On the benefits of retaking advanced linear algebra

In summary: A physics student has the option to take advanced math courses, including real analysis through Rudin and beyond, functional analysis if they have time, and algebra through Artin. The course is known for having a high failure rate and a class average in the low to mid 60s. The student did well in the course material that they were weak on and did not need to study for the applications chapter. If they had practiced computation questions, they may have had a higher score on the final exam. The student's grade is based on percentiles, and will go down by 1% this term due to their previous quantum physics grade. If the student retake linear algebra next term, they have the opportunity to get an 80+.
  • #1
mcabbage
14
4
I'm a physics student who has the option to take some advanced math courses (Real analysis through Rudin and beyond, functional analysis if I have time, as well as algebra through Artin). I'm only just going into my second year this term, and will either be retaking linear algebra 2, or taking group theory.

I just completed advanced linear algebra (fundamental theorem, isomorphisms, principal axis, shurs theorem, spectral theorems, gram schmidt, SVD, quadratic forms, etc), and got between 55-60. Now this course is known for being tough: it often has a 20-25% failure rate and a class average in the low, low 60s (which is barely a C by Canadian scales).

I didn't manage my time properly and didn't study for a big chapter on applications (SVD, linear regression, minimization). To my bad luck, 30% or more of the final exam was based on those bits. If I had ground out an hour or two of practice computation questions I would have had a 70 in the course at the very least.

Luckily, my gpa is measured by percentage: It will only go down by 1% this term by my current estimate since I got an 89 in quantum physics 1, and I have the ability to raise it to somewhere in the 80s by the time i am applying to grad schools (which is enough for the schools I'm interested in according to most professors and students I talk to).

My main question is: Should I retake lin alg next term and try to get an 80+? I understand the content of the course on the pure math side, and I can almost definitely succeed in the following math courses. I just don't know whether it will look better to retake a course, or to go on and take the next one regardless.

Thanks for any advice!
 
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  • #2
My two cents: Learn the material you were weak on by self-study and move on. But do not cut corners in understanding linear algebra. It is fundamental.
 
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  • #3
All are important for physicists:
  • real analysis
  • functional analysis
  • linear algebra 2
Group theory is a bit different. Beside the easy examples ##\mathbb{Z}\; , \;\mathbb{Z}_2\; , \;(\mathbb{R},+)\; , \;\mathcal{Sym}(n)## it are mainly the linear groups which are used in physics. But group theory often means theory of finite groups, and detailed knowledge about them is rarely required for a physicist. So if it was a lecture about linear group, geometric groups, algebraic groups or how ever the subgroups of ##GL(n,\mathbb{F})## are called, I would answer: good idea. But the few occasions you really need classical group theory in physics can be learned on demand (IMO) - orbit-stabilizer formula, normal subgroups, center, isomorphism theorems.
 

1. What is advanced linear algebra?

Advanced linear algebra is a branch of mathematics that deals with the study of vector spaces, linear transformations, and linear equations. It builds upon the concepts of basic linear algebra and applies them to more complex mathematical problems.

2. What are the benefits of retaking advanced linear algebra?

Retaking advanced linear algebra allows for a deeper understanding and mastery of the subject. It also provides the opportunity to review and reinforce important concepts, which can be helpful for future coursework or research in related fields.

3. Can retaking advanced linear algebra improve my grades or GPA?

Yes, retaking advanced linear algebra can improve your grades or GPA if you struggled with the subject the first time around. By retaking the course, you have the chance to learn the material more thoroughly and potentially earn a higher grade.

4. Is it necessary to retake advanced linear algebra if I passed the first time?

No, it is not necessary to retake advanced linear algebra if you passed the first time. However, if you plan on pursuing a career or further education in a field that heavily utilizes linear algebra, retaking the course may be beneficial in strengthening your understanding of the subject.

5. How can I make the most out of retaking advanced linear algebra?

To make the most out of retaking advanced linear algebra, it is important to attend all lectures, actively participate in class discussions, and complete all assignments and practice problems. It may also be helpful to seek extra help from the professor or a tutor if needed.

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