Results 1 to 5 of 5

Math Help - What to study after linear algebra

  1. #1
    Kgm
    Kgm is offline
    Newbie
    Joined
    Feb 2011
    Posts
    2

    What to study after linear algebra

    Hey MHF,

    I've been teaching myself linear algebra for giggles. I have Strang's Linear Alegra and its Applications and I've been watching his lectures on youtube. I have 3 years of calc behind me (all of Anton's 8th edition). I've also read the first half of Murray Spiegel's Applied Differential Equations. (I stopped after the solution methods by use of series and before systems of ODEs.) What should I study next? I was thinking of doing PDEs, though I'm kind of bored with DEs. I'd be super grateful for a few suggestions =D

    Kgm
    Thanks in advance!
    Follow Math Help Forum on Facebook and Google+

  2. #2
    A Plied Mathematician
    Joined
    Jun 2010
    From
    CT, USA
    Posts
    6,318
    Thanks
    4
    Awards
    2
    I don't know if you're into physics, but if you are, quantum mechanics is a fantastic follow-up to linear algebra. Prerequisites for quantum mechanics (in my opinion) are:

    Freshman and Sophomore-level physics.
    Junior-level classical mechanics (although I survived without having had that first - it is a little better if you do it first).
    Calculus 1, 2, and 3.
    Differential Equations.
    Linear Algebra.

    That'd be my recommendation. If you're not into applications so much, you might go with Advanced Calculus, Real Analysis, Complex Analysis (a particularly beautiful subject), or even Abstract Algebra.
    Follow Math Help Forum on Facebook and Google+

  3. #3
    Senior Member
    Joined
    Nov 2010
    From
    Staten Island, NY
    Posts
    451
    Thanks
    2
    If I remember correctly, then Strang's book is not very theoretical. If you want to start study more rigorous mathematics I would suggest abstract algebra or real analysis. You may want to look at a slightly more theoretical book on linear algebra first though. Linear Algebra tends to be a nice bridge from the computational to the theoretical.

    Complex Analysis is very nice, but you will have to accept some results from Real Analysis as you go.
    Follow Math Help Forum on Facebook and Google+

  4. #4
    MHF Contributor Swlabr's Avatar
    Joined
    May 2009
    Posts
    1,176
    Quote Originally Posted by Kgm View Post
    Hey MHF,

    I've been teaching myself linear algebra for giggles. I have Strang's Linear Alegra and its Applications and I've been watching his lectures on youtube. I have 3 years of calc behind me (all of Anton's 8th edition). I've also read the first half of Murray Spiegel's Applied Differential Equations. (I stopped after the solution methods by use of series and before systems of ODEs.) What should I study next? I was thinking of doing PDEs, though I'm kind of bored with DEs. I'd be super grateful for a few suggestions =D

    Kgm
    Thanks in advance!
    Everything in Linear Algebra is finite-dimensional. If you wanted, you could crank everything up a knotch and look at the infinite-dimensional analogues of Hilbert spaces and Banach spaces. It is, admittedly, graduate level stuff, but very interesting all the same.

    This stuff can be found in the book `functional analysis' by Rudin.
    Follow Math Help Forum on Facebook and Google+

  5. #5
    Senior Member
    Joined
    Nov 2010
    From
    Staten Island, NY
    Posts
    451
    Thanks
    2
    Quote Originally Posted by Swlabr View Post
    Everything in Linear Algebra is finite-dimensional. If you wanted, you could crank everything up a knotch and look at the infinite-dimensional analogues of Hilbert spaces and Banach spaces. It is, admittedly, graduate level stuff, but very interesting all the same.

    This stuff can be found in the book `functional analysis' by Rudin.
    I think you mean that a basic course in Linear Algebra only looks at finite dimensional spaces. You can certainly study infinite-dimensional vector spaces. This would still be considered Linear Algebra.

    Personally I think that Functional Analysis is too big a jump from Linear Algebra. You may want to study it after you've been exposed to a bit more theoretical math.
    Follow Math Help Forum on Facebook and Google+

Similar Math Help Forum Discussions

  1. Replies: 1
    Last Post: March 2nd 2011, 08:30 PM
  2. Study Techniques for Algebra?
    Posted in the Math Topics Forum
    Replies: 6
    Last Post: July 30th 2010, 10:07 AM
  3. Advice/Study plan for Algebra?
    Posted in the Algebra Forum
    Replies: 0
    Last Post: May 5th 2010, 11:03 PM
  4. Replies: 6
    Last Post: May 3rd 2010, 02:43 AM
  5. exam study, Algebra II
    Posted in the Algebra Forum
    Replies: 0
    Last Post: October 6th 2008, 12:27 PM

Search Tags


/mathhelpforum @mathhelpforum