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- #2

lavinia

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I don't know the book but working out examples is always instructive. I would try to categorize the theorems into an architecture to get a big picture of what the theory says.

- #3

jedishrfu

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Some books are setup with tracks where the student goes through all chapters doing track 1 reading and problem solving and then go back and do a second reading for track 2...

For your book, you could read and outline the chapter then use your outline to solve a few problems then go back, reread the chapter and refine your outline and do more problems. Also it wouldn't hurt to digress to other books when you're stuck on a problem or proof. In the case of proofs, there are often multiple ways to prove things and doing the digression you'd learn these alternatives.

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verty

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No, you don't need to prove every theorem. If the proof is given, you just need to understand it. Once you understand it, you will believe it. Think of the proof as a reason why the thing is true. If you have the proof in front of you, you just need to understand it.

- #6

lavinia

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It doesn't hurt to try but only to understand why the theorems are true.

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verty

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- #8

lavinia

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I glanced at the book on line and it seems difficult to read. Perhaps you could use companion books to make things easier.

Alfors book on Complex Analysis has a chapter on infinite seres in the Complex plane. Also Courant and Hilbert's book on mathematical methods in Physics covers series.

Fourier series can be studied in an analysis book. I will try to think of others.

Also try doing the exercises at the end of the chapter first then research backwards to fill in the holes in your ideas.

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verty

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verty

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Okay, I think I misunderstood what your question was. I thought you were saying you were struggling with the book because you were trying to prove every theorem and it was difficult. So I replied that I think proving theorems is infeasible in general because if one proves every theorem without looking at the proofs that are given, it'll be very difficult and will take a lot of time. If the proofs are given, surely the author means you to read them; that is what I was saying.

But I see now you weren't actually saying you were struggling. It sounds like you can just continue because you understand everything, so I guess it isn't using things that one is assumed to know. So it sounds like a good book and it sounds like you are doing fine with it so far, I would just continue.

I liked Lavinia's first suggestion, that studying the examples is very important and seeing the theorems as some kind of large architecture is helpful to understand how they all fit together. And to do that, reading all of it in one book is nice, if you understand it all and aren't having problems.

If you did try to pick it up from separate books, it might be more difficult to see it all together because each author would cover it a bit differently. So I do recommend continuing with this book, seeing as you seem to be enjoying it.

But if you do find that you need to know analysis first then by all means defer learning this material till you learn the analysis stuff.

And if you did need to know things from analysis, companion books would be a way to just get what you need.

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verty

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But why would this kind of math be more popular at that time?

- #16

jedishrfu

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Throughout history, some math is more popular than others. During the Greek era it was Geometry then centuries later Algebra came into ascendency and then later still Analytic Geometry. It tracks the expansion of knowledge and the great trends in thinking.

An analogous one in physics is the popular interest in Newton then Maxwell then Relativity and QM and more recently String theory. At least it seems that way.

Math timeline

http://www.snipview.com/q/Mathematics_timelines

An analogous one in physics is the popular interest in Newton then Maxwell then Relativity and QM and more recently String theory. At least it seems that way.

Math timeline

http://www.snipview.com/q/Mathematics_timelines

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- #17

lavinia

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I think this is true for sure in Mathematics. Chaos theory went mad popular in the 1980's and 1990's. Now it's glow has faded.Throughout history, some math is more popular than others. During the Greek era it was Geometry then centuries later Algebra came into ascendency and then later still Analytic Geometry. It tracks the expansion of knowledge and the great trends in thinking.

An analogous one in physics is the popular interest in Newton then Maxwell then Relativity and QM and more recently String theory. At least it seems that way.

Math timeline

http://www.snipview.com/q/Mathematics_timelines

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