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Comment by magicalist | Hacker News Reader

> Mathematics is arguably (besides perhaps logic) one of the most pure, unbiased sciences one could imagine.

But teaching math absolutely is not. It is a very human process, helping students find handholds in what they know to make the next conceptual step. Absolutely breaking their minds with a new topic, then returning to it a month later and they find it obvious now. There are no platonic math lesson plans out there to tap into, and finding more effective ones has been one of humanity's jobs for at least as long as there has been written language.

(FWIW, real analysis is generally considered one of the easier courses in a typical math degree)

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Real analysis courses vary a lot between schools. On YouTube I’ve seen 3rd year real analysis exam questions that were covered in my first year calculus course. All math students at my school had to deal with them.

On the other hand, in my real analysis course we worked with metric spaces, topological spaces, Hilbert spaces, the Baire Category Theorem, etc. I doubt most students in “a typical math degree” would be studying these topics outside of a pure mathematics specific degree program.

> (FWIW, real analysis is generally considered one of the easier courses in a typical math degree)

Quite a few colleges seem to use it as a filter class to determine who has the requisite aptitude and interest in pure math. At my college, the material wasn't particularly bad, but the evaluations were designed to be pretty challenging and grades weren't curved at all.

This is partly because the first course in real analysis (and usually the first upper division linear algebra course) is the first proof oriented course most students face. The material isn't necessarily the hardest, but the proof stuff is new to many people.

Chongli's experience is much more similar to mine, we covered basic real analysis topics in calculus classes, and the class titled real analysis was a third-year pure math course. It was designed for students who had taken multiple proof oriented classes already and were pursuing a pure math major. It's just one of those things that varies between colleges I guess.

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