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Small-Scale Question Sunday for December 4, 2022

Do you have a dumb question that you're kind of embarrassed to ask in the main thread? Is there something you're just not sure about?

This is your opportunity to ask questions. No question too simple or too silly.

Culture war topics are accepted, and proposals for a better intro post are appreciated.

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Terms:

H/M/L (high,mid,low) R (ranked)

  • High: Ranked 100 or above.

  • Mid: Ranked 600 or above.

  • Low: Ranked 600 or below.

Why is calculus in university so computationally hard?

I tutor university students in introductory math courses as a side hustle, and a pattern I noticed is that you can more or less approximate how "prestigious" a university is by ranking the difficulty of their calculus 1,2 courses/exams. My observations should apply to universities in North America and Canada because most of the exam papers I see are from there.

For example, if you want to integrate a polynomial fraction, the most common questions involve completing the square, long division, and partial fraction decomposition. In my observation, LR unis will have questions requiring only one technique. MR will have two. And HR will often have all 3.

However, this trend does not hold for any other math course. Let that be Linear Algebra, Stats, or Diff Eq. A good chunk of LR unis has much harder stats and differential equation classes than the MR ones. HR unis are consistently difficult.

For example here is a Lin Algb exam from the University of Waterloo. An HR/MR (Engineering HR no questions about it) university. This Lin Algb exam is about the same difficulty I had in my MR uni. But their calculus exams are way harder.

If this pattern is true, is this some administrative artifact? Cal 1,2 are common "weed out" courses. And I assume given the large number of students from various departments that have to take them, there are more voices than the math department deciding the course content?

Moreover, why are so many calculus questions testing algebra skills? I went to an MR uni, and I never had to use anything more complex than a partial fraction decomposition when solving an integral in a higher-level course (For everything else it was Laplace/Fourier transform all the way down). And lin algb and stats and complex analysis or any nonintroductory math classes did not rely as much on raw algebra skills as cal 1,2.

Moreover, why are so many calculus questions testing algebra skills? I went to an MR uni, and I never had to use anything more complex than a partial fraction decomposition when solving an integral in a higher-level course

partial fraction decomposition is algebra though