Math and Physics (A call for guidance)

[guguma]

Hello and good days,

This is the first time I am posting in Physics Forums, and I need guidance about a depressing matter that has been haunting me for years.

I am a physics major and I am about to go to graduate school, so far I managed to do pretty well on my career but I am experiencing a major problem. It is concerning mathematics and the use of mathematics in physics. Simply put I am terrible at math, or I see myself terrible but I am totally lost and do not know what to do about it. No matter what I have tried I could not fix this situation.

We both show and solve everything using mathematics, so perfecting mathematics is extremely important but I cannot do it well. I find myself very good at understanding general concepts and ideas and seeing the big puzzle and relations, but this does not mean anything if I cannot work my way out through even a simple problem.

Understanding a general concept is good but as the applications get more complex and as problems get more complex I simply get lost, especially when geometric situations are involved. I cannot see what a mathematical expression tels me about physical situation at hand and when I miss it, it is gone forever.

Sometimes it is a simple line integration, sometimes it is a differential equation involving dirac delta functions, sometimes it is an algebraic expression... I get lost easily, all those summations, transformations, gradients, curls, divergences, fields, waves, infinitesimal sections, coordinates, integrations involving these... when I come across them in a certain simple condition I am fine, but when the situation gets more complex I get totally lost.

Let me give you an example, there is a particular problem asking the energy stored in a certain length "l". It involves a volume integration of the square of the magnetic field and the surface integration of the cross product of the vector field and the magnetic field. It should be easy but I get stuck instantly Which Volume? Which Surface? is associated with each quantity...

As you can see I really fail at associating the physical condition at hand with the mathematical tool at hand. So I need to know what my problem is, and how to fix it.

So if anyone of you experienced trouble with mathematics and physics like this and managed to fix it or can guess what my problem is I would really appreciate your help. Maybe my books fail, maybe I need to practice, maybe I have to do some intensive study concentrating on specific topics, maybe I have to start anew from someplace...

As I said I will be going to a good grad school soon, and I prefer to spend my time doing my research and I do not want to get frustrated at every other step and coursework. To be able to enjoy my work on physics, I have to solve this problem.

Thanks in advance

 

[budala]

i do understand that students can have problems but i am curious have did you get such good marks to be accepted to a very good grad school if you have such a big problem with math, just curious, thanks

 

[mgb_phys]

I do experimental physics - I haven't needed any maths beyond high school calculus.
My view ( I can't remember who originally said this ) = don't do the maths until you understand the physics in a process and once you understand the physics the maths is just book-keeping.

ps. This doesn't work for quantum mechanics!

College over-emphasises maths, both because you need it for some areas, but mostly because it is easy to teach and set exams for.

 

[mgiddy911]

problems like the one you listed above are oin to require some thought (I'm in E&M currently)
they are the type you can do in your head and you shouldn't be expected to be able to spit out the answer right away.
Draw out a picture first, that helps me when trying to think of what surface to use or which volume to integrate over, this also helps me visualize what the limits of integration should be.

doing problems is probably the only way to feel comfortable with the math as if you never use the math you won't know how to when the time comes.

 

[guguma]

i do understand that students can have problems but i am curious have did you get such good marks to be accepted to a very good grad school if you have such a big problem with math, just curious, thanks

I never said that I was retarded did I?

Maybe I should have expressed myself in a less obscure manner. I am simply not as fluent as I want to be. When I come across a problem I can get stuck easily, and I have to look back so often that it makes me feel uncomfortable.

Getting into a good grad school is easy. You study for your exams, you take the GRE and "poof" you are in a good grad school. Undergraduate courses and the GRE does not ask for a magnificent mathematical knowledge anyway and all courses are separate from each other and you have a great deal of time to study for each of them.

It is not that I cannot do math, it is that I am not organized. Let me give you an example, in primary school if you have learned to factor out an algebraic expression and learned it good and if you are given a long division involving functions you just see that the two expressions have a common factor and go on solving it right? Now in my case as the techniques and methods I have learned expanded, I started not SEEING things, and not combining what I have learned with the problem at hand, it became harder and harder...

