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Does my Philosophy of Sexuality Professor Have a Point? (It's a mandatory gen-ed)

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You will also have classes in subjects which don't touch directly on the culture war where your professors will be both experts and trustworthy within the subject matter of the course. Don't take the attitude of scepticism which JTarrou (and I) are recommeding into a maths or biochemistry class.

Don't take the attitude of scepticism ... into a maths class

I recommend the opposite if it is math math. All the skepticism, yes! After a while, it is a useful exercise to read a little bit about non-standard analysis, and then if you feel courageous, venture into essays by Zeilberger and other ultrafinitists, if for nothing else but to get an idea that a difference in opinion in math is possible.

In an actual maths class targetted at maths majors, you won't need to take that attitude into the class because a good prof will teach it. "Maths for physics and engineers" is "Here are handles you will need to turn to solve the problems you are going to need to solve. I will tell you how the handles work in case you are interested, but it won't come up on the exam and if understanding it is too much effort the prof next door is teaching the same material without the explanations." If you ask too many questions and try to understand the answers you won't have the headspace for the physics and engineering you actually care about. "Maths for future world leaders" is a gut course where everyone wants to get the A with the minimum effort and the prof is in on the scam. Asking questions makes getting the easy A harder for everyone. "Maths for premeds" is presumably somewhere in between, but medicine is an extended undergraduate degree in the UK system so I have no experience of premeds.

If you ask too many questions and try to understand the answers you won't have the headspace for the physics and engineering you actually care about

Is this typical in, I presume, the US? 60%, more or less, of my math classes were in common with people studying math degree and we don't have any choice on the courses in our degree. Even the not-math-degree classes were proof based.

It's also typical in eastern Europe. Engineers are taught the math without proofs, generally speaking though sometimes they'll be explained if it's instructive. More with an eye towards actually using it to get solutions.

In my experience most math majors took AP calculus in high school and skipped Calc 1 and Calc 2 which are about as far as most Gen Ed gets. After those there might be a Calc 3 to take in common but most of the engineering math is engineering focused math after that point.