<p>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? </p>
<p>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?</p>
<p>Thanks.</p>
<p>I haven’t taken Physics yet, but for Math it is best for me to find sample problems and attempt to solve them, and then compare answers. It works every time. Personally, I never read through textbooks when it comes to Math; I find the examples, find problems and recognize what my answer will most likely look like. When it is not a simple formula to learn, instead of finding patterns I try to find the logic behind it. “What is this solving, anyway??”</p>
<p>Taking a class can provide more motivation to do things, instead of putting them off. I know I could never self-study Math without a direct need for it (good GPA, for a job, etc.) but I would procrastinate much more if I did self-study. Advantages of self-study? Work at your own pace and when the time is convenient.</p>
<p>Thanks just two more things
1)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 of the top in math and physics research career?</p>
<p>2) 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 regarding competitions was math team and contests like ARML.</p>
<p>From what I understand, official competitions are important for admission purposes and personal satisfaction.</p>
<p>“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?”</p>
<p>If you can do the problems or problems that involve proofs, and do them correctly, then you have learned what had to be learned. Physics problems give wrong answers when done wrong, mathematical proofs get you stuck or lead to conclusions that make no sense.</p>
<p>“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?”</p>
<p>Long. Courses are sped up from what reading an entire course book would take. Studying is especially slow in math, because there are so many definitions.</p>
<p>You should try to do both. The majority of studying is self-studying, you read what had to be read and go to the lecture to listen about the same thing explained by a professor. Then you might go back and revise what you didn’t get. The two reinforce (or they should reinforce) each other, although in exact sciences self-studying is totally possible as well (because all it requires is understanding the definitions and knowing the rules to apply them, sometimes the book explanation is much clearer than the sped up and abstracted explanation that a professor gives).</p>
<p>thanks. just two more questions:
1)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 of the top in math and physics research career?</p>
<p>2) 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 regarding competitions was math team and contests like ARML.</p>