How helpful has the "algebra" been in understanding physics?

[Catria]

I feel as if my understanding of physics require increasingly rigorous mathematical derivations the more advanced the notions get... since I started even high school physics, I lost track of the number of instances where the bulb lighted up in my understanding of physics due to a rigorous mathematical derivation of equations and whatnot, and the density of instances increased as I climbed the ladder of physical notions.

But often, in class, the professors often skip over part of what is termed "the algebra", that is, the step-by-step mathematical derivations. When I get lost in my attempts to understand a given physics notion, I often ask about where to find the remainder of "the algebra" because, often, without a rigorous mathematical derivation, I do not understand the physics, or the conditions of applicability.

However, I understand that the reverse is also true in other people. So, for you, which one happened more often: that it has been "the math made you understand the physics" or "the physics made you understand the math"?

 

[Dr. Courtney]

It's a little of both for me. When I teach physics, I tend to leave the math used in developing the big ideas for students to read from the textbook and other reliable sources given as assigned reading.

I focus class time on doing all the algebra when solving example problems and reviewing homework problems at the board. I recognize that most students need some review of the algebra and practicing algebra in cases where you have multiple symbols, and one of them at most is called x.

 

[PWiz]

"the math made you understand the physics" or "the physics made you understand the math"?

It's always been the first case for me. All of theoretical physics simplifies incredibly if you know the underlying mathematical concepts IMO.

 

[Catria]

It's always been the first case for me. All of theoretical physics simplifies incredibly if you know the underlying mathematical concepts IMO.

My grad-level instructors claimed, in office hours, that I was too hung up on the mathematical details of the material; however, by the same token, they understood why I wanted to pursue theory on some level.

Perhaps that's an indication of maybe, maybe I could earn a PhD in math (applied math most likely, but math nonetheless; I do not think pure math is for me) if I can pull myself out of the hole that caused me to drop out of Minnesota after a semester-long tenure as a physics PhD student there...

 

[S.G. Janssens]

maybe I could earn a PhD in math

Do it!

applied math most likely, but math nonetheless; I do not think pure math is for me

Dr. Courtney once wrote about the "False Dichotomy: Theorist or Experimentalist?". In turn, I think that the dichotomy between pure and applied mathematics is often presented as being much stronger than it actually is.

 

[Catria]

There has been a few moments of each of the following in my life: "the math made you understand the physics" and "the physics made you understand the math". Admittedly many people that can do physics at a high level will probably have had a combination of these, hence why I ask about how often each type happens.

 

[BobG]

But often, in class, the professors often skip over part of what is termed "the algebra", that is, the step-by-step mathematical derivations. When I get lost in my attempts to understand a given physics notion, I often ask about where to find the remainder of "the algebra" because, often, without a rigorous mathematical derivation, I do not understand the physics, or the conditions of applicability.

Perhaps that's because some of the equations required calculus to derive.

You said this was high school physics? I think the course pretty much has to be kept at the "algebra" level and there will necessarily be some equations that are just tossed out there to be used without really explaining how they got from some reasonably simple principle (moment of inertia, for example) to the equations used in the real world (different equations to find the moment of inertia for different shape objects, for example).

(Do they even teach rotational motion in high school physics? I would think most of the concepts are similar enough to linear motion that they could, but I'm not sure that they do.)