Is Solving Physics Problems the Only Way to Understand the Subject?

[ice109]

the end. I'm sick and tired of chasing down all the leaps of mathematical logic in all my physics books. it's impossible. you know why everyone screams that you need to do problems to know physics? because there's no other way.

the way i see it there exist two ways to know how a construction works: knowing the details of its innards or observing it in tons of scenarios. it's deductive versus inductive reasoning. in my opinion the former is much more efficient but apparently the physicists see it otherwise; that i should learn how to do physics by osmosis.

and you know that's fine, it's their prerogative. maybe for experimentalists their method of choice is even comparably as efficient/beneficial but i question how in the hell theorists learn to do anything except solve the problems they've already been taught to solve.

summary: math >> physics. note the strict inequality.

 

[Jimmy Snyder]

the end. I'm sick and tired of chasing down all the leaps of mathematical logic in all my physics books. it's impossible. you know why everyone screams that you need to do problems to know physics? because there's no other way.

The margins of my physics books are full of notes to myself on how I filled the gaps between the equations. I never needed to do that in my math books. Unlike you, I enjoy tracking them down. Now I'm reading "QFT a Tourist Guide for Mathematicians" by Folland. Perhaps you would like it.

 

[ice109]

The margins of my physics books are full of notes to myself on how I filled the gaps between the equations. I never needed to do that in my math books. Unlike you, I enjoy tracking them down. Now I'm reading "QFT a Tourist Guide for Mathematicians" by Folland. Perhaps you would like it.

i do enjoy it, but like i said it's impossible. there are huge amounts of work, for example, between almost every step of the derivation of the euler-lagrange equations. i can't reasonably fill that stuff in and still have time to actually do the physics.

 

[Jimmy Snyder]

i do enjoy it, but like i said it's impossible. there are huge amounts of work, for example, between almost every step of the derivation of the euler-lagrange equations. i can't reasonably fill that stuff in and still have time to actually do the physics.

That's pure math. You can find a derivation in any book on Calculus of Variations.

 

[ice109]

That's pure math. You can find a derivation in any book on Calculus of Variations.

does calling it pure math make it less of a gap? and you can't just jump into the middle of a calculus of variations book, which is where the derivation will be, and not be puzzled by seeming gaps in that argument. if it were that easy i wouldn't be complaining. in fact it's exactly my point that understanding the euler lagrange equations requires an understanding of calculus of variations which itself requires an understanding of calculus which itself requires an understanding of real analysis. hence I'm about 3 book away from really knowing what the hell is going on when I'm finding extremals of the lagrangian.

 

[Ivan Seeking]

the end. I'm sick and tired of chasing down all the leaps of mathematical logic in all my physics books. it's impossible. you know why everyone screams that you need to do problems to know physics? because there's no other way.

the way i see it there exist two ways to know how a construction works: knowing the details of its innards or observing it in tons of scenarios. it's deductive versus inductive reasoning. in my opinion the former is much more efficient but apparently the physicists see it otherwise; that i should learn how to do physics by osmosis.

and you know that's fine, it's their prerogative. maybe for experimentalists their method of choice is even comparably as efficient/beneficial but i question how in the hell theorists learn to do anything except solve the problems they've already been taught to solve.

summary: math >> physics. note the strict inequality.

I think your frustration results in part from the fact that the people who first figured this stuff out were brilliant. It isn't easy to try to walk in their footsteps, but that is partly what you are asked to do.

When I was going to college, as a rule, I spent every weeknight doing math and physics till the wee hours of the morning. If I was lucky, I had one or two full days on the weekend to do the homework for my other three classes.

 

[Jimmy Snyder]

does calling it pure math make it less of a gap? and you can't just jump into the middle of a calculus of variations book, which is where the derivation will be, and not be puzzled by seeming gaps in that argument. if it were that easy i wouldn't be complaining. in fact it's exactly my point that understanding the euler lagrange equations requires an understanding of calculus of variations which itself requires an understanding of calculus which itself requires an understanding of real analysis. hence I'm about 3 book away from really knowing what the hell is going on when I'm finding extremals of the lagrangian.

