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Math Review before Grad School

  1. Apr 23, 2014 #1
    After 13 years of on and off schooling, I am (yay!) getting my B.A. in mathematics in... a couple of weeks.

    As most undergraduates I am intimidated at the prospect of graduate school and the pace of the work. When I talk to grad students I hear how bone-crushingly hard everything is, yadda yadda.

    There are two approaches I can take to studying over the summer and I'm wondering which is better. I can focus on a few topics, or even just one (like Analysis) and concentrate on those. That will prepare me (maybe?) for one or more classes.

    But I sometimes feel like undergrad went by so fast, that I want to reign in everything I've learned, and be able to access it (mentally) a bit more easily, rather than having to say "Oh, right, I haven't had calculus in 3 years..."

    So my other approach is to go through Garrity's book "All the Mathematics You Missed But Need to Know for Graduate School."

    It's a really cool book and I'm excited about the prospect of being able to go through this. Though the idea of plunging into Analysis and really trying to sink my teeth into it is also exciting.

    Curious which approach is warranted. I can give a list of the classes I'm taking and what not, but I'm pretty sure it's standard in the first few years of grad school - not much left up to the imagination there.

    -Dave K
     
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  3. Apr 23, 2014 #2

    micromass

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    What research would you like to do in grad school? Something related to analysis? Algebra? Differential Geometry?

    Going through some analysis would not be a bad idea, certainly if you're planning to do analysis-related stuff.

    My experience with this book: when the book explained something, then either I already knew it, or it turned up not to be useful for graduate school at all. There was a lot of math that I wish I knew before starting graduate school, but this book did not contain it. It's still useful as a (very brief) revision of undergrad though.
     
  4. Apr 24, 2014 #3
    Typically, the first big hurdle that trips most people up is the qualifying exams, so that's what I would focus on, if they have any syllabus or anything for them. Most of the people in my program who left early were knocked out by that. You don't necessarily have to remember how to do every last integral for calculus, aside from teaching purposes, but analysis is good to know.

    The classes are bone-crushingly hard in their content, but typically grades don't matter that much in grad school, so as long as you don't slack off and know what you are doing enough to get accepted, it's probably not too big of a deal. Quals can be an obstacle for a lot of people, but to me, everything I have ever done in my life, including the rest of grad school, pales in comparison to my dissertation. But first things first.
     
  5. Apr 24, 2014 #4
    I know what I think I like, and that is more on the side of algebra, combinatorics/graph theory. I really like applications in theoretical computer science, information theory, things of that nature. I have no shortage of ideas of what I want to research. But in my first few years of undergrad, I'm not sure how much this matters.

    I like Analysis, don't love it. It is not my best subject. I think I have to take an Analysis qualifier either way. For these reasons I think I should perhaps spend more time on it because it does not come as easy.

    What compels me to do this review is that, when I see people presenting research, they appear to seamlessly weave together different aspects of mathematics... "I've got a matrix here, based on a graph, but I had to throw some probability distributions in it, and toss in some combinatorics." (Yes, that is complete nonsense what I just said, but this is what it sounds like to an undergrad).

    I feel like I need to have these different topics closer to the front of my brain than they are now. I don't want to forget them.

    However, that is about being "wide" but not deep, and I suspect graduate mathematics is about being deep. (Maybe wide too).

    -Dave K
     
  6. Apr 24, 2014 #5

    If there's been one oft-repeated bit of advice I've gotten so far it's to study for the qualifiers. My first semester will be algebra heavy. (Linear Algebra and Algebra I in the first semester, in addition to Analysis). So it's been recommended that this is the first qualifier I take. That would mean studying Algebra over the summer, if that's the goal.

    But Analysis is (I think) going to be more challenging for me.

    You can perhaps see why I'm wavering so much.

    -Dave K
     
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