I have completed my B.Sc. in math and will be starting M.Sc. math in a few months. During my undergraduate classes I found the real analysis and general topology courses the most interesting and the algebra courses(especially linear algebra and ring theory) not so much. Since I have a few months before I am able to consult a professor in person, I am undecided on what I should study in the meantime. I am tempted to focus exclusively on the real analysis and general topology topics but not if I would be expected to maintain an equal understanding of the algebra topics in my further studies.

Can I focus my efforts solely on the analysis topics I find interesting and only study algebra just to pass my classes or would it be better to focus on both equally, in case further studies/research in analysis will inevitably require me to truly understand and appreciate algebra?

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    $\begingroup$ You should learn as much as you can. Every field of math interacts with every other, and while analysis may require less algebra than say, algebraic geometry, algebra certainly appears (especially linear algebra) $\endgroup$ – leibnewtz Apr 29 '18 at 17:39
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    $\begingroup$ You'll never know beforehand what you'll use in your research. Better study like the devil. $\endgroup$ – chhro Apr 29 '18 at 17:47
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    $\begingroup$ Follow your heart, study what you're interested in, but you'lll want to be well-versed in the basics $\endgroup$ – David Bowman Apr 30 '18 at 0:08

I think you will find the connections between analysis and topology to be stronger than connections between analysis and algebra. If others think I'm wrong about that, no doubt you will hear from them

In comments you seem to have conflicting advice which might be interpreted as (i) to study hard on everything vs. (ii) to study what interests you most. Each is good advice in its own way, but it's hard to follow both at once.

Bear in mind that your current mathematical passions may be due to the faculty members you have had and the texts you have used as much as they are due to your fundamental capabilities. So it is important to pay attention to (i) because you probably can't predict your future interests as well as as you might imagine. Don't ignore algebra to a point that you foreclose possibilities.

However, to a large extent you may make the most productive use of your time by following (ii). If you're really 'on a roll' with a particular topic it may be best to focus on that for the short term.

Obviously, some balance is required and only you can choose what balance is best at this point in your career. In the natural course of things you will be working on your PhD thesis soon. For that period of time, I think single-minded focus on your thesis topic has to take precedence. After that, you have the whole rest of your life to decide what new interests to pursue.


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