How useful was Linear Algebra II after Linear Algebra I?

[MathewsMD]

I am a Physics major looking into Mathematical Biology (perhaps) in the future, and regardless of where I go, I'm trying to build a solid math background for myself.

I've taken (or plan to take):

Linear Algebra I
Calculus I, II, III, IV
ODE
Non-linear ODE
PDE
Complex Variables (I will hopefully take this soon, but there have been timing conflicts unfortunately)
Statistics

I don't have too many more electives, so I am trying to take courses that I am very interested in and think will be useful. I'm sure these courses vary somewhat by each University, but how did you find Linear Algebra II? I've spoken with a small sample of students from my University, and a lot of them say the same thing: there's not much new content in this course compared to Linear Algebra II, and if there was any new content, it was already covered in our other Physics courses. With that being said, how was your experience in this course?

Any advice for other math course you enjoyed or found useful would be greatly appreciated, too!

 

[Vanadium 50]

I am sure the contents of Linear Algebra I and II are specific to your university.

 

[JorisL]

[...]
Any advice for other math course you enjoyed or found useful would be greatly appreciated, too!

It really depends on your interests and what you plan to do in your physics career.
In general a course on numerical methods in mathematics(eigenvalue problems, solving (systems of) differential equations, ...) is never wasted.

Take me, I'm sorry I never took an introductory course on measure theory which is used in some fields of mathematical physics (which I'm drawn to lately).
It could've saved me a lot of time I had to spend getting familiar with the basics. (I like an intuitive idea whenever possible)

I am sure the contents of Linear Algebra I and II are specific to your university.

This is quite annoying and happens too often.

 

[QuantumCurt]

Course descriptions of both linear algebra I and II could be helpful here. Most schools that I've seen don't really have linear algebra 'I and II'. They tend to just have both abstract and applied versions of linear algebra, and then typically have some graduate level courses on linear algebra as well.

It may be annoying that course content differs, but it's the nature of the material. A linear algebra course can take many different directions depending on how the professor approaches it. This isn't necessarily a bad thing. It's just an example of the fact that math is not so cut and dry once one passes a certain point.

 

[Almeisan]

You take Linear Algebra I to take Linear Algebra II. And if you really want to be a mathematician, you need a basic course in LA.

 

[jack476]

Any advice for other math course you enjoyed or found useful would be greatly appreciated, too!

I really loved abstract algebra, but my favorite by far has been complex analysis (which would be especially useful for physics).

However, they both required linear algebra. LA is way, way too important to neglect. If your school says you need and is being generous enough to give you 2 semesters of it (most of us get it all crammed into 1) then my advice is to take it.

OTOH, if linear algebra II is an elective meant primarily for math or CS majors, then maybe it would be up for debate. Could you go to your university website and copy/paste the course descriptions here?

 

[MathewsMD]

Sorry for the late reply.

Linear Algebra I:
Properties and applications of vectors; matrix algebra; solving systems of linear equations; determinants; vector spaces; orthogonality; eigenvalues and eigenvectors.

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.

 

[MathewsMD]

Course descriptions of both linear algebra I and II could be helpful here. Most schools that I've seen don't really have linear algebra 'I and II'. They tend to just have both abstract and applied versions of linear algebra, and then typically have some graduate level courses on linear algebra as well.

It may be annoying that course content differs, but it's the nature of the material. A linear algebra course can take many different directions depending on how the professor approaches it. This isn't necessarily a bad thing. It's just an example of the fact that math is not so cut and dry once one passes a certain point.

Yes, the Linear Algebra I is offered as a pure math course, while Linear Algebra II is an applied math course. Not that I'm necessarily against it, but I feel like this credit might have better use in another course instead.

 

[Mark44]

Yes, the Linear Algebra I is offered as a pure math course, while Linear Algebra II is an applied math course.

Why do you think that? Unless you've been told this by someone who is teaching the class, I would say that there is a lot of "pure math" in the LA II course, together with a few applications of it.

Not that I'm necessarily against it, but I feel like this credit might have better use in another course instead.

For your intended major, mathematical biology, linear algebra and ODE would be good choices, IMO.

 

[MathewsMD]

Why do you think that? Unless you've been told this by someone who is teaching the class, I would say that there is a lot of "pure math" in the LA II course, together with a few applications of it.

For your intended major, mathematical biology, linear algebra and ODE would be good choices, IMO.

Sorry. I should have been more clear. We have an Applied Math and Mathematics department at our school. Linear Algebra I is offered by the Mathematics department, while Linear Algebra II is offered by Applied Mathematics department.

 

[QuantumCurt]

If you'd like to go into mathematical biology, then taking an applied linear algebra course certainly isn't going to put you at a disadvantage. Likely the opposite actually. I think it would be quite beneficial in a field like that.

 

[MathewsMD]

If you'd like to go into mathematical biology, then taking an applied linear algebra course certainly isn't going to put you at a disadvantage. Likely the opposite actually. I think it would be quite beneficial in a field like that.

Yeah, I guess I'm just trying to decide what courses to take with the few spaces I have left since these are all electives I'm discussing. I'd really like to take more statistics or differential equations, but the ratings and students' (poor) past experiences with a lot of these courses kind of put me off from pursuing some particular courses (like Linear Algebra II) since I want to make the most of my electives. A lot of these courses have some genuinely interesting content, but that combined with a good instructor is what I'm currently searching for to get the most from a course I enrol in.

 

[IGU]

There's a lot to be said for choosing a good instructor, even if the course isn't the best fit with your goals. Personally, for a great instructor, I would take whatever course is being taught regardless of relevance (memories of Feynman's Physics X).