>I also believe that humanities should master at least basic calculus.
I agree that mathematics is underappreciated by most people who work in the humanities. But I strongly disagree that they should learn calculus.
In fact, I would argue that calculus is the problem with the perception of math in the social sciences. There are plenty of types of math that could potentially be applied in sociology and its variants, particularly mathematical logic and graph theory. Statistics needs no introduction. Calculus by contrast deals with continuous changes in well-defined quantities, which are not like anything a sociologist encounters.
I suspect that the reason that many sociologists believe that most of mathematics is basically an extended version of calculus -- as seen in this essay:
-- is because a social scientist's primary interaction from math is by way of economics, who do use calculus to track nearly-continuous changes in well-defined quantities.
However, economics is unique among the social sciences in that the phenomena it seeks to describe can be readily quantified. This leads to the mistaken belief, evident in the article, that mathematics is only able to contribute to the study of things which are easily quantifiable, which is not true at all!
Students in sociology should really be taught statistics and discrete math, with special attention to any techniques that may be useful in describing human behavior.
Statistics needs no introduction. Calculus by contrast deals with continuous changes in well-defined quantities, which are not like anything a sociologist encounters.
Calculus comprises the foundation of statistics. Without calculus you can learn to apply statistical experiments, but you can’t really understand what’s going on. That makes for brittle insight. Just because the set of all humans is strictly finite doesn’t mean the underlying continuity in statistical theory ceases to exist.
A two semester sequence of single and multivariable calculus is really not a lot to ask in return for delivering a robust understanding of statistics. It’s not like demanding knowledge of analysis, topology, and measure theory before learning rigorous probability theory.
I feel like I would have been a lot more interested in calculus in high school if I had first understood how statistics could be used for inference, and how calculus was vital for understanding statistics.
As someone who struggled with the "engineering calculus" track and switched to the "humanities calculus" track to do an economics major, I don't think the problem is with the material. I think it's a combination of poor teaching and overemphasis on computing results as if it were "fancy arithmetic" to be used daily.
It's worth being made aware of calc so that you can seek it out. It has applications aplenty. But that's a different role than the one it's presently in. For many calculus problems encountered in the real world, you can hand your data set over to the computer and get a numerical approximation back. For the ones that don't respond to that treatment, you can, most likely, look up tables of identities and find the ones you need to get the analytic solution.
There's some pedagogical idea that you can build your math intuition from working calculus problem sets, but that really isn't what happens in most classes. It's done by rote to keep continuity with high school math - the students because it's what they know, and the professors because it eases their lives. And so they struggle through a few semesters, and then some students go on to try advanced mathematics and encounter a completely different universe where math becomes proof-centric and they have to engage a different skillset that is more reminiscent of philosophical reasoning than anything they have probably encountered in prior math courses.
So it's a charade. You could spend much less time on any one field as a single topic, approaching higher math from an information-sciences perspective where you learn to seek out the forms of mathematics you need, engage in some inductive and deductive reasoning, and learn study techniques for math texts and papers(and hence, how to really gain insight on advanced math topics) to supplement your primary field - and not make any of it a bogeyman of higher education.
agree re: econ's use of calculus (at the undergrad level), since everything gets reduced to a constrained optimisation problem (with potentially slack constraints that require use of Kuhn-Tucker, if one gets fancy).
But at the graduate level and beyond, it goes way beyond that. one essentially cannot get into a good phd programme in economics without having done at least up to real analysis as an undergrad. my ugrad profs used to say it is easier to get into grad school in econ with a math ugrad than an econ one.
game theory, information economics, social choice theory all make use of lots of pure math. e.g. you have to understand brouwer and kakutani before you understand nash's proofs.
discrete math, functional analysis, topology could be useful for 'formal modelling' (which is what the other social sciences call econ-style theorising).
I agree that mathematics is underappreciated by most people who work in the humanities. But I strongly disagree that they should learn calculus.
In fact, I would argue that calculus is the problem with the perception of math in the social sciences. There are plenty of types of math that could potentially be applied in sociology and its variants, particularly mathematical logic and graph theory. Statistics needs no introduction. Calculus by contrast deals with continuous changes in well-defined quantities, which are not like anything a sociologist encounters.
I suspect that the reason that many sociologists believe that most of mathematics is basically an extended version of calculus -- as seen in this essay:
https://www.edge.org/conversation/rory_sutherland-this-thing...
-- is because a social scientist's primary interaction from math is by way of economics, who do use calculus to track nearly-continuous changes in well-defined quantities.
However, economics is unique among the social sciences in that the phenomena it seeks to describe can be readily quantified. This leads to the mistaken belief, evident in the article, that mathematics is only able to contribute to the study of things which are easily quantifiable, which is not true at all!
Students in sociology should really be taught statistics and discrete math, with special attention to any techniques that may be useful in describing human behavior.