No one is required to read my mid-quarter rambling (but you can if you want to)

I’m really starting to notice the strain of taking too many classes this quarter. (I never learn, do I?) Classes that require a hundred pages of reading a week take a lot of time, especially for people who read as slowly as I do. I’m pretty lost in differential geometry, and I have been getting more and more lost since about halfway through the last quarter. There isn’t much excuse for that given that he is going very slowly. I’m not having too much trouble understanding the material in my other classes, fortunately.

But now the work is really starting to pile up. The main problem is that we have a homework assignment for quantum groups due on Monday, and the professor likes to give problems that are very difficult (at least for me). And I basically try to do them all by myself since there aren’t any other undergraduates in the class. So normally I’d spend all weekend on these problems and (hopefully) solve them. But this time I also have a history midterm due on Tuesday, a quiz in homological algebra on Monday to prepare for, and an abstract for a paper in music due on Thursday. And I should spend some time on algebraic number theory problems that have no deadline but really ought to get done at some point. And I should always be trying to catch up in differential geometry.

On the bright side, I found out that a problem we did in math club last quarter is really nice! The problem asks whether it is possible for a countably infinite set to contain uncountably many nested subsets. The answer, surprisingly, is yes. And if you have taken a course in real analysis, you already knew that. One of the problems on my homological algebra assignment I’m going to turn in in about an hour and a half is to show that if K is a field, the functor D from K-Mod to K-Mod given by D(V)=V* (the dual space) is not a duality. To do that, we show that a countably infinite dimensional vector space is not isomorphic to a dual of any vector space. So you find uncountably many linearly independent functionals on an infinite dimensional vector space, and we’re done! We were given the hint of finding uncountably many subsets of Q so that any two have finite intersection, and the obvious way of doing that is to take a Cauchy sequence of rationals converging to each real number. But I like mine better!


About Simon

Hi. I'm Simon Rubinstein-Salzedo. I'm a mathematics postdoc at Dartmouth College. I'm also a musician; I play piano and cello, and I also sometimes compose music and study musicology. I also like to play chess and write calligraphy. This blog is a catalogue of some of my thoughts. I write them down so that I understand them better. But sometimes other people find them interesting as well, so I happily share them with my small corner of the world.
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5 Responses to No one is required to read my mid-quarter rambling (but you can if you want to)

  1. eigenvalue says:

    i don’t think it’s necessarily a good thing to take a zillion classes at once. (and i’m not just saying that because it’s my last semester and i’m barely taking anything.) perhaps this is especially true for math — i get this sense that most subfields of math are in some way equivalent or at least analogous to each other, so learning one is as good as learning them all (loosely speaking). being a good mathematician is not about knowing a little bit about everything, but about knowing a few things very well.

    • Simon says:

      Yeah, there are definitely analogues in various branches. But I’m not taking all these classes so much because I feel that a good mathematician ought to know all this stuff (although I am taking differential geometry for that reason, so it’s unfortunate that I don’t really understand it, but I feel it will be less painful to take it now with this professor than more or less any other time) but because I’m curious and impatient to learn stuff, and because I don’t handle boredom well.
      But I think that nowadays mathematicians need to know quite a lot of different things. It seems that number theorists in particular (which I’m guessing I will be, although that is by no means certain) need to know a huge amount of analysis and algebra in addition to number theory.

  2. rippledance says:

    Oh dear. I hope you don’t end up burning out, although I doubt that will happen. All the best with getting caught up – and how many classes are you taking this quarter anyway?

    • Simon says:

      I won’t get burned out. I’m just concerned about the next week or so. I have seven classes this quarter, which is the number I have taken every quarter since fall quarter sophomore year.

      • Anonymous says:

        While reading this blog, I for a moment thought it was my blog, the work load… the tonnes of work, sounds painfully familiar. My problem is similar to this, I can’t afford the lecturers, so I have to study the 8 subjects without them, just rock up for the exam. (and hand in assignments like 40 of them in 6 months).
        Someone said something about not needing to take so many. Well the more you know the better off you are. Many proofs require some knowledge of other fields. There’s not that much overlap, but there are enough to make maths an exciting subject. Undergrads is an especially good time to take as many fields as possible, so that you can make an informed decision as to what you will continue doing. That’s my reason (and I didn’t want to take operations management lol, so I took all mathematics subjects).
        Good luck CZ, you won’t burn out, but it is draining – pace yourself for this 🙂

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