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I think most of us had the experience of not knowing how to solve problems in a course in university and then somehow we find, or someone teaches us, some rules to make problems in some subgroups and how to tackle the problems in each subgroup. and then the course becomes so easy and obvious. and you pass it without to much effort with great marks.

lets take an example. Rudin's analysis. i solved many of it's problems, but in the end i didn't know such rules and it still makes no sense for me and i still find it a scary book.

Are you aware of any such rules, that make Rudin's mathematical analysis a simple book?

PS: I am looking for specific things like "when you want to prove $x = 0$, show that it is smaller than every $\epsilon$. " but 'more' specific. for example when this approach is probably going to work. and when not. i am not claiming that these exist. i know there are such things for 'physics Holiday' that make it very simple. it might not be possible for Rudin.

Also note that when i say Rudin or Holiday i actually mean mathematical analysis or physics in that level. not the books.

there might always be some problems that we can not put into a category. i am looking for things that MOST OF THE TIME work.

for example check out: terrytao.wordpress.com/2010/10/21/245a-problem-solving-strategies/

i want something like this but with more details so that it becomes more fool-proof.

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closed as not constructive by vadim123, O.L., user1729, vonbrand, Dennis Gulko May 27 '13 at 15:28

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I have no idea what rules you are talking about... –  user1729 May 27 '13 at 15:06
I am still confused. Are you saying "If someone tells me how to solve the problem it is easy!"? And I am therefore presuming that you are claiming that Rudin's text book stands as a bastion of the "The point of understanding mathematics is to become better able to solve problems" camp (from Gower's article)?! –  user1729 May 27 '13 at 16:09
Okay, but then I re-ask the second sentence of my previous comment: Are you saying "If someone tells me how to solve the problem it is easy!"? –  user1729 May 27 '13 at 16:36

1 Answer 1

There is a lengthy discussion of Rudin's Principles of Mathematical Analysis compiled by and available through Dr. Silvia at the University of California, Davis: see her webpage for Companion Notes to Prinicples of Mathematical Analysis.

Moved from comments: I don't think that the key to success in math, in the "long run", is in finding "rules" to deal with everything. At some point, better sooner than later, one needs to comprehend at a deeper level, what one is learning, and this will foster agile thinking and creativity of thought.

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There is another skeleton key to Rudin (and other books) at George Bergman webpage, math.berkeley.edu/~gbergman/ug.hndts/#Rudin –  zyx May 27 '13 at 15:07
Thanks, @zyx That's one of two I was initially looking for - but couldn't find it in my bookmarks! –  amWhy May 27 '13 at 15:11
@user76556 I think I understand what you mean. What you're calling "rules": kind of what I like to think of as "strategies"... So, no, I didn't you were a "lazy student" asking your question. –  amWhy May 27 '13 at 15:36
@amWhy: i really agree that you need to understand things. but there are many things that we understand intuitively and very clearly but yet we can't prove them. for example atiyah says "there are many conjectures that i completely understand and i am sure they are true. but i can't prove them." proving is a technical thing. so we need to learn 'strategies' how to tackle them. –  user76556 May 27 '13 at 17:02
I'd be happy to talk more with you about this, perhaps in a chat room when we both have the time. There are resources addressing how to think, mathematically, how to "prove" things, etc. But not specifically addressing Rudin's work. –  amWhy May 27 '13 at 18:36

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