Answers to questions from the book: Real Analysis by Stein

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Discussion Overview

The discussion revolves around the challenges of self-studying Measure Theory using the book "Real Analysis" by Stein and Shakarchi. Participants share their experiences and opinions on whether seeking solutions to exercises is beneficial or detrimental to the learning process.

Discussion Character

  • Debate/contested
  • Conceptual clarification

Main Points Raised

  • One participant expresses a desire to verify their answers to exercises from chapter 1 of the book and seeks help from others.
  • Another participant suggests that the original poster should have found existing solutions online and questions the need for further assistance.
  • A participant emphasizes the importance of engaging with the material independently rather than relying on solutions, arguing that this strengthens understanding.
  • In response, another participant acknowledges the value of solving problems independently but argues that it is acceptable to consult solutions after putting in effort, especially for particularly challenging problems.
  • Further, this participant notes that not all problems are equally valuable in terms of learning, suggesting that some may not provide significant insights despite their difficulty.

Areas of Agreement / Disagreement

Participants exhibit disagreement regarding the appropriateness of seeking solutions. While some advocate for independent problem-solving, others argue that consulting solutions can be justified under certain conditions, indicating a lack of consensus on the best approach to learning.

Contextual Notes

Participants express varying views on the balance between independent problem-solving and seeking external solutions, highlighting the subjective nature of problem difficulty and learning outcomes.

the_dane
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Hi

I am trying to teach myself Measure Theory and I am using the book: Real Analysis by Stein and Skakarchi from Princeton.
I want to check if my answers to the questions are correct, so I am asking: Does anyone have the answers to the questions in chapter 1 ?
 
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Velkom Dane :welcome:

You did google "stein real analysis solutions" I suppose ? And want more than I found e.g. here ?
 
BvU said:
Velkom Dane :welcome:

You did google "stein real analysis solutions" I suppose ? And want more than I found e.g. here ?

Hi.
Thank you for your help. Yes I did find this one. Not every exercise is on that link, and I wanted to do those exercises which is about proving some claims, and there is not many of those on that link. That's why I asked in here.

Thanks though
 
It is better to actually think of the material, then finding solutions. The more you start thinking and solving things, albeit they may be small or insignificant, is one more time your brain grows stronger. If you need solutions for Analysis, then you are doing it wrong.
 
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MidgetDwarf said:
It is better to actually think of the material, then finding solutions. The more you start thinking and solving things, albeit they may be small or insignificant, is one more time your brain grows stronger. If you need solutions for Analysis, then you are doing it wrong.

I don't know about this. Sure, ideally it would be good to solve all problems of an analysis book yourself without any help. But you only have so much time. And some problems are really tricky. So I'd say that if you searched for a solution for some time, it is ok to look a bit at the solutions.

Sure, it's not good to look at the solutions of all the problems. If you can't solve a single problem, then something is wrong. But if you have a tough problem that requires some ingenious trick that you just can't find, then I'd say look at the solution. Just be sure to actually put some effort in the problem before looking at the solution. That is the important part.
 
micromass said:
I don't know about this. Sure, ideally it would be good to solve all problems of an analysis book yourself without any help. But you only have so much time. And some problems are really tricky. So I'd say that if you searched for a solution for some time, it is ok to look a bit at the solutions.

Sure, it's not good to look at the solutions of all the problems. If you can't solve a single problem, then something is wrong. But if you have a tough problem that requires some ingenious trick that you just can't find, then I'd say look at the solution. Just be sure to actually put some effort in the problem before looking at the solution. That is the important part.

Add to this that not all problems are created equal. And then I'm not talking about how difficult it is to solve. I'm talking about that you will gain more out of one problem than the other. There might be very difficult problems which are just a waste of time because they don't get you any cool intuition or problem solving tool. Or there might be very easy problems which actually can cause a big landslide in your worldview. This is something to keep in mind when deciding how much time you spend on a problem and when to look at the solution.
 

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