Is honors linear algebra worth it?

[ThomsonT]

Hey everyone, I'm majoring in physics and will be starting my first year in the fall. I'm currently registered in honors linear algebra, but have been thinking that it might be beneficial to take the regular linear algebra course. I'm also in honors calculus, but I know I want to stay in that. I do enjoy math quite a bit, however I am unsure if the honors course will be incredibly helpful. If anyone has any advice on this it would be greatly appreciated, thanks!

 

[ZombieFeynman]

If you want to go on to graduate school (or simply excel as an undergraduate) and you are a motivated student, honors courses can only help. The additional rigor they emphasize and pressure they place you under are good for developing the mind. What do you think would get you in better shape: a twice a week Pilates class or Navy SEAL boot camp?

Generally schools have a 2-3 week no penalty drop/add should they be too much.

 

[dipole]

Linear Algebra isn't really that useful of a course IMO. You will use tons and tons of linear algebra in physics, but most of it you won't see in that class. You'll spend most of your time proving theorems about abstract vector spaces that have nothing to do with physics.

I think you're better off learning LA as you go along with the physics, and not getting so distracted on highly abstract math courses that even though you think will benefit you, in the end are usually a waste of time (for the physicist). This coming from a physics senior.

 

[ZombieFeynman]

Linear Algebra isn't really that useful of a course IMO. You will use tons and tons of linear algebra in physics, but most of it you won't see in that class. You'll spend most of your time proving theorems about abstract vector spaces that have nothing to do with physics.

I think you're better off learning LA as you go along with the physics, and not getting so distracted on highly abstract math courses that even though you think will benefit you, in the end are usually a waste of time (for the physicist). This coming from a physics senior.

Abstract vector spaces are the mathematical framework of much of modern physics. Proving theorems about them give the student insight into this framework. They also provide the mathematical maturity and intuition to solve problems in advanced undergraduate and graduate classes. I agree that you can learn LA as you go along. But the student who has a rigorous theory of vector spaces ingrained into her head from countless proofs and calculations will be more confident and adept with their further studies.

 

[Jorriss]

Linear Algebra isn't really that useful of a course IMO. You will use tons and tons of linear algebra in physics, but most of it you won't see in that class. You'll spend most of your time proving theorems about abstract vector spaces that have nothing to do with physics.

I think you're better off learning LA as you go along with the physics, and not getting so distracted on highly abstract math courses that even though you think will benefit you, in the end are usually a waste of time (for the physicist). This coming from a physics senior.

I don't entirely agree. A lot of physics problems in quantum mechanics are mathematical subtleties that are not covered in physics courses. As a simple example, [q,p]=ihI. Tr([q,p])=0=tr(ihI)=/=0. What went wrong? The difference is the difference between dealing with infinite and finite dimensional vector spaces which is covered on a pretty superficial level during physics courses.

As a person with an interest in physics though, those types of 'seeming' contradictions in the formalism are bothersome.

I wouldn't take an honors course in place of a physics course though.

 

[WannabeNewton]

You'll spend most of your time proving theorems about abstract vector spaces that have nothing to do with physics.

This couldn't be farther from the truth.

 

[A. Bahat]

Surprisingly, the usual computational matrix stuff that's often dubbed "linear algebra" is not nearly as useful as the vector space/linear operator point of view, at least in quantum mechanics.

 

[micromass]

Maybe it would be nice if you could tell us the difference between LA and honors LA?? What topics are not covered in regular LA?

 

[ThomsonT]

Here's the descriptions for both courses.

Math 125 Linear Algebra I:
Systems of linear equations. Vectors in n-space, vector equations of lines and planes. Matrix algebra, inverses and invertibility. Introduction to linear transformations. Subspaces of n-space. Determinants. Introduction to eigenvalues and eigenvectors. The dot product and orthogonality. Applications in a variety of fields, numerical methods.

Math 127 Honors Linear Algebra I:
Sytems of linear equations, vectors in Euclidean n-space, span and linear independence in Euclidean n-space, dot and cross product, orthogonality, lines and planes, matrix arithmetic, determinants, introduction to eigenvalues and eigenvectors, introduction to linear transformations, complex numbers, vector space axioms, subspaces and quotients.

 

[nuclear85]

As so many classes do, it's going to depend on the professors... there is no standard for making something an 'honors' class; it varies tremendously between schools, and even within schools. They could end up being more or less identical classes. Or, the honors one could be incredibly proof heavy. If you know who is teaching them, talk to people who have taken their classes. If you need honors classes to stay within some kind of honors program at your school, take it. Otherwise I woudn't worry that much about it...