Analysis Problems and Theorems in Analysis by Polya and Szego

[SrVishi]

Hi, apparently (as seen in my school's online library page) my school has Problems and Theorems in Analysis by Polya and Szego. I hear this book is really good, but I am wondering if this book is good for learning real analysis. I haven't looked inside the book, but is it like an inquiry based learning approach? Is it a self-contained book with definitions, that can in theory (as in, of course maybe having outsource a bit if the problems are too difficult) learn analysis from? I am in general trying to find guided discovery/inquiry based problem books for most subjects since I think they are amazing, but whenever I find one, it is usually not very deep. For example, this book seems okay, but doesn't cover much. I was hoping to find one for analysis that is very expansive., and I am hoping Polya and Szego's book is of this type. Thanks in advance for any response.

 

[one]

I haven't read this book but it looks like a good shot. Pólya was very interested in mathematics education; whether that translates to a good text remains to be seen. There is another problem book with a similar title, subscript advanced calculus of the real line i think, which i have read. It seemed to be more geared at putnam-style problems, but is an interesting book to look through. There may be a pdf online

 

[one]

Another thing to point out is that "inquiry based" means "slow", which usually clashes with expansive knowledge.

 

[SrVishi]

Thanks for your reply! I'll probably just check it out anyways. As far as inquiry based goes, I don't really know what to call it. I know inquiry based learning is more "guided discovery" type learning, and the books are generally a slower pace, lower level. The thing that really got me into was one of my professor's lecture notes that were under the title of "guided discover." It was essentially just a sequence of problems theorems for you to prove all on your own, with the occasional blurb of extra explanation and hints. Even though it was "guided discovery" it got pretty deep for the number of pages. I went to look for some similar style of material, but they usually, in whatever subject they were, were again, slow and low-level. I was just hoping to find sources of similar quality.