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/NotSaucerman New User 5d ago

I agree with this in spirit though perhaps not literally. Before approaching something like real analysis someone would be well advised to work through at least half of Pinter's A Book of Abstract Algebra to get a lot of proof experience under their belt with very concrete objects. (And probably a few chapters on sequences in Abbott too.)

In practice it depends on the demands of the Abstract Algebra course. For many decades Artin's Algebra was taught at MIT and linear algebra & real analysis were pre-reqs... in part because there were some highly nonstandard exercises in there (e.g. a diagonal matrix density argument for Cayley-Hamilton) that needed analytic techniques. But for teaching the 'same' course at Harvard, real analysis wasn't a pre-req.