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elliti123

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In summary: 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.Yes indeed i do actually refer to other sources on any detail that i find that does not appeal or i do not understand it. Just one note about the book, it is basically full of theorems: theorem after theorem sometimes maybe sometimes there examples and explanation about the definition or any detail that needs to be pointed out. So overall it is kind of dry so i thought of teaching myself analysis side by side too. Although i have tried the spivak chapter on limits it really really helped me

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elliti123

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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.elliti123 said:

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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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elliti123

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verty

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elliti123 said:

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.

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lavinia

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elliti123 said:

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

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verty

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lavinia

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elliti123 said:

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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elliti123

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verty

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elliti123 said:

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?

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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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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.jedishrfu said:

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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The best way to approach studying Konrad Knopp's book on infinite series is to start with a clear understanding of the basics of calculus, including limits and derivatives. It is also helpful to have some familiarity with mathematical notation and terminology before delving into the book.

To stay focused while studying Konrad Knopp's book on infinite series, it is important to set specific goals for each study session. Break up the material into smaller chunks and take breaks when needed. It can also be helpful to review and summarize what you have learned after each chapter or section.

Yes, there are many supplemental resources available to help understand the concepts in Knopp's book on infinite series. Some options include online lectures, practice problems, and study guides. You can also seek help from a tutor or join a study group to discuss the material with others.

The amount of time you should dedicate to studying Knopp's book on infinite series will vary depending on your individual learning pace and the complexity of the material. It is important to set aside regular study sessions and allocate enough time to fully understand and absorb the concepts.

To effectively retain the information from Knopp's book on infinite series, it can be helpful to actively engage with the material by taking notes, summarizing key points, and practicing problems. It is also important to regularly review the material and make connections between different concepts to solidify your understanding.

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