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Advanced Undergrad Linear Algebra classes

  1. Jan 25, 2012 #1
    Last semester I took a combined course of Diffy Q and Linear Algebra. I feel I know the basics of LA and want to explore things a bit further. After talking to some professors at my school they told me that the next linear algebra class is a graduate class.. After looking at the course notes for that grad class it's definitely out of my range because it's all proofs. They suggested to take real analysis and abstract algebra to prepare for that grad class. I know I won't be taking those classes, probably ever, and now I'm kinda disappointed that a class that sounds interesting is most likely out of reach.

    Does linear algebra usually have a big jump in class level similar to my school? Intro undergrad class then full blown grad class?

    I know the other classes (real analysis, abstract algebra) would develop math maturity but are they really necessary specifically for linear algebra? Is this a normal sequence?

    My options are: 1) self study like mad and develop proof skills on my own and convince an adviser to let me take the class 2) audit the class, which I don't know if I can do because it's a grad class or 3) do an independent study with a professor.

    Any help/guidance is appreciated.
  2. jcsd
  3. Jan 25, 2012 #2
    Linear Algebra does often take an awkward spot in curricula.

    Are you a math major? If so, take analysis and algebra (only algebra will likely be required but analysis builds up a lot of maturity) then take the graduate course. If not, I would take a math professor about doing a reading with them to learn more linear.
  4. Jan 25, 2012 #3
    Thanks for the response. I wish I was a math major but I'm an EE major. :wink: I guess an independent study does seem to be my best option.

    Another question, what class(es) cover the theory of vector spaces? My class last semester only skimmed the surface of vector spaces and I feel like there's a lot more to them.
  5. Jan 25, 2012 #4
    There is. Finite dimensional vector spaces, what most schools cover in an applied undergraduate course I believe, are not immensely interesting or complicated. But what's more important and very cool is infinite dimensional vector spaces. So much to say about those.

    The only place where you are likely to be taught vector spaces in a real rigorous manner is linear algebra. Anywhere else, it's likely presupposed you already know a fair amount about them.

    A reading is a great idea, because it also never hurts to get to know a professor really well.
  6. Jan 25, 2012 #5


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    Hey DrummingAtom.

    There is a book published by Springer that is called: "The Linear Algebra a Beginning Graduate Student Ought to Know" 2nd Ed by Jonathan S. Golan.

    It's a very comprehensive book that might be beneficial to you.
  7. Jan 25, 2012 #6
    Ok thanks. I'll check out those things.
  8. Jan 25, 2012 #7
  9. Jan 26, 2012 #8
    As far as prerequisites, more advanced linear algebra usually wouldn't require algebra and analysis. It's probably more for getting a comfort level with proofs. But in some cases, you might want to do linear algebra over an arbitrary field instead of real number or complex numbers or something like that, and then abstract algebra would be relevant.

    And, I actually only understood linear algebra when I took 2nd semester analysis because you need linear transformations for taking "total derivatives". I just wasn't that good at math when I took linear algebra, and this time, the prof explained it in such a way that it finally made sense. I usually feel like I don't owe much to my profs in terms of what I have learned because I'm self-sufficient, but I shudder to think what might have happened if I had missed out on that.
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