Courses Should I take harder math or physics as a first year?

[fissifizz]

Hello physics forums. I'm a freshman at a top school for physics and have two general options for my track this semester.

(1) I can take the standard multivariable and linear algebra class that provides an introduction to proofs and an extremely rigorous first year mechanics course. The average workloads of the classes are roughly 10 hrs/wk and 14 hrs/wk, respectively.

(2) I can take the extremely rigorous multi/linalg class that is completely done with proofs and the intermediate level mechanics course sort of designed for physics majors. The average workloads of the classes are 17 hrs/wk and 9 hrs/wk, respectively.

Before arriving, I was inclined to pick (1), but now I feel that it is important for me to have good foundations in math with more abstract thinking, especially if I decide to go into theoretical physics in the future, which is why I'm considering pouring a lot of time into (2). It is said that the math class in (2) will crush you but mold you into a great mathematical thinker if you stay diligent.

Which should I pick?

 

[Choppy]

If you plan to be a physics major, take the most rigorous math AND physics classes you have the prerequisites for.

At least where I went for undergrad, "standard" meant the course was oriented for the pre-med crowd. It didn't necessarily imply the course was horrible. But students in those courses were 1 in 800 or so. In the more challenging courses, the profs knew who was left at the end of the term.

 

[ZapperZ]

Hello physics forums. I'm a freshman at a top school for physics and have two general options for my track this semester.

(1) I can take the standard multivariable and linear algebra class that provides an introduction to proofs and an extremely rigorous first year mechanics course. The average workloads of the classes are roughly 10 hrs/wk and 14 hrs/wk, respectively.

(2) I can take the extremely rigorous multi/linalg class that is completely done with proofs and the intermediate level mechanics course sort of designed for physics majors. The average workloads of the classes are 17 hrs/wk and 9 hrs/wk, respectively.

Before arriving, I was inclined to pick (1), but now I feel that it is important for me to have good foundations in math with more abstract thinking, especially if I decide to go into theoretical physics in the future, which is why I'm considering pouring a lot of time into (2). It is said that the math class in (2) will crush you but mold you into a great mathematical thinker if you stay diligent.

Which should I pick?

This is the question I find myself asking multiple times on here, and I will ask it again:

Have you asked your academic advisor this exact question?

Zz.

 

[Dr.D]

You can never know too much math!

 

[fissifizz]

If you plan to be a physics major, take the most rigorous math AND physics classes you have the prerequisites for.

At least where I went for undergrad, "standard" meant the course was oriented for the pre-med crowd. It didn't necessarily imply the course was horrible. But students in those courses were 1 in 800 or so. In the more challenging courses, the profs knew who was left at the end of the term.

Perhaps I should have been more specific. When I wrote standard, I meant that most physics majors at our school start with this course, so it is intended for physics majors. There are many more mechanics courses beneath it geared for premed or just the general science community. The extremely rigorous course higher than it, however, is only taken by few people.

Also, taking both the extremely rigorous math and mechanics course was my plan, but my advisor specifically warned against that because people have tried it in the past and have, in most cases, burnt out very quickly. This is why I am planning to choose one or the other and just sacrifice a little rigor in one area.

Thank you for your answer :)

 

[fissifizz]

This is the question I find myself asking multiple times on here, and I will ask it again:

Have you asked your academic advisor this exact question?

Zz.

Hey, thanks for the reply. I have talked to my advisor repeatedly about this, as well as members of the physics department. My advisor is a classics person and told me I'd be fine choosing either option, and it was up to me depending on my personal interests. The physics faculty responded in the same way, and one encouraged me to do the most rigorous physics course simply because he loves teaching it haha.

So I am trying to determine if it would be better for a theoretical track to take the extremely rigorous, abstract math course and just sacrifice a little rigor in intro mechanics.

 

[robphy]

Have you spoken to more senior students who may have followed these different paths?
What specific textbooks are used in these courses? Have you looked inside them?
What is your prerequisite preparation for these courses?
What are the textbooks of the next courses?
How many students follow in these various tracks? (that is, how large or small would your cohort be?)
Specifics are better than vague generalities.

 

[fissifizz]

Have you spoken to more senior students who may have followed these different paths?
What specific textbooks are used in these courses? Have you looked inside them?
What is your prerequisite preparation for these courses?
What are the textbooks of the next courses?
How many students follow in these various tracks? (that is, how large or small would your cohort be?)
Specifics are better than vague generalities.

Sure thing. I have looked inside the textbooks. The one used for both physics courses is Morin's Classical Mechanics. The book for the harder math class is Spivak Calculus and Axler Linear Algebra Done right, while the one for the easier class is Vector Calculus, Linear Algebra and Differential Forms by Hubbard.

I've studied calc up to the multivariable level but haven't really done much Lin alg apart from the basics. Either way, according to the guide, I do have the prereqs for all the courses.

And as for size, the more rigorous courses, expectedly, have a smaller class size, which I do like.

I think I'm going to go with my option (2) since I really want to improve my math skills, but I just wanted to come here and check if anyone would advise going with option (1).

 

[Dr. Courtney]

My experience is that decisions regarding course difficulty need to be made with the input of knowledgeable parties who know both about the pros and cons of each course, student strengths and weaknesses, and the totality of ones workload for the term.

Otherwise, it's like asking if you want a more powerful car without knowing whether you have the money to pay for gas.

 

[radium]

You definitely should consult with your academic advisor before making a decision, but based on my own experience in theoretical physics, I would definitely take the more advanced physics course if you can only take one. Proof based math courses may not be as useful, even for most theorists since physicists are much usually less rigorous with math.

For example, in an algebraic topology course, you will likely spend a few weeks before you are able to gain the tools needed to prove that the first homotopy group of a ring is nontrivial. On the other hand, in a quantum mechanics course the professor may spend a lecture or two introducing Lie groups and almost right away show you that SU(2) is the double cover of SO(3) (which explains why a spin 1/2 state gains a minus sign under a rotation of 2\pi and also why you get a minus sign when you exchange two spin 1/2 particles which results in the Pauli exclusion principle) with the intuitive argument that two antipodal points on a sphere define a rotation axis and are in that sense the same point.

You generally will learn the math you need in physics courses (differential geometry in general relativity, Lie groups in quantum mechanics etc.) or on your own as you go, escpecially in research. This applies to most research areas in theoretical physics, even those that may first appear to be very mathematical.

 

[ISamson]

Hello physics forums. I'm a freshman at a top school for physics and have two general options for my track this semester.

(1) I can take the standard multivariable and linear algebra class that provides an introduction to proofs and an extremely rigorous first year mechanics course. The average workloads of the classes are roughly 10 hrs/wk and 14 hrs/wk, respectively.

(2) I can take the extremely rigorous multi/linalg class that is completely done with proofs and the intermediate level mechanics course sort of designed for physics majors. The average workloads of the classes are 17 hrs/wk and 9 hrs/wk, respectively.

Before arriving, I was inclined to pick (1), but now I feel that it is important for me to have good foundations in math with more abstract thinking, especially if I decide to go into theoretical physics in the future, which is why I'm considering pouring a lot of time into (2). It is said that the math class in (2) will crush you but mold you into a great mathematical thinker if you stay diligent.

Which should I pick?

Even though I am not even close to the time I will be entering university, I am aware that mathematics will really help you with physics, so you should pick more advanced mathematics before harder physics. Mathematics is constantly used in all areas of physics.