How to know whether I can handle analysis or not and how can I prepare

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I m a first year engineering student and contemplating taking real analysis class next year.
I have already done single variable calculus, linear algebra and multivariable calculus and did relatively well in them but I am not sure whether I will handle analysis.

Analysis is not a prerequisite in my degree program, but in order to take classes like PDE's, higher statistics classes, discrete mathematics, I must have done real analysis. If I end up deciding to do electrical engineering (currently between mechanical and electrical), I would have to do complex analysis which requires a good understand of real analysis.

How can I prepare for real analysis, what resources do you recommend? By preparing, I am not trying to get ahead, I just want to prepare to know whether I can handle it or not.

Would very much appreciate your help!
 

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  • #2
jbunniii
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If you have not done any rigorous calculus (with epsilon-delta proofs) then you will probably find analysis quite challenging. I would recommend that you get hold of an elementary analysis book and see if you are able to read and understand at least some of it. If so, then you may be in OK shape for the course if you are willing to put in a lot of work.

A cheap Dover book which is pretty introductory is

Belding and Mitchell, Foundations of Analysis

It is specifically written as a first exposure to rigorous mathematics, assuming only a year of calculus as a prerequisite. From what I have seen, it looks well written. And it's only $20 at Amazon, so there isn't much downside if you don't like it.

Also, see if you can find out what text is normally used for the analysis course you wish to take. If it is something like Rudin's "Principle of Mathematical Analysis" then you can expect the course to be quite challenging. On the other hand if it is something like Ross, "Elementary Analysis" then it will be much gentler.
 
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Thank you so much for the very helpful reply!

There is no textbook for the course. The lecturer wrote notes which we would have to annotate during the lecture. I heard that the notes are very good.

The lecturer recommends the following textbook: S.R. Lay, Analysis with an Introduction to Proof, 4th ed., 2004 so the course is probably simple. However, it is known to be a very difficult class so probably the recommended book isn't a good way to judge the course.

Do you know anything about S.R. Lay's "Analysis with an Introduction to Proof"? Would it be a good idea to read it or should I read the books you recommended?

I also heard good things about Abbott's "Understanding Analysis", what do you think of it?
 
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jbunniii
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No, I don't know the book by Lay, but if the lecturer recommends it and you can afford the investment, then it's a very good idea to read it instead of my recommendation. The only reason I recommended the one I did is that it is a very inexpensive title aimed at the right level.

Abbott's "Understanding Analysis" is very good! The only possible issue is that he leaves a lot of (fairly simple) things for the reader to prove, which is a good way for you to learn actively but it might be frustrating if you try to read it ahead of time before you enroll in the course. But I highly recommend the book nonetheless.
 
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I will go with Abbott's then because I already have it.
Will ask questions if I get stuck on a proof.

Thank you very much!
 
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jasonRF
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Do you know anything about S.R. Lay's "Analysis with an Introduction to Proof"? Would it be a good idea to read it or should I read the books you recommended?
I worked through the 2nd edition. It was clearly written and reasonable to learn from on my own - I don't think analysis can get much easier. I would call the book uninspiring, though.

I also heard good things about Abbott's "Understanding Analysis", what do you think of it?
From what I have read it is much more interesting than Lay - since you already have it don't bother with Lay unless you look through it at the library and decide you really like it. If you need help with proofs / logic you can always look at the free "book of proof" below:

http://www.people.vcu.edu/~rhammack/BookOfProof/index.html

jason
 
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One skill that I know I've used quite frequently in my intro. to analysis course was constructing inequalities. In my experience, inequalities aren't really taught (well, anyways) before analysis, so it might be worth practicing them now.
 

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