Its on page 8 of "An Introduction to The Calculus of Variations" by Charles Fox. It requires nothing more than calculus. It uses integration by parts. I'm confused by your 'understanding of calculus which itself requires an understanding of real analysis." I studied calculus first and then real analysis. But if you are studying physics without first learning calculus, then I can see why you are so frustrated. There is a book called "College Physics" by Sears and Zemansky which does not require calculus.

 

[Jimmy Snyder]

As I said, when I read a physics book, I write notes in the margins on how I filled the gaps between the equations. What I forgot to mention is that I can't understand physics books either on first reading. I read them over and over. However, from the second reading on, I am no longer held up by the math since the notes are there to help me. I often do have to look up derivations in math books. It's work.

 

[Math Jeans]

the end. I'm sick and tired of chasing down all the leaps of mathematical logic in all my physics books. it's impossible. you know why everyone screams that you need to do problems to know physics? because there's no other way.

the way i see it there exist two ways to know how a construction works: knowing the details of its innards or observing it in tons of scenarios. it's deductive versus inductive reasoning. in my opinion the former is much more efficient but apparently the physicists see it otherwise; that i should learn how to do physics by osmosis.

and you know that's fine, it's their prerogative. maybe for experimentalists their method of choice is even comparably as efficient/beneficial but i question how in the hell theorists learn to do anything except solve the problems they've already been taught to solve.

summary: math >> physics. note the strict inequality.

It honestly depends on what level you're at. Where are you in your studies of the subjects?

 

[rootX]

I usually read 4-5 times over my whole semester. First reading is always frustrating and sometimes books are bit advanced (In our case, we usually get books that aren't for our level because it is pretty hard to find good material).

I read first time. And then, do all sample questions.
Second time, and then do all exercise questions, and refer back to topics.
And then do homework assignments while referring to the material again (3rd time)
And then do assignments near exams and skim over my material (4th time)
And then do more questions for exam and again refer to my book material.

I always prefer
do questions --> refer back to the material

if I keep on reading thing, it just goes out of my mind as soon as I finish.

 

[ice109]

I think your frustration results in part from the fact that the people who first figured this stuff out were brilliant. It isn't easy to try to walk in their footsteps, but that is partly what you are asked to do.

When I was going to college, as a rule, I spent every weeknight doing math and physics till the wee hours of the morning. If I was lucky, I had one or two full days on the weekend to do the homework for my other three classes.

so then all practicing physicists are brilliant? I'm doubtful.

Its on page 8 of "An Introduction to The Calculus of Variations" by Charles Fox. It requires nothing more than calculus. It uses integration by parts. I'm confused by your 'understanding of calculus which itself requires an understanding of real analysis." I studied calculus first and then real analysis. But if you are studying physics without first learning calculus, then I can see why you are so frustrated. There is a book called "College Physics" by Sears and Zemansky which does not require calculus.

reading as we "speak"

and i don't know of many introductory physics classes that cover the lagrangian formalism. and what i meant by my comment about calculus is that even there there exist leaps of logic which require investigation.

As I said, when I read a physics book, I write notes in the margins on how I filled the gaps between the equations. What I forgot to mention is that I can't understand physics books either on first reading. I read them over and over. However, from the second reading on, I am no longer held up by the math since the notes are there to help me. I often do have to look up derivations in math books. It's work.

it's stupid is what it is.

It honestly depends on what level you're at. Where are you in your studies of the subjects?

i'm a senior

I usually read 4-5 times over my whole semester. First reading is always frustrating and sometimes books are bit advanced (In our case, we usually get books that aren't for our level because it is pretty hard to find good material).

I read first time. And then, do all sample questions.
Second time, and then do all exercise questions, and refer back to topics.
And then do homework assignments while referring to the material again (3rd time)
And then do assignments near exams and skim over my material (4th time)
And then do more questions for exam and again refer to my book material.

I always prefer
do questions --> refer back to the material

if I keep on reading thing, it just goes out of my mind as soon as I finish.

that's an absurd amount of work. not that it isn't laudable but it's simply impractical.

