# Image Maps / Inverse Images

## Main Question or Discussion Point

Does anyone know of a good resource for these types of problems?

I took an Intro to Real Analysis class as an undergrad and didn't do so well in it, but now I am working back through the book, and it is making A LOT more sense than it did back then.

However, I was looking for some worked out examples, and possibly graphing, to help me understand this stuff better as I go through it. . .

Does anyone know of a good book / site?

Thanks!!

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Stephen Tashi
Does anyone know of a good resource for these types of problems?
What types of problems? The title of your post suggests something more elementary that the central themes of a real analysis course. Are you asking for a recommendation for another real analysis text? Or do you need a text that explains the prerequisites for the real analysis text that you already have?

What real analysis text do you have?

Text: Bartle & Sherbert, Introduction to Real Analysis, 3rd Edition

https://www.amazon.com/dp/0471321486/?tag=pfamazon01-20

The class is the first proof writing class for undergrads that our school offers for math majors and other students who want to take more advanced math classes.

This is all in the first chapter of the book.

Stephen Tashi
Fo those pages, you need a "pre Real Analysis" book. I don't keep track of modern math texts and I haven't been a student since the 1980's. Let's hope some other forum member will know of such a book.

I don't know your purpose in reviewing the Real Analysis coures. I sense that what you want is the type of presentation that one see's in secondary math texts - useful graphs, detailed examples, important things highlighted in red etc. That would be nice, but for the material in a Real Analysis course, it maybe an unrealistic expectation. Also, that sort of presentation doesn't prepare you for advanced mathematics courses. In advanced courses, you should form the habit of making your own examples. The material must be understood in a verbal and legalistic fashion, not a graphical one. The exercises won't consist of ten or fifiteen problems that are solved by essentially the same technique.

I think "how to prove it" by Velleman contains a lot of such exercises...

Fo those pages, you need a "pre Real Analysis" book. I don't keep track of modern math texts and I haven't been a student since the 1980's. Let's hope some other forum member will know of such a book.

I don't know your purpose in reviewing the Real Analysis coures. I sense that what you want is the type of presentation that one see's in secondary math texts - useful graphs, detailed examples, important things highlighted in red etc. That would be nice, but for the material in a Real Analysis course, it maybe an unrealistic expectation. Also, that sort of presentation doesn't prepare you for advanced mathematics courses. In advanced courses, you should form the habit of making your own examples. The material must be understood in a verbal and legalistic fashion, not a graphical one. The exercises won't consist of ten or fifiteen problems that are solved by essentially the same technique.
Thanks, I think I need to change my way of thinking to this -- I really am trying to bridge the gap between traditional "math" courses and these types of advanced math courses.

I think "how to prove it" by Velleman contains a lot of such exercises...
Thanks, I will check this out!!