Effective Problem Solving: Balancing Necessary Literature with Time Management

[trees and plants]

Hello. When i have some problems i want to solve should i read only the needed literature, topics, things to the problem i am trying to answer? Which should be these topics and papers and textbooks i should read to help me answer what i want to answer?Is there any advice on this you could give me?If you want give me some examples.Should i read only what is needed for the problems to be answered or other things too?How will i know what to read to help me? Thank you.

 

[gleem]

I think that we can effectively address your question only if you tell us the subject of the problems that you are interested in so we do not use examples with which you are not familiar.

 

[trees and plants]

I think that we can effectively address your question only if you tell us the subject of the problems that you are interested in so we do not use examples with which you are not familiar.

General relativity, differentiable manifolds.

 

[gleem]

Considering the advanced nature of your interests, it would seem that you should by now have determined the answer to your question. What is your background?

 

[trees and plants]

Considering the advanced nature of your interests, it would seem that you should by now have determined the answer to your question. What is your background?

I am an undergraduate student at a math department at university but i read on my free time other math and physics. I want to say that until now i tend to get stuck on math problems not all of them but perhaps also elementary ones. But i try to read works from researchers in math and physics that i find from arxiv or archive or from lectures and other works and papers from other sources on the web.

 

[Vanadium 50]

1) Perseverance - walking away from a problem won't help. You've walked away from the "prove all numbers are either even or odd" proof twice now. Apart from being deeply disrespectful of those people who were trying to help you, how are you ever going to get better if you don't finish what you start?

2) Humility and self-awareness - your first thread asked for fifty - fifty - problems that resisted attack by the finest minds so you could solve them. Solving even one would be a major accomplishment, but you wanted fifty. You are not that smart. Nobody is.

If you ignore advive (and you've got a lot) from people who know more than you because you think you know more than them, you won't get very far.

The good news is that these are choices. You can improve. But only if you want to.

 

[trees and plants]

1) Perseverance - walking away from a problem won't help. You've walked away from the "prove all numbers are either or odd" proof twice now. Apart from being deeply disrespectful of those people who were trying to help you, how are you ever going to get better if you don't finish what you start?

2) Humility and self-awareness - your first thread asked for fifty - fifty - problems that resisted attack by the finest minds so you could solve them. Solving even one would be a major accomplishment, but you wanted fifty. You are not that smart. Nobody is.

If you ignore advive (and you've got a lot) from people who know more than you because you think you know more than them, you won't get very far.

The good news is that these are choices. You can improve. But only if you want to.

How will i solve that problem? I got stuck, i do not know how.I want to improve that is my choice. How will that happen? Thank you.

 

[Vanadium 50]

How will i solve that problem? I got stuck

Do you think walking away is the answer whenever you get stuck?
Really?

 

[trees and plants]

Do you think walking away is the answer whenever you get stuck?
Really?

See if you want https://www.physicsforums.com/threads/classification-of-mathematical-objects.995992/page-2

 

[fresh_42]

I have the impression that "walking away" is used differently here. You should not walk away from studying manifolds, general relativity and differential geometry prior to any creative activities in these fields. But once in creative process, walking away (for hours or a day) can help to find new perspectives. But before you get into such a process, you have to learn what is written in the textbooks. "walking away if stuck" means: for a short while, not for long.

 

[onatirec]

General problem solving advice is to break down a problem into smaller pieces and deal with them individually.

It can be tricky to know where exactly the difficulty lies in a problem, where the gaps in your understanding are. Once you have a small piece or detail you are having trouble with (i.e. a clearly defined problem), a forum like this can be very helpful... until then, it's not really clear what you expect...

Personally, I struggled more with GR than any other subject. When I took it as an undergrad, I referenced no less than 20 GR books trying to wrap my head around certain concepts, plus a number of books on differential geometry, tensors, etc.

So yes, you only need to read the things you need to read to understand something. Unfortunately, you probably aren't going to know where those things are written until you read them.

 

[Keith_McClary]

https://www.physicsforums.com/threads/good-problem-solving-book.420113/
https://www.physicsforums.com/threads/books-similar-to-art-of-problem-solving.997149/
https://www.google.com/search?channel=fs&client=ubuntu&q=site:physicsforums.com+"problem+solving"

 

[Frabjous]

When i have some problems i want to solve should i read only the needed literature, topics, things to the problem i am trying to answer?

What do you mean by problems you want to solve? Do you have something specific in mind or does it mean that you find general relativity/differentiable manifolds interesting.

 

[mpresic3]

Hello. When i have some problems i want to solve should i read only the needed literature, topics, things to the problem i am trying to answer?

Good god no! Probably the most important part of any textbook is the preface, where the author tells the reader what the goals of his/her presentation/exposition is going to be, and what his/her approach is going to be. Before I even buy the textbook, I at least skim the preface. This does not mean I will not use the text if I don't like the approach, or topics, but at least I like to know where the exposition is going.

Since Covid, I have been reading general relativity with 5 or 6 textbooks with varying treatments. I have to be selective in which problems I consider, but I am reading:

old treatments (non-geometric): Adler, Bazin, Schiffers
newer non-geometric: Ohanian, Ruffini. and Weinberg
Modern treatments: Carroll, Wald
Modern treatment in a class by itself: Misner Thorne, Wheeler

All these add to the understanding of GR. I know some authors will say in the preface, theirs is the only book needed, but all these present good points.

I also now understand why my profs, never settled on one book in QM, but taught from their own notes, and put several books on reserve. I think in any advanced study, our education should be to expose ourselves to various treatments, and even stretch our thinking in areas that we do not immediately resonate with.

Clearly, just because you can do every problem in Carroll, you may not be able to solve every problem in Weinberg, or Wald, or MTW. I think problems are an important part of learning, but they should not be the end goal by themselves.

No author has ever wrote in the preface, I hope the reader will selectively scan the textbook after reading the problems and ignore what I have written if I cannot use it on any of the problems in this textbook. Any author is going to tell you, every word on every topic is important to either the current chapter or later chapters, (otherwise, why would it be included at all). Moreover, suppose you can solve all the problems in the current chapter with the limited material you read. What about the later chapters, where reference is made to notes that the author could not develop into a problem until later material is digested.
In addition, many readers in this forum have read Feynman's lectures, Sommerfield's lectures or Dirac's QM, not for the power of what they add to problem solving, but for the deep appreciation that shows up in the material.

 

[Frabjous]

Good god no! ...

Since Covid, I have been reading general relativity with 5 or 6 textbooks with varying treatments. I have to be selective in which problems I consider, but I am reading:

old treatments (non-geometric): Adler, Bazin, Schiffers
newer non-geometric: Ohanian, Ruffini. and Weinberg
Modern treatments: Carroll, Wald
Modern treatment in a class by itself: Misner Thorne, Wheeler

I think this post should have started with “Good god yes!“ This post is a great illustration of what it means to dive into a topic in order to achieve mastery. This is only the first step: the mastery of what is known. The next step is to move to the journal literature to figure out what is unknown. Notice what the mpresic3 is doing. mpresic3 is not merely reading, he/she is is internalizing and synthesizing, i.e., learning.

 

[Vanadium 50]

There is a difference between taking time off from a difficult problem and abandoning it completely. There is an even bigger ifference between taking time off from a difficult problem and abandoning an elementary problem completely.