I'm entering my second year of undergrad (majoring in mathematics), and I've found that I am really bad at Linear Algebra, but very good at Calculus and Differential Equations. I'm hoping to venture onto Sci. Computing/Applied Maths, but I'm worried my inadequacy (as quite personally, unfortunate lack of interest) for Lin. Alg. will prevent me from being successful in topics such as Numerical Analysis, Algebra, as well as Scientific Computing.

Does anyone in the applied maths field/experience with applied maths have any advice on what I should do? That is, what else is there like Calculus/DEs that will help me in this field? Or do i just need to buck up and get on my Lin. Alg. horse in order to get remotely close to where I want to go?

I appreciate any and all input.

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    $\begingroup$ Oh goodness. Linear algebra is perhaps the cornerstone of applied math in some way or another. You seriously need to better your linear algebra skills if you'd like to do any sort of math, especially applied math. "Buck up and get on my linear algebra horse" might just be one of the funniest math-related quotes I've read. $\endgroup$ – Cameron Williams Aug 26 '15 at 2:11
  • $\begingroup$ Oh gosh, all right thanks. I wouldn't say I'm terribly bad at it, but I definitely am about a full letter grade behind in it when comparing it with Calc/etc. I guess it's time I work on that. $\endgroup$ – Turra Aug 26 '15 at 2:15
  • $\begingroup$ chances are you've taken one or two courses in linear algebra, and I wouldn't write off an entire field based one bad course $\endgroup$ – Elliot G Aug 26 '15 at 2:16
  • $\begingroup$ Linear algebra is a bit weird in some ways since it is very different in spirit from a lot of other math you do early in your math education and degree, but if you invest the time, it'll be second nature. $\endgroup$ – Cameron Williams Aug 26 '15 at 2:16
  • $\begingroup$ I completely agree, I just wish I had a knack for it. I understand and follow all the material in class but I always get unmotivated when it comes to studying/doing homework. Regardless, I guess there's no time for that attitude anymore (in any course). $\endgroup$ – Turra Aug 26 '15 at 2:20

Like you, I also had little motivation for Linear Algebra at university, especially as a young engineering student who could care less about abstract proofs. However, I've come to both appreciate and really enjoy linear algebra once I saw how it ties together so many other subjects and also allows one to develop nice algorithms for numerical computations.

My advice is to stay the course, and focus on the unifying nature of Linear Algebra. To wit:

-The formula of the Fourier Coefficients is not intuitive based on the pure calculus derivation. However, linear algebra will let you see that each coefficient is really the inner product of a "basis function" (like a basis vector) with the function you are approximating. Thus, your function acts like a vector, and the various sine and cosine functions are the "elementary vectors" that form the basis of the trigonomentric functon space.

  • If you can formulate a problem in terms of array and vector operations, then there usually exists an extremely fast algorithm for solving it. This is especially apparent in interpreted languages like R and Python, where a lazy "for" loop will add an order of magnitude to your running time.

  • Eigenvector decomposition of covariance matrices is the heart of a lot of statistical and machine learning approaches, which use eigenvectors to find lower-dimensional representations of a dataset.

  • Quantum mechanics' formalism is based on linear algebra and Fourier series, so you will have access to this area of science.

And many, many more uses. Really, Linear Algebra has turned out to be an incredibly unifying and intellectually broadening subject for me, to the extent that I actually got interested in Abstract Algebra (once you go abstract you don't go back ;-P

  • $\begingroup$ Thanks so much for your response! I hope, like you, I can eventually learn to appreciate the greater greatness of Lin. Alg. I will be taking a computing course that relies heavily on Lin. Alg. this upcoming year, so I hope it will enlighten me even just a little. And I'm so glad you ended up liking Algebra though, because I was hoping to do some of that in the future too! Thanks again!!! $\endgroup$ – Turra Aug 26 '15 at 14:06

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