Which course would be more useful? Linear algebra II or Numerical Analysis

[tripsky]

Hey guys,

I'm currently in a 2nd year Honors Physics program & I need to decide within the next ~2 weeks which of these two classes to take. Either Linear algebra II or Numerical Analysis.

Heres are course descriptions as given on my Universities website

Linear Algebra II
Vector space examples. Inner products, orthogonal sets including Legendre polynomials, trigonometric functions, wavelets. Projections, least squares, normal equations, Fourier approximations. Eigenvalue problems, diagonalization, defective matrices. Coupled difference and differential equations; applications such as predator-prey, business competition, coupled oscillators. Singular value decomposition, image approximations. Linear transformations, graphics.

Numerical Analysis
Introduction to numerical analysis; polynomial interpolation, numerical integration, matrix computations, linear systems, nonlinear equations and optimization, the initial value problem. Assignments using a computer and the software package, Matlab, are an important component of this course.Which of these would be the most useful as an undergraduate?

I appreciate all input, thanks!

 

[Clever-Name]

I would strongly recommend linear algebra II. I took the same course last year (in my 2nd year) and it has come in handy quite a bit in my 3rd year courses and 2nd semester 2nd year courses.

While I haven't taken numerical analysis I have heard that the prof (Western, right?) isn't the greatest, whereas Wahl teaches linear algebra 2 and if you just took ODE's then you should appreciate her teaching style. Linear Algebra is also extremely important in quantum as the math in quantum exists in an abstract vector space, which is exactly what is studied in that course. Numerical Analysis is also important in some aspects but at this level you're better off with linear algebra, it is still possible for you to take numerical analysis next year.

 

[tripsky]

Hey Clever!

Yeah you're right I've just had her and she is great! Coupled with what you've mentioned now (and in the past) about its usefulness in other courses, I'm currently enrolled in lin alg II. (BTW, which 2nd semester 2nd year course did it come in handy? modern phys?)

Anyway, I guess my hesitation arises from the following two reasons:
1) that if I manage to land a nserc/ some summer position, wouldn't the matlab/numerical skills be more useful to the employer than, well, linear algebra II? (or does Wahl by any chance make us use Matlab in the course as well? )
2) I talked to a couple of profs (Holt & Wahl) and both recommended Numerical Analysis over Linear algebra II :S

 

[Clever-Name]

It didn't really end up having a practical use at all in second year, what I was referring to was during modern physics the TAs mentioned using sin and cos as a basis set for solving certain problems. Most people had no idea what it meant for something to be a basis but since I was taking linalg concurrently it made sense to me.

1/2) I suppose they may be right. I'm biased against the numerical analysis class just because I have heard so many horror stories about it. I can't argue against its usefulness, no doubt it is useful in any computational stuff you may do. But I have also heard that most of the useful things you may learn in Num Anal you will take up in Computer Simulations (which I hope you are taking next year).

Ultimately you won't go wrong taking either course, Num Anal might have a more versatile general use, but for my own interests Lin Alg seemed like the more important course to take. You might want to send an email to a few of the PASA execs and ask them about what they think. (check your PMs).

 

[tripsky]

It didn't really end up having a practical use at all in second year, what I was referring to was during modern physics the TAs mentioned using sin and cos as a basis set for solving certain problems. Most people had no idea what it meant for something to be a basis but since I was taking linalg concurrently it made sense to me.

1/2) I suppose they may be right. I'm biased against the numerical analysis class just because I have heard so many horror stories about it. I can't argue against its usefulness, no doubt it is useful in any computational stuff you may do. But I have also heard that most of the useful things you may learn in Num Anal you will take up in Computer Simulations (which I hope you are taking next year).

Ultimately you won't go wrong taking either course, Num Anal might have a more versatile general use, but for my own interests Lin Alg seemed like the more important course to take. You might want to send an email to a few of the PASA execs and ask them about what they think. (check your PMs).

I've also heard horror stories as well. Actually going off what you said, I've also heard that some people take numerical analysis AFTER comp sims and finding that helpful... Have you heard of this as well? From this am I right in guessing that comp sims builds your foundation of some numerical techniques better?
Also just curious, In comparison to Wahls ODE course... how much more/less time consuming is lin alg II?
And thanks for the idea i'll definitely email an exec

 

[Clever-Name]

I haven't heard that but it doesn't surprise me. Comp Sims starts off with the assumption that you're brand new with MATLAB and have no coding experience, though the 2nd year curriculum has been changed recently to adopt some coding in the waves class.

If you took math 1600a this past semester then the second course won't be too much work, at least it shouldn't, and wasn't for me. Compared to ODE I can't really comment, when I took it last year ODE wasn't extremely difficult and the assignments were tame, from what I hear this semester it has been much harder and much more work. I would expect the same thing from Wahl next semester.

 

[DuncanM]

My background is engineering, not physics, but I recommend taking the Numerical Analysis course. I took both a Linear Algebra II (LA) course AND a Numerical Analysis (NA) course, and I found the practical return on the NA course WAY bigger than from the LA II course. In fact, I think I rarely used material from the Linear Algebra II course afterwards, almost everything else we needed in terms of LA material had been covered in the Level I course.

However, material from the NA course was used frequently in subsequent courses, and I was a little peeved that the course had not been given to us previously. At the time, I think I took it in the spring term of second year. Before that, I had been trying to solve simultaneous equations, solve for roots of equations, compute eigenvalues, etc. with a hand calculator and pen and paper. As far as I am concerned, the NA course should have been taught in the fall term of first year because with it came many programs and much code for solving many of the problems we faced later. It would have saved us all a lot of time and stress if that course had been given to us right away, instead of having us wait three terms to get some of these important tools.