Which Is More Crucial for a Physics Major: Geometry or Advanced Linear Algebra?

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Discussion Overview

The discussion centers around the importance of Geometry versus Advanced Linear Algebra for a physics major. Participants explore which course might enhance mathematical ability and interest, as well as its relevance to physics studies.

Discussion Character

  • Debate/contested
  • Exploratory
  • Technical explanation

Main Points Raised

  • Some participants express concern about taking Linear Algebra II without having completed Linear Algebra I, suggesting it may be challenging or impossible without prior knowledge of vector spaces and transformations.
  • Others argue that Linear Algebra II is more useful for a physics major, citing its widespread application in science and engineering.
  • A few participants find the geometry course potentially boring and question its value compared to Linear Algebra II.
  • Some participants emphasize the necessity of understanding trigonometric functions, which are part of the geometry course, for success in physics.
  • One participant mentions that Linear Algebra II is a requirement for their physics degree, indicating its perceived importance in the curriculum.
  • A participant who has started their physics major expresses a preference for Linear Algebra, suggesting that geometry can be self-taught.

Areas of Agreement / Disagreement

Participants do not reach a consensus on which course is more crucial. There are multiple competing views regarding the relevance and usefulness of Geometry versus Advanced Linear Algebra for a physics major.

Contextual Notes

Some participants highlight the potential challenges of taking Linear Algebra II without prior knowledge of Linear Algebra I, while others focus on the practical applications of Linear Algebra in physics and engineering. The discussion reflects varying levels of familiarity with the courses and their content.

tme92
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Which course is more important to a physics major? Which is more likely to improve one's mathematical ability? Which is more interesting? (I haven't even had Linear Algebra I so I don't know if I like the subject.). Unfortunately, I have to decide now.

Descriptions:

Geometry

Foundations of Euclidean plane geometry. Similarity of triangles. Circumferences and trigonometric functions. Notable points of the triangle. Coordinates the plan. Structure of vector. Conics. Geometric transformations.

Linear Algebra II

Symmetric and alternating multilinear functions. Determinant function. Inner products. Orthogonal subspaces. Additional orthogonal. Orthogonal projection. Euclidean analytic geometry. Hermitian form. Diagonalization of a symmetric matrix. Orthogonal arrays. Unitary matrices. The classical groups O (n), SO (n), U (n), SU (n) for n equal to 2 or 3. Classification of quadratic forms. Method of principal minors. Jordan canonical form for matrices of order 2 and 3
 
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tme92 said:
Which course is more important to a physics major? Which is more likely to improve one's mathematical ability? Which is more interesting? (I haven't even had Linear Algebra I so I don't know if I like the subject.). Unfortunately, I have to decide now.

Descriptions:

Geometry

Foundations of Euclidean plane geometry. Similarity of triangles. Circumferences and trigonometric functions. Notable points of the triangle. Coordinates the plan. Structure of vector. Conics. Geometric transformations.

Linear Algebra II

Symmetric and alternating multilinear functions. Determinant function. Inner products. Orthogonal subspaces. Additional orthogonal. Orthogonal projection. Euclidean analytic geometry. Hermitian form. Diagonalization of a symmetric matrix. Orthogonal arrays. Unitary matrices. The classical groups O (n), SO (n), U (n), SU (n) for n equal to 2 or 3. Classification of quadratic forms. Method of principal minors. Jordan canonical form for matrices of order 2 and 3

Withou having taken Linear Algebra (a beautiful subject in its own right I might add), Linear Algebra II will be very challenging at best and impossible at worst. If your professor begins the first day assuming you're familiar with the basics of vector spaces, transformations, etc. (likely) then you're going to have a tough time to say the least.

Now, I'm a math major so I can't really speak toward its usefullness in that regard, but having a course in classical geometry under your belt is always a good thing.
 
Not much of a choice here. I don't know why you would even consider taking LA II without Linear Algebra I.
 
I didn't explain myself. I haven't yet taken Linear Algebra I but I will have when I eventually take Linear Algebra II. The course that I have to pick I will only take it six months from now.
 
And you have to pick it now?

Which physics courses have you already taken? You can't get very far in physics without knowing about trigonometric functions (which are listed as part of the geometry course). Have you studied trigonometry already?
 
I'd think linear algebra 2 would be much more useful.
 
And you have to pick it now?

Yes.

Which physics courses have you already taken? You can't get very far in physics without knowing about trigonometric functions (which are listed as part of the geometry course). Have you studied trigonometry already?

Of course. I studied it in high school. This geometry course is a university level course. I don't think I'll be exposed to a lot of new concepts; I suppose it will be a proof-based course.
 
The geometry course sounds really boring, maybe you should find out the text they use and see if it really worth taking at all.

Linear algebra is definitely more useful, it is used everywhere in science and engineering. Even it says it is linear algebra 2, the topics covered doesn't sound too difficult, it all depends on what is expected of you and how it is taught. The best way to judge is again find out the text they use and see if you are capable to take it.
 
chingkui said:
Linear algebra is definitely more useful, it is used everywhere in science and engineering. Even it says it is linear algebra 2, the topics covered doesn't sound too difficult, it all depends on what is expected of you and how it is taught. The best way to judge is again find out the text they use and see if you are capable to take it.
How can he possibly be the judge of that if he hasn't yet taken Linear Algebra I and has to decide before taking it?!
 
  • #10
Linear algebra will be very Important to you in physics,, and it's better to be exposed to it in a separate course than to learn about it in physics courses,, also most of the proofs in it are very straight forward
 
  • #11
At my university Linear Algebra II is required for the physics degree.
 
  • #12
I started my physics major this year and I am taking linear 1 i love it. I vote linear algebra all the way. you can teach yourself geometry.
 
  • #13
LinAl 2
 

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