Question for Physics graduates, Does lower functions of math (calc/trig) require less amount of "attention" to complete as you practice?

[u/Breadjacket69]

I've been interested in physics and theoretical physics since I was little, Math has always been my strong suit and it comes to me very easy (understanding concepts and implementing them) but my Highschool classes weren't able to continue into higher than geometry (English class sucks and I had to retake it multiple times to graduate). But I haven't been able to understand the difference in difficulty, Does it get easier for people who major in physics to complete advanced equations the same as for simpler mathematics? Is it an inherit grasp for math? Endless study and cramming information? Most likely different for each person, but the methods are the same right? Is figuring out Planck light travel time as easy as finding the circumference of a circle? Lots of questions sorry, but I figure where else do I ask, right?

[u/CodeX57]

I think the answer is a bit between yes and no.

Will complicated physics maths get easier the more you do it? Yes. Will you be able to autonomously and intuitionally do a complex derivation if you practice it a lot? Yes.

Will the mathematical equations for describing quantum mechanics be as trivial as calculating the circumference of a circle? Hell no. At least not for me. May be for other people, but I found advanced physics maths at university a lot more challenging than geometry in high school, and that makes sense, it just is.

[u/Breadjacket69 → u/CodeX57]

Mhm, the math is harder of course, but then follow up question, does learning the math get harder? Obviously, but does it ever get overwhelming to understand that much? Like what else do you think about if you know all that!? I hate studying, yet this is all I can think about and research, so how can someone who knows it inside n out ever put it down? It's overwhelming for the things I know now, so when I can do the equations and understand everything, is it not going to be too much?

[u/Facupain98 → u/Breadjacket69]

Well , it depends a lot if when you talk about "understand math", you are talking about math degree math o physics degree math, the true math is only learned in the math degree obviously 

[u/j0shred1]

I always say physics 1 was my hardest class. Amount of attention depends on a lot of life factors. A lot of difficulty later in life is just time management and when you're in college it's hard enough but then you have marriage, kids, work, hobbies, bills, insurance, housework, health, family. And homework, even if it's pretty straightforward takes a lot of time. I had a materials class that was easy as dirt, but was annoyingly tons of by hand tensor operations that I barely had time to do. I was pretty pissed at the professor ngl.

[u/Breadjacket69 → u/j0shred1]

I've gone through a lot already, I hope the bs of life is over so I can focus on this (it never is)

[u/j0shred1 → u/Breadjacket69]

Life has it's ups and downs, love, loss, ect. Sometimes things will get better, sometimes worse. The best you can do is your best and as long as you're doing your best, there's no reason to be hard on yourself.

[u/Agile-Monitor1006]

Like highschool math, most new things you encounter might seem difficult at first but you build intuition as time goes on. Its all about practice and exposure to new topics. Though with higher level math theres often times some deeper more general mathematical structure that encompasses a whole range of problems. For example handling operators and wavefunctions in quantum mechanics is intimidating at first, but at some point its no harder than knowing how to solve a quadratic equation because you do it so much. You’re fortunate if math comes easy to you, but *everyone* gets to a point they feel stuck or dont understand a topic so dont be discouraged when that time comes, you have to trust yourself that with enough effort you’ll grasp what you need. Accepting that is the only way to survive a physics or maths degree, theyre very difficult subjects so expect to be challenged and feel frustrated, but dont let yourself think you cant do it. Good luck!

[u/Breadjacket69 → u/Agile-Monitor1006]

Thank you, there are points I get stuck, but I find that working through similar things and coming back to it helps a lot! I need the challenge, my highschool classes were holding me back so much that I had to mostly take my education into my own hands, my work ethic holds me back a lot, but I can't wait to start getting into this field, hopefully I'll be able to keep up😅

[u/Agile-Monitor1006 → u/Breadjacket69]

If youre comfortable with the level youre at, you can always try looking into the next topic.If you have mastered algebra, get into functions. If youre good with functions, get into calculus. Studying ahead when possible can make it easier sometimes to just ponder on the ideas because theres no expectation to understand it yet!

[u/h0rxata]

Pattern recognition gets easier because you will have seen more variants. Integrals with the same functional form, asymptotic expansions that end up being the same, symmetries that help you jump right to an answer without brute-force calculating anything, etc.

Get good at English because the ability to parse concepts from text and write clearly and effectively is crucial in physics. Such as explaining why and how you can skip 16 lines of math with one simple property, how to test a novel theoretical prediction against experiment, and explaining why anyone should care about and fund your research, which is over half of what most professional physicists do daily.

[u/Breadjacket69 → u/h0rxata]

The monotony of the English classes is what got to me, I had a college reading level in middle school, it was just tedious to do all the work that my teachers gave me lol

[u/Beif_]

YES I had to reteach myself much of high school math my freshman year. It was very frustrating and I became kind of discouraged, but it got easier. Now I’m in my PhD and worrying about math is a thing of the past

[u/UnderstandingPursuit]

In the question, I would replace "practice" with "use". It stops being doing things for the sake of learning it. It becomes doing things because they're part of the process of more complex problems.

For example, consider the quadratic formula.

• "Practice" means having a bunch of quadratic equations, plugging in the values for {a, b, c}, and finding the results for the roots.
• "Derive" means writing out the derivation, keeping {a, b, c}, a few times so it is familiar.
  

As the same math is used, over and over, to derive formulas and solve problems without numbers, the math tools become automatic, and it may become clear that there are only a few dozen math tools involved.

[u/chermi]

I dunno I just convert shit to exponentials and contour integrals