I assume it is due to a lack of practice, I did not practice much calculus and physics and differential equations and linear algebra in earlier undergrad years because everything was easy. But as the context of physics we were doing got deeper and deeper, I see that I should have practiced them a great deal because I had to look back so often and started not to see things on the spot.

Bu this is just my assumption, this may not be the case, maybe I am missing something out. That is why I asked for help.

I am also quite offended by your response. I am asking for guidance here and as I said it could be in any manner of help (book suggestion, practice suggestions etc.). Being curious about how I ended up in a grad school and asking about it in an anonymous forum neither adds anything significant to your persona nor helps about my problem.

I am still open to suggestions if you appeased your curiosity.

Thanks

 

[CPL.Luke]

the best thing to do is just do the math slowly, personally I have problems wit dropping terms and the like, the only solution is to really think each step through. In the case of E&M I believe the problem is that it often becomes unclear what are your (r)s and your (r')s are, if you follow the derivations this becomes a bit clearer, but it takes time

 

[budala]

I never said that I was retarded did I?

Maybe I should have expressed myself in a less obscure manner. I am simply not as fluent as I want to be. When I come across a problem I can get stuck easily, and I have to look back so often that it makes me feel uncomfortable.

Getting into a good grad school is easy. You study for your exams, you take the GRE and "poof" you are in a good grad school. Undergraduate courses and the GRE does not ask for a magnificent mathematical knowledge anyway and all courses are separate from each other and you have a great deal of time to study for each of them.

It is not that I cannot do math, it is that I am not organized. Let me give you an example, in primary school if you have learned to factor out an algebraic expression and learned it good and if you are given a long division involving functions you just see that the two expressions have a common factor and go on solving it right? Now in my case as the techniques and methods I have learned expanded, I started not SEEING things, and not combining what I have learned with the problem at hand, it became harder and harder...

I assume it is due to a lack of practice, I did not practice much calculus and physics and differential equations and linear algebra in earlier undergrad years because everything was easy. But as the context of physics we were doing got deeper and deeper, I see that I should have practiced them a great deal because I had to look back so often and started not to see things on the spot.

Bu this is just my assumption, this may not be the case, maybe I am missing something out. That is why I asked for help.

I am also quite offended by your response. I am asking for guidance here and as I said it could be in any manner of help (book suggestion, practice suggestions etc.). Being curious about how I ended up in a grad school and asking about it in an anonymous forum neither adds anything significant to your persona nor helps about my problem.

I am still open to suggestions if you appeased your curiosity.

Thanks

I do apologize if you took it in such offensive way. I never, never did think that you are retarded, far, far from it. I have to say; please cool down and grow much thicker skin, IMO.
I did think that math is much more important to get good marks in physics and that's why I ask how did you manage to get into a good grad school . Yes, I am still curious as to how you say that it is sooooooo easy to get into grad school although I read it here from some other students who said how they have a very tough time to get into grad school.
I wish you the best in your studies but your reply really expressed to me what kind person you secretly are .

 

[CaptainQuaser]

I am an experimental physicist too...
I like Maple, or Matlab. They do all the math I need, if I need something more complicated I usually find I theoretical physicist.

 

[robphy]

Some thoughts from my own experience...

One of the best ways to learn something is to teach it. Take advantage of opportunities to teach or tutor.

As a TA in grad school, I learned a lot by teaching and by writing detailed solutions for students.

It's helpful to disentangle the main physical concepts from the applications, as well as to disentangle the physics from the mathematics. In a derivation, it's good to indicate WHY the next step follows from the previous one... is it a definition? mathematical substitution? invocation of new physics? You may be able to uncover the big-picture storyline of the derivation and then take note of the possibly more-tricky steps.

In the course of teaching and writing detailed solutions, I had many "aha" moments..."so, that's what was going on [back in my college physics and math courses]!". (Arguably, the solutions were better for me rather than for the student [who, unfortunately, often merely skims what I wrote].)

 

[xaos]

try this: Calculus --> Vector Analysis --> Multi-Variable Calculus -->Differential Equations -->Linear Algebra.

this should be enough to get you up to graduate level mathematics in about a year.