 

[Hurkyl]

I think your frustration results in part from the fact that the people who first figured this stuff out were brilliant. It isn't easy to try to walk in their footsteps, but that is partly what you are asked to do.

But how much of that is really necessary, or even worthwhile? If physicists and mathematicians have spent decades distilling and clarifying the key ideas, then wouldn't it be better to follow that path, rather than trying to repeat the difficult and treacherous journey through unclear territory the originators underwent?

 

[Oerg]

But how much of that is really necessary, or even worthwhile? If physicists and mathematicians have spent decades distilling and clarifying the key ideas, then wouldn't it be better to follow that path, rather than trying to repeat the difficult and treacherous journey through unclear territory the originators underwent?

Well said, sometimes when I see an interesting concept, it is easy for me to go through a text or ask from my tutors the mathematical proof or physical insight behind it but I try to give myself a little challenge and see how is it that something like that got to be. Of course it isn't easy, given that the physicists that came up with it have the time while I still have a lot of coursework to cover.

 

[ice109]

But how much of that is really necessary, or even worthwhile? If physicists and mathematicians have spent decades distilling and clarifying the key ideas, then wouldn't it be better to follow that path, rather than trying to repeat the difficult and treacherous journey through unclear territory the originators underwent?

none of it. i swear i don't understand why I've learned anything that i have i.e. what is the pedagogical purpose? most of the time the historical perspective ( the only worthwhile part of any of it! ) is not discussed and hence all I'm learning is arcane methods. no discussion of how these results were arrived at, which would actually teach me how to solve problems and not just do calculations, most often no real direct application. is it for hazing purposes? is it to teach me all the stupid little math tricks?

i'm at the end of my second year in this program and i haven't learned anything useful from my physics classes and I've been frustrated by the poor presentation the entire way through. the ill-phrased problems, the apathetic professors, the odd peers :yuck:

i really think it's not the physics that scares people off, it's all the other stuff. contrary to what people say this stuff isn't difficult; senior level quantum and the scariest (read:sarcasm) thing I've seen is a DE soluble by a series solution ( Fourier and otherwise ) but the presentation of all of it is horrible, i mean really how many indices upper/lower can a function ( I'm looking at you soln to hydrogen atom problem ) have before you just give up and refine the notation?

never have i ever been on this much of a run around in a math class and I've taken just as many of those as i have physics classes.

i really think it speaks to the state of the discipline whether it can be exposited clearly. physics is just magic with a tiny tiny bit of reasoning thrown in.

sorry /rant

 

[waht]

Einstein didn't complain about discovering E=mc2, he only complained it could be used to make an atomic bomb.

 

[Ben Niehoff]

and i don't know of many introductory physics classes that cover the lagrangian formalism. and what i meant by my comment about calculus is that even there there exist leaps of logic which require investigation.

Goldstein (a graduate-level text) has an excellent discussion of the Lagrangian formalism, with a simple, easy-to-follow proof of its equivalence to Newtonian dynamics, and also with a simple, explicit derivation of the Euler-Lagrange equations.

Problems in every book are often worded with imprecise language (although sometimes, the terms are precise, but archaic, and the text does not explain them). Part of the task of physics is to translate such language into precise mathematical form. What exactly do we mean when some quantity is small, or some material is perfectly conducting, etc.? It's necessary to think about and learn these things, though I agree they could probably be taught better.

 

[phreak]

V.I. Arnold's 'Mathematical Methods of Classical Mechanics' also provides a rigorous treatment of Lagrangian and Hamiltonian formalism. It is quite true that elementary (read: undergraduate) physics texts often lack mathematical rigor, but once you get into the higher texts, you'll see a proper emergence of pure mathematics.

 

[Kurdt]

I think the self-discovery is fun. To follow derivations gives me a fresh insight into what I'm reading about and often a deeper understanding. Like jimmy I keep notes in files or notebooks, filling in the gaps in some textbook derivations or referencing other books where I can find them. Its important to have a system because often you forget when you come back a few months or years later.