How Much Time Studying Is Too Much?

[middleCmusic]

Hey there guys,

I'm a junior studying mathematics at BU and thinking about a Masters or a PhD, and I've been struggling lately trying to balance my coursework.

My concern is whether the amount of time I feel I need to spend on studying/taking notes/doing exercises etc. is more time than anyone who is actually talented enough to go for a PhD would need - i.e. in a cost-benefit analysis where cost = time and benefit = knowledge, am I "losing money"? (Keep in mind that I do love doing math, but I'm also not naive enough to think I can just love my way to a paycheck.)

At the moment, if I'm taking notes - which is usually the only way I can really absorb the material - I read about 2-4 pages per hour, depending on the text [Munkres' Topology, for example], and I'm concerned that this speed is untenable in the long run, that I simply don't "have what it takes".

I should add a couple other things: 1) I struggle with attention to the material, and as a musician, I have a lot of issues with songs getting stuck in my head (usually annoying popular ones) and preventing me from understanding the material. 2) I'm probably more "talented" at things like music or languages, but they don't interest me nearly half as much as math does. 3) I'm also struggling with whether I should type things in LaTeX or just write them down, because right now I sometimes do both and it's extra time-consuming.

So I guess my main question is: what amount of time did others who spend studying a few pages of math at the undergraduate or even graduate level - and do you think I'm spending too much time? Or any general advice about what I've said?

I hope that this post isn't too "emo" or self-indulgent for everyone - I'm just really feeling down about all of the above at the moment, and it's been bugging me for a while.

EDIT: Just so everyone can get a sense of where I'm at / how much "mathematical maturity" I have or don't have, here are the courses I've taken so far/plan to take:

So far: Calculus I/II/III, Linear Algebra, Diff EQs, Probability, Intro to Higher Math [proof techniques],
Graph Theory, Abstract Algebra, Math Methods for Physicists, Chaotic Dynamical Systems, Analysis I
Currently: Number Theory, Analysis II, Topology
Plan to take before graduating: Differential Geometry, PDEs I, PDEs II, History of Math, Modern Geometry, Modern Algebra I, Modern Algebra II

 

[Simon Bridge]

Depends what you mean by "studying" ... I would typically spend no more than a few minutes just on the pages but I may spend quite a lot of time (10-30hours ofer a week say) in exercizes to try to understand it... but I was considered "slow".

There is a sense though in that you never really stop studying some of those pages.

At senior undergrad and post-grad level the work-load is usually something of a killer.
I remember 70+ hour weeks being normal. Sleep - what's that? The trick is to find a group to study with.

 

[halo31]

I think 2-4 hours for one page is time consuming and normal . I assume you are having to spend a lot of time with analysis II and topology. For topology i'd recommend this book "Introduction to Topology: Pure and Applied" by Colin Adams and for analysis II analysis on manifolds by munkres. I think it works well and much more efficiently when you reference other books.

 

[middleCmusic]

@Simon Bridge: When I'm on task, I'm probably averaging about 50+ hours a week at the moment, so 70+ hours doesn't seem so crazy. But there was a long period of time where I would not get anywhere near 50+ hours, so it's possible that I'm just doing "catch-up" time right now, and that it will get easier later.

@halo31: Thanks for the tips and book recommendations. I just wanted to clarify that it's 2-4 pages per hour, not 2-4 hours per page, :P, not that the latter is so unbelievable...

 

[jbunniii]

At the moment, if I'm taking notes - which is usually the only way I can really absorb the material - I read about 2-4 pages per hour, depending on the text [Munkres' Topology, for example], and I'm concerned that this speed is untenable in the long run, that I simply don't "have what it takes".

That's actually quite a brisk pace for mathematics. To quote Sheldon Axler in the preface to his book Linear Algebra Done Right, "if you zip through a page in less than an hour, you are probably going too fast." The important thing is to be sure you are understanding what you are reading.