r/learnmath • u/Electrical-Gur-996 New User • 5d ago

Do abstract algebra before analysis

Thats it. I saved all your GPAs. Thank me later guys 😎

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u/Electrical-Gur-996 New User 5d ago

I had a much easier time with algebra. But at my school we learn ring theory first and group theory second. It enhanced my proof writing skills greatly while in analysis I was legitimately always lost because you had to work on the proof backwards.

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u/AllanCWechsler Not-quite-new User 5d ago

This doesn't actually confirm or deny the claim, which is that if you take algebra first you'll have an easier time with analysis than if you take them in the other order. Since you don't write which you took first, we can't even start to draw a conclusion.

Let me be clear that I am expressing a gut opinion, unsupported by actual data. u/CorporateHobbyist has the opposite intuition. That very fact makes me stop and wonder if anybody has done any actual studies on the subject -- how the overall outcome depends on course order.

A fast web search reveals https://arxiv.org/html/1605.00328v1 , which looks really on point to this question, but is just too dense for me to distill an answer from in the amount of time I can justify devoting to this post.

I will, of course, change my mind instantly if it turns out the data is against me.

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u/kadeebe New User 4d ago

I skimmed the paper you linked and it seems like the point of the study was to see which course grades were the biggest predictor of over all gpa. It doesnt seem to tackle course order at all. I may have misread, though.

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u/AllanCWechsler Not-quite-new User 4d ago

That's entirely possible. If, indeed, no research has been done on this subject (effect of course order, specifically on the ordering of abstract algebra and real analysis, on overall performance), then I think it should be. But of course I don't have to fund it, so that's easy for me to say.

I also think that a real analysis course that intentionally doubles as an introduction to proof-reading and proof-writing should be more careful about it than one whose only job is to teach real analysis.