I learn math by reading books. Usually I read 3 books (about 3 different subjects) simultaneously and switch focus every couple of days. The books i'm studying right now are Rudin's functional analysis, Aluffi's algebra, and Jefferey Lee's Manifolds and differential geometry.

Recently I find it very hard to switch to Rudin's book. It feels like a totally different realm and whenever I pick it up (again) I spend a lot of time building up my motivation and interest in the topic. Apart from being frustrating, it feels like an inefficient use of my time.

Don't get me wrong, I Love functional analysis and think it's beautiful (and Rudin's book fits me quite well). It's just hard for me to routinely switch between these subjects since I'm still in the level where they don't interact that much. Whereas differential geometry and algebra are pretty much fused in my brain to a big blob that can grow in either direction.

I'm not asking for examples where functional analysis touches algebra or differential geometry. I am very much aware of a lot of connections. (geometric analysis/operator algebras for example). What i'm asking is what of the 2 should i do:

  1. Leave Rudin's book for when you'll have a more concrete motivation to read it and pick up the next book on the list and read on some other topic you're passionate about (algebraic topology, algebraic curves). Something closer to your current mindset (but not too close since you do want to have experience with different types of math). Flow is important!
  2. Grind through this phase and continue to switch between the topics. Eventually you'll develop flexibility and it would be easier. You'll gain a lot from this. Flexibility is important!

So, what should i do?

I realize this is highly opinion based but i think a detailed answer about the pros and cons of learning about different subjects simultaneously will help many self learners like myself.


closed as primarily opinion-based by user98602, yoknapatawpha, muaddib, Batominovski, Fly by Night Aug 3 '15 at 15:27

Many good questions generate some degree of opinion based on expert experience, but answers to this question will tend to be almost entirely based on opinions, rather than facts, references, or specific expertise. If this question can be reworded to fit the rules in the help center, please edit the question.


I don't think this is the place to ask that kind of question. But since you asked, if you're having difficulty with this book and you're having trouble finding motivation to read it, why don't you just leave it for a bit, and come back to it after you're done with your other books? Or perhaps it is a too complex book for your level? I don't really know...

  • $\begingroup$ What would be a better place for this question? I don't think the book itself is too advanced. I manage about 70% of the exercises. I'm interested in whether there is a tangible benefit in learning different stuff simultaneously (like what happens in the university) as opposed to taking a more linear route. $\endgroup$ – Saal Hardali Aug 3 '15 at 14:21
  • $\begingroup$ Honestly, I don't know what would be a better place, it didn't seem to me a math question as much as an education question. I understand your point of simulate a University way of learning (which I think is good) but nothing prevents you from leaving it for a bit and coming back to it later (as in a University). $\endgroup$ – Anthony Aug 3 '15 at 14:29
  • $\begingroup$ Yes, i agree that this is an education question. Maybe a moderator could migrate it to matheducators stack exchange where it will hopefully be more appropriate. $\endgroup$ – Saal Hardali Aug 3 '15 at 14:32
  • $\begingroup$ I suggest that at first study the [Erwin_Kreyszig]Introductory_Functional_Analysis it is very nice book for self study. $\endgroup$ – Ali Aug 3 '15 at 14:32
  • $\begingroup$ @Ali Thanks, but I'm not asking for a book recommendation because i like Rudin very much both for choice of topics and for style. $\endgroup$ – Saal Hardali Aug 3 '15 at 14:36

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