Linear algebra among physicists

In summary, the conversation discusses the relevance and requirement of linear algebra for physics majors. While it is not a required course at some schools, it is highly recommended and often seen as essential for understanding topics such as quantum mechanics and differential equations. Some schools have multiple courses in linear algebra, with varying levels of difficulty and emphasis on proofs. Overall, the conversation highlights the importance of linear algebra in a physicist's mathematical education.
  • #1
CPL.Luke
441
1
how many physics majors take formal courses in linear algebra?

I got it done this semester and found it to be one of the most applicable mathematical subjects out there, just thinking about doing differential equations without linear algebra gives me the willies, and looking at the physics curricula at a number of schools I see that its not required, so I have to wonder how many people take it?
 
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  • #2
Linear algebra is highly recommended at the school I did undergrad at. Not only is it extremely helpful, like you said, but it was also a pre-req for some of the higher level courses in the math department. They had two courses actually. One was rigorous with proofs and mainly for the main majors. Another was mainly learning the concepts and for everyone else.
 
  • #3
Linear algebra along with PDE's and DE's is an essential part of a physicists math education, you will not get too fat in QM without it.
 
  • #4
Dr Transport said:
...you will not get too fat in QM without it.

Geez, I knew QM required lots of study time but I thought I might at least have SOME time for exercise next semester; I'm fat enough as it is. :tongue2:
 
  • #5
unit_circle said:
Geez, I knew QM required lots of study time but I thought I might at least have SOME time for exercise next semester; I'm fat enough as it is. :tongue2:

A professor of mine called this sitzfleisch, which I always assumed meant the fat ass you get from doing lots of deskwork.
 
  • #6
CPL.Luke said:
how many physics mamors take formal courses in linear algebra?
Every physicist has taken them. I had such courses in high school (eg linear vector theory, eigenvectors), first (Jordan normal forms, vector spaces etc etc) and second year of college. Thery are an essential part of the theoretical framework behind physics


marlon
 
  • #7
it's actually not a requirement at UF, even though i think it should be. i also think that the proof-oriented course (as opposed to a mere computational one) should be taken by the serious physics student. you'll see a lot of the proofs again, especially with inner product spaces, etc.
 
  • #8
Linear Algebra is not a requirement in the physics dept at my school, Loyola Chicago, however I am doing their combined math and physics major and it is a requirement for that, I am in it this comming semester, I am hoping it is better than my calc 3 class
 
  • #9
For me it was compulsory in the first year of university studies. In the second semester, just as mathematical analysis was in the first semester. Its relevance for a physics student is mainly due to the QM course. If that course is taught in a superficial manner, then it's probably not required of the student to take the linear algebra b4, since in the introductory lectures (of the QM course) some elementary linear algebra absolutely necessary for QM can be dealt with.

Daniel.
 
  • #10
At UW it's required first year for all physics students. The math phys kids take another course second year as well.
 
  • #11
Linear Algebra was not a requirement for me, but was highly recommended.
 
  • #12
At my school, physics students have to take two linear algebra courses in the first and second years. The first one covered up to eigenvalues and eigenvectors, and involved very little proofs since it's primarily taught for engineers. From what I've seen from my former physics classmates, apparently the second one is much more challenging and proof-based.
 
  • #13
Yea Linear Algebra isn't required at my school either, they just take up to ODE and then a course on Mathematical Physics. Alot of them are doing math minors (like me but I'm an EE) and Linear Algebra is a required course for a math minor.

In fact the whole reason I'm doing a math minor is because I wanted to take linear algebra and after that I just needed 2 more classes.
 

1. What is linear algebra and why is it important in physics?

Linear algebra is a branch of mathematics that deals with vector spaces and linear transformations. It is important in physics because it provides a powerful framework for representing and solving physical problems, such as systems of equations and transformations of coordinates.

2. How is linear algebra used in quantum mechanics?

Linear algebra is used extensively in quantum mechanics to describe the physical states of particles, as well as the operators that act on these states. Quantum states are represented as vectors in a complex vector space, and operators are represented as matrices that act on these vectors.

3. Can you give an example of a real-world application of linear algebra in physics?

One example is the use of eigenvalues and eigenvectors in quantum mechanics to calculate the energy levels of a system. These values can also be used to determine the probabilities of different outcomes in experiments, such as the spin of an electron in a magnetic field.

4. How does linear algebra relate to the study of special relativity?

In special relativity, the Lorentz transformation equations that describe the relationship between different frames of reference can be expressed using matrices. This allows for the use of linear algebra techniques to analyze and solve problems involving relativistic effects.

5. Are there any software tools or programs that can assist with using linear algebra in physics?

Yes, there are many software tools and programs available that can assist with solving linear algebra problems in physics. Some popular examples include MATLAB, Mathematica, and Python libraries such as NumPy and SciPy.

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