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I'm an undergraduate who doesn't find analysis particularly interesting, but I'm taking a calculus on manifolds course next semester, so I'm reviewing measure and integration theory since my grasp on the subject should be stronger, but it's so difficult to actually sit down and learn the material when I'm uninterested in it. With subjects I like, I can sit down and read a textbook for hours every day without any problem.

Does anybody have any advice? Topology was my favorite course so when I can think of problems topologically or have some topological motivation, it helps me want to learn these other subjects, but the textbook I use doesn't take a topological approach. If anybody has any advice (or textbook recommendations), I'd greatly appreciate it.

Also, I can't just not learn this subject, either

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  • $\begingroup$ Although there were plenty of math areas I didn't like and/or had difficulty with (see my comments to this question, for example), your question brings to light one of the differences between undergraduate study in the U.S. and undergraduate study in some other countries. In my case, classes I took (for required non-science electives) as an upper level undergraduate included abnormal psychology, cognitive psychology, existentialism (philosophy), feminism, French (failed twice), and philosophy of the mind (Dennett, Fodor, Ryle). $\endgroup$
    – Dave L Renfro
    Commented Jan 14, 2022 at 18:04
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    $\begingroup$ Maybe get drafted for a couple of years into military? This would change your "I cannot do stuff that I don't like" attitude. $\endgroup$
    – Rusty Core
    Commented Jan 15, 2022 at 2:36

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Back in my student days I found that: Studying my favorite subjects could be done in almost any setting, regardless of distractions. But to study less favorite subjects I had to be a a quiet place with no distractions. This was in the Olden Days when I did not have distractions like an iPhone in my pocket that went with me everywhere. Believe it or not: back then libraries were quiet places with books, not lively places with computers!

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Do you think you will enjoy learning calculus on manifolds? I think there is a lot to appreciate there, and it opens the doors to a lot of beautiful mathematics and physics(differential geometry, differential topology, general relativity, de Rham cohomology, Hodge theory, etc).

You can mostly get by in calculus on manifolds with just Riemannian integration. Measure theory isn't really needed (although it is certainly a nicer theory of integration, and makes a lot of things easier and more coherent).

My personal advice would be to stop forcing yourself to study something which you are not currently excited about. If you care about calculus on manifolds and measure theory crops up during your study, that might provide you with a more natural motivation to brush up on it. Seeing it used for something you care about can be the key to starting to care.

I thought my measure theory class was the most boring thing ever. I could barely will myself to study, and then only for the grade. It wasn't until I started learning some functional analysis that I gained an appreciation for measure theory and was able to return to its study with gusto.

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    $\begingroup$ Agreed. Find a subject that does interest you and uses measure theory - perhaps fractals or ergodic dynamics or probability, to name just three examples. $\endgroup$
    – J W
    Commented Jan 14, 2022 at 12:43

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