Quick questions about studying math and physics?

[Ishida52134]

Just curious about how people usually self study these subjects.
Is it the most efficient to read through the chapters, and write down theorems, definitions, and take notes of important parts and work out all the proofs and examples? And then make sure you can re-prove everything after finishing a chapter? Like for example, studying analysis, topology, etc. And the same with physics.
Or is it better to just do all the problems and move on?

And how long does it usually take one to finish a textbook? What are the advantages to taking a class than self-studying assuming one would put in as much work as needed if one had to take a final exam?

Thanks.

 

[mfb]

Is it the most efficient to read through the chapters, and write down theorems, definitions, and take notes of important parts and work out all the proofs and examples? And then make sure you can re-prove everything after finishing a chapter? Like for example, studying analysis, topology, etc. And the same with physics.
Or is it better to just do all the problems and move on?

I would try to combine both, probably with more focus on problems in physics and advanced lectures in both.

And how long does it usually take one to finish a textbook?

Depends on too many parameters to give any estimate.

What are the advantages to taking a class than self-studying assuming one would put in as much work as needed if one had to take a final exam?

You see things not in the textbooks, you can ask questions and you get feedback on your homework problems.

 

[Ishida52134]

Just a few more questions

What would be the most efficient method of studying considering time and being able to understand it 100%?
Like, I know it's good to use multiple books too, and the optimal method would be to work out everything, but it seems too time-consuming to be able to learn enough and go into the research field and publishing faster.

And where exactly does talent play in the process? Is it just about understanding things quicker and applying it more efficiently? I find that I can do math and physics with relative ease; are there people with varying degrees of talent and how pertinent is it to have the "most" talent in terms of being one the top in math and physics research career?

thanks.

 

[mfb]

What would be the most efficient method of studying considering time and being able to understand it 100%?

Is that possible?
Helping other with their problems is certainly a method to improve the understanding.

And where exactly does talent play in the process? Is it just about understanding things quicker and applying it more efficiently? I find that I can do math and physics with relative ease; are there people with varying degrees of talent and how pertinent is it to have the "most" talent in terms of being one the top in math and physics research career?

That question will get 5 different answers within 4 replies, I don't want to add yet another opinion about that.

 

[jtbell]

And how long does it usually take one to finish a textbook?

I have never taken or taught a class that actually used an entire textbook. Textbooks generally cover a set of core topics that are considered essential for whatever field they cover, plus a range of secondary topics that exceeds what can actually be covered in any real course.

Every instructor has his/her own set of favorite secondary topics. Textbook publishers don't want to lose any sales by omitting someone's pet topic(s).

 

[Sentin3l]

Just curious about how people usually self study these subjects.
Is it the most efficient to read through the chapters, and write down theorems, definitions, and take notes of important parts and work out all the proofs and examples? And then make sure you can re-prove everything after finishing a chapter? Like for example, studying analysis, topology, etc. And the same with physics.

I like to read sections, and then re-write them in my own words, taking care to place importance on the concepts that require it and clearly show derivations and important theorems. I take notes with the (semi-paranoid) theme that if I wake up with amnesia tomorrow, I should be able to learn from just my notes. I do this with math and physics; the only downside is that it takes some time.

Or is it better to just do all the problems and move on?

After I'm done with my notes, I attempt the problems, usually they are all fairly simple as the note taking process really forces you to understand the chapter well.

And how long does it usually take one to finish a textbook? What are the advantages to taking a class than self-studying assuming one would put in as much work as needed if one had to take a final exam?

Thanks.

I usually work through about 2-3 textbooks at a time, assuming you're focusing on one at a time and spend an hour a day on it, I would say no more than two months (and probably quicker). But there are many other factors in this and by no means is that an absolute estimate.

One advantages to class is that you have a clear indication of how well you're understanding the material. In addition, having a good teacher explain a difficult concept can really make the difference.

 

[Ishida52134]

An hour a day for 2 months would really be adequate? Like over the summer, I was working with the book, "Vector Calculus, Linear Algebra, and Differential Forms," by Hubbard, and it was split into at least 60 different sections. It was pretty impossible to cover a whole section and rewrite everything and do all the problems in even 3 hours.

By the way, just one more question, how important is like physics or math competitions to physics or math careers in research? I only got interested in these subjects very recently, so although they were my best subjects in school and I understood them easily, I never really practiced for olympiads or anything. And the only thing I did was math team in competitions like ARML.

What do you guys think about my natural talent question?

thanks.

 

[Astrum]

An hour a day for 2 months would really be adequate? Like over the summer, I was working with the book, "Vector Calculus, Linear Algebra, and Differential Forms," by Hubbard, and it was split into at least 60 different sections. It was pretty impossible to cover a whole section and rewrite everything and do all the problems in even 3 hours.

I didn't care much for Hubbard, he's very very wordy, and I don't think he explains things all that well.

Don't focus so much on time restraints. If you're constantly thinking about time, you'll end up rushing through the text. Give yourself the time YOU feel you need. We can't tell you how fast you should be working through any given text. Learning is a very individual thing, one persons method is not guaranteed to work for anybody else.

Try to enjoy what you're learning.

 

[Ishida52134]

Thanks. Still, unless it's a relatively small book, I don't think it'd be possible to finish in that time period.
What do you think of the other questions?
"1)By the way, just one more question, how important is like physics or math competitions to physics or math careers in research? I only got interested in these subjects very recently, so although they were my best subjects in school and I understood them easily, I never really practiced for olympiads or anything. And the only thing I did was math team in competitions like ARML.
2) And where exactly does talent play in the process? Is it just about understanding things quicker and applying it more efficiently? Like getting through a textbook quicker? I find that I can do math and physics with relative ease; are there people with varying degrees of talent and how pertinent is it to have the "most" talent in terms of being one of the top in math and physics research career?"