real solutions of the cubic.
– Adam
38 mins ago
1
1
In particular, history of math class should deal with how Tartaglia/Cardano introduced the notion of imaginary numbers in order to get real solutions of the cubic.
– Adam
38 mins ago
In particular, history of math class should deal with how Tartaglia/Cardano introduced the notion of imaginary numbers in order to get real solutions of the cubic.
– Adam
38 mins ago
add a comment |
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1
My answer. Numerical solution in calculus. Solution in radicals should not be taught before Galois theory. And even in Galois theory maybe you do only the proof that solution in radicals is possible for cubic and quartic, but do not waste time carrying out all the cases.
– Gerald Edgar
1 hour ago
I don't remember learning them also. Jacobson put them after groups, rings and modules but before polynomials. Here's the ToC: 1, 2 and 3.
– BPP
1 hour ago