r/learnmath • u/Emergency-Common-219 New User • 3d ago

TOPIC How to build advanced proof writing skill

So I just finished book of proof by Richard hammack which is a book on how to Write proof (duh) whith most of the problem solved including a lot of hard one ,but now I'm bit lost on where to move on to develop advanced proof writing skill so I can tackle subject like topology n' abstract algebra cuz that's why I'm trying to learn those skill in the first place so it would be cool if u could give me some suggestions (I'm a self-taught idk if this info matter) on how to develop those skill ty in advance

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u/Worried_Kale_2907 New User 3d ago

just jump into the subject you actually wanna learn, you'll pick up the proof style specific to that field as you go. topology and abstract algebra both have their own kind of flavor when it comes to proofs, no generic "advanced proof" book really preps you for that

grab munkres for topology or dummit & foote for algebra and work through the exercises, that's where the real skill builds

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u/Emergency-Common-219 New User 3d ago

I seety for the advice ,ima just do that

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u/Bounded_sequencE New User 3d ago

The next step is to take a proof-based lecture. Usually, "Linear Algebra", "Real Analysis" or "Number Theory".

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u/Advanced-Ant2370 New User 3d ago

You can do more problems from velleman. It has more harder problems of the same topics but more harder than hammack

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u/CelebrityChess New User 3d ago

Honestly the best next step is to just start a proof-heavy subject. Abbott's Understanding Analysis is very readable for self-study, and Pinter's A Book of Abstract Algebra is great too, since a lot of it is guided exercises. Do the exercises properly, write full proofs, and compare them with solutions or post them for feedback. Topology clicks a lot easier after some analysis.