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:
- 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!
- 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.