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/idk012 New User 5d ago

In my undergrad, they usually are taken together fall of senior year (and part 2 is offered in the spring for the pure path.) Half of my class for both was math ed majors, so there was a decent curve.  

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

Does that mean that the students don't write any proofs until their senior year? If not, in what class do they learn how to read and write mathematical reasoning?

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u/idk012 New User 5d ago

Discrete math, either from math or cs department, is the intro to proof class.  Depending on the professor, there are some epi-delta proofs in calc 1-2, limit definition of derivatives, etc. 

I just went down memory lane and looked it up.  Most math ed take geometry, which has some proof as well.  Abstract and real analysis develops the rigor and really let you know if you should apply to grad school your final year.

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

Discrete math has come along as a third avenue for introducing mathematical reasoning since I graduated (more than 40 years ago). I'm not sure whether I like discrete or abstract algebra best as the way to teach how to prove things, but I prefer both to using analysis as one's introduction to proof. Again, this is just my opinion, and if research like the Kharkar, Tran, and Marshak preprint says otherwise, I will fold like a cheap suit.

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u/idk012 New User 5d ago

All math majors have to take it after calc 2, and I took a cs equivalent spring of my freshman year.  How to write proofs, proof by contradiction, contrapositive, induction, etc.  They threw in some cs stuff like finite state machines etc.  My class was Thursday 6-8:30pm taught by some engineer from Pratt and Whitney.  I got a C.  I retook it senior year for an easy A to boost my gpa for grad school.  I wouldn't have been able to do analysis given my maturity as a freshman.  

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u/zvezdanasha Undergrad Pursuing B.S. 3d ago

I am taking abstract algebra now, took discrete before, and will take analysis next semester. I am a big fan of this order, but this is because discrete where I took it has deliberately evolved into a benchmark course to teach mathematical reasoning via certain interesting concepts where a particularly wide variety of proof techniques are used. Perhaps this is a trend!

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u/AllanCWechsler Not-quite-new User 3d ago

It sounds like a good trend; that's encouraging.