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







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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















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







share|improve this question


















  • 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













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







share|improve this question













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






share|improve this question













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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














  • 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










1 Answer
1






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2
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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.






share|improve this answer

















  • 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











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1 Answer
1






active

oldest

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1 Answer
1






active

oldest

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active

oldest

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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.






share|improve this answer

















  • 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















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.






share|improve this answer

















  • 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













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.






share|improve this answer












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.







share|improve this answer












share|improve this answer



share|improve this answer










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














  • 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


















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