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I have started to read the book A Treatise on Advanced Calculus written by "Philip Franklin" book. I want to read this book seriously. Nearly 3 or 4 years ago I studied "Calculus An Introductory Approach" by Ivan Niven. I have some basic knowledge of calculus but some of the proofs were omitted in that book so I have started to read more advanced texts.
While reading the books I sometimes do not understand what the author tries to convey, that is the way author deals with some specific concept.
I will basically ask these kind of questions:

  • Why and how the author explained concept$X$ this way? What if we reject definition$Y$? What is the logic behind assumption$Z$? etc etc.

  • The definition$X^{'}$ can be proved from the definition$Y^{'}$ so why the author quote $X^{'}$ as a definition? etc etc.

Sometimes advanced contexts skips some obvious logic (because they are assumed to be understood, that is need not to be mentioned) so i would also ask:

  • How the author deduced the statement$Y$ from the statement$X$

I will refuse to ask how to solve this question or that question? I might ask for a hint for some difficult questions.

I've already asked one question of the type I described above here. I got a very nice answer.

P.S: On other stack exchange sites I got banned and suspended for some reasons (out of which one was that most of my questions were silently downvoted). I want to make a clear edge before posting questions on this site.
I will mostly ask questions. I will not contribute much by answering because I have not apt knowledge of mathematics so sorry about this.

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  • $\begingroup$ If you are studying Advanced Calculus, there are plenty of questions you will be able to answer, should you choose to spend your time that way. $\endgroup$
    – Gerry Myerson
    Commented Mar 7, 2014 at 11:25
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    $\begingroup$ Keep in mind that the best questions to ask are ones with a definite answer, as the site is built around the assumption that these are the kinds of questions that will be asked. That's not to say that questions with a more involved, less clear-cut answer are not valuable, but you have to be wary that you might not get the kind of answer you expect, and in extreme cases the question might even be closed for being too broad or primarily opinion based. $\endgroup$
    – Dan Rust
    Commented Mar 7, 2014 at 11:25
  • $\begingroup$ @GerryMyerson I would be pleased to answer the questions which i could. I have school level knowledge of physics and math. I did spend more time studying physics at school that's why i said i would mostly ask questions here. I can write answers too and i will write when question of my level will occur. I have written some good answers in the past. $\endgroup$
    – user103816
    Commented Mar 7, 2014 at 13:48

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Here are a few notes about the specific types of questions you mention:

"Why and how the author explained conceptX this way?"

Questions like this will rarely have a good answer unless the author happens to be available for providing it (the rest of us can at most speculate on his reasons). This is not to say that it may not turn out to have a good answer in some special cases (sometimes, the reason will be clear to people with more experience in the field), but it means you need to be a bit careful with them.

"What if we reject definitionY?"

It depends on what you mean by "reject". If you mean "do not accept as the definition" then that is not really a question about math (technically, you can define things precisely how you want).

"What is the logic behind assumptionZ?"

The answer to a question like this will almost always be "look through the proof and see where it is used", though sometimes there might be some subtlety involved, in which case it can make for a good question.

"The definitionX′ can be proved from the definitionY′ so why the author quote X′ as a definition?"

Definitions cannot be proved, so I don't quite see how a question like this could arise.

"How the author deduced the statementY from the statementX"

These are generally good questions, and the more specific you can be about which step in a given proof seems like it is missing detail, the better.

All in all, if you keep the above comments in mind, I think you will find that your questions will be well received, and that you should be able to learn a lot from using this site.

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  • $\begingroup$ I asked a question on ""The definitionX′ can be proved from the definitionY′ so why the author quote X′ as a definition?""math.stackexchange.com/questions/705286/…. My question might be incorrct but this type of question can arise. $\endgroup$
    – user103816
    Commented Mar 16, 2014 at 10:36
  • $\begingroup$ @anupam No, as also stated in the comments to that question, you cannot prove definitions. $\endgroup$
    – Tobias Kildetoft
    Commented Mar 16, 2014 at 10:38
  • $\begingroup$ But I do not see any fallacy in my proof in any of the answers given and in comments. $\endgroup$
    – user103816
    Commented Mar 16, 2014 at 10:39
  • $\begingroup$ @anupam That fallacy has also been pointed out in the answers. $\endgroup$
    – Tobias Kildetoft
    Commented Mar 16, 2014 at 10:41
  • $\begingroup$ At least one author agrees with me.<math.stackexchange.com/questions/705286/…> I agree that a definition cannot be proved and my question might be wrong. You said:"I don't quite see how a question like this could arise.". I'm just explaining you that this type of question can arise. $\endgroup$
    – user103816
    Commented Mar 16, 2014 at 16:14
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It is sad that you were downvoted, because I don't see any valid reason whatsoever to do so, provided that your behavior on other SE sites was the same as what you have described it will be here.

I myself am new to this community, having been a member of a little under a month now, but I believe that that kind of behavior is perfectly acceptable here. As for your statement about asking for solutions to questions, I think the people here are perfectly happy providing solutions as long as you show your work, and clarify where it is exactly that you got stuck. The principle is that this is a place for leaning for people who are enthusiastic about, and love maths. This community is not an answer machine for students who need to get a passing grade in their maths subjects, and it those questions that are downvoted( at least I downvote only those questions). I myself am perfectly happy helping others understand proofs or providing my own proofs, provided I myself understand it of course.

You seem to be enthusiastic about your learning, and any kind of help you need regarding that, be it proof verifications, explanations, hints towards solutions, or in some cases complete solutions if you really are stuck, the community will happily to do its best. I speak from my experience here at math.se in this last one month, and I have never seen any behavior that would lead me to believe that this site isn't warm and welcoming towards people wanting to learn mathematics, or at least take an interest in the subject.

Still some questions may get closed as 'off-topic', for instance if they are primarily opinion based, but that happens to all of us, and shouldn't be considered as that big of a deal. I can assure you you will get all legitimate questions answered.

And welcome to the site. :)

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