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Comment by jjgreen | Hacker News Reader

It can be really hard. I'd suggest: 1) Don't take on something too ambitious, it will demoralise you, 2) do _all_ of the exercises, even (especially) the ones that look easy, 3) Learn the basics of LaTeX so that you can ask coherent questions on stackexchange mathematics, 4) don't ask questions on mathoverflow until you actually reached research level.

Good luck!

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> 2) do _all_ of the exercises

that is a tall order. Not doing any exercises is the same as not studying at all, I concede, but more bang for buck can be gotten not getting bogged down by exhaustive problem solving.

I stand by it, if you're not prepared for exhaustive (and exhausting) problem-solving then don't start down this road, try something easier like Philosophy or bear-wrestling.

Have you written a maths textbook? Do you know how arbitrary some of those exercises can be? Most textbook writers cobble together sundry, some of which have only the slightest relevance to the chapter at hand. Maths generally is a leisurely pursuit, particularly when "self-studying", and will not require slavish turning of all stones.

I agree with you. Doing everything is not always the best option for many people. If you can do it, great. But sometimes it's better to just do the most important exercises that are the most mentally stimulating and interesting, rather than invest time in the less interesting ones.

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