Re: [Maxima-discuss] Feature request: step by step

[Stavros M. <mac...@gm...>]

Well, actually, one of the most important and basic concepts in economics
is the differential, known as the "marginal X".
And the criterion for equilibrium in classical microeconomics is
"equalizing the marginal utilities".

https://en.wikipedia.org/wiki/Marginal_utility
https://en.wikipedia.org/wiki/Gossen%27s_second_law

On Wed, Jan 14, 2026 at 12:13 PM Richard Fateman <fa...@gm...> wrote:

> I have a particularly cynical view of required calc courses.
> What would be lost if we just admitted that some percentage of students
> really
> never learned this stuff, but just hired a human tutor or asked an AI bot
> to
> do the homework/ show all work / cheated on exams / got a passing grade?
>
> I suspect passing the required calc course is, in reality, a competency
> test for algebra
> (presumably it is necessary to do algebra for calc...),  and calc per se
> is not needed for,
> say, the lifetime activities of economics majors, should we be asking
> questions about
> what students should be taught?  And how (by youtube??)
>
> (My wife, who studied philosophy in college ... no calc..., yes logic ...,
> retired
> years ago from her job as the director of central computing at UC
> Berkeley. She
> told me at that time  -- "See, I never used *cosine*.")
>
> RJF
>
> On Wed, Jan 14, 2026 at 11:57 AM Raymond Toy <toy...@gm...>
> wrote:
>
>> On 1/14/26 11:19 AM, Richard Fateman wrote:
>>
>> If you are expecting Maxima to improve your math skills as in some of the
>> on-line tutoring programs,
>> by some nearly automatic process  (like tracing existing programs), that
>> is highly unlikely to work.
>>
>> Elaborating on Stavros' note -- typically Maxima DOES NOT USE THE STEPS
>> USED BY BEGINNING
>> STUDENTS OF ALGEBRA, CALCULUS, ETC.
>>
>> Exactly.
>>
>> But really, what is the goal of seeing the step-by-step solution? If
>> you're a calc 1 student, would it be useful to know that uses keyhole
>> integration over the complex plane to evaluate some definite integrals? I
>> suppose for motivated students, that would encourage them to learn new
>> math, but I suspect that would basically turn off most students. (Perhaps
>> even worse now when you hear stories about how college students can't do
>> basic arithmetic.)
>>
>> And would this be better done by looking up Youtube videos that explain
>> how to solve interesting problems? I think blackpenredpen is really good
>> for calc 1/2 level math. For more interesting questions, I like Michael
>> Penn. Maths 505 has really interesting integration and diffeq problems.
>> Maxima can't do most of them, I think.
>>
>> There are zillions of math channels on Youtube.
>>
>>
>> 2. There is a mystique of "calculus is hard, uses heuristics, requires
>> intelligence and problem-solving" promoted by
>> teachers, textbooks, etc.
>>
>> Well, I think that's kind of true when it comes to integration. If you
>> watch Maths 505 doing integrals, many of them uses insights that I would
>> not think of doing. Maybe I could, if I spent enough time to thinking about
>> them, but probably not.
>> &#8203;
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