Analysis Problems and Theorems in Analysis by Polya and Szego

  • Thread starter Thread starter SrVishi
  • Start date Start date
  • Tags Tags
    Analysis
AI Thread Summary
The discussion centers on the suitability of "Problems and Theorems in Analysis" by Pólya and Szegö for learning real analysis. The inquirer seeks a self-contained, inquiry-based learning resource that encourages guided discovery through problem-solving. They express a desire for a book that is expansive and deep, contrasting it with other resources that tend to be slower and less comprehensive. The mention of Pólya's interest in mathematics education raises questions about the book's effectiveness in fostering understanding. Additionally, there is a reference to another problem book focused on advanced calculus, which is noted for its Putnam-style problems but may not meet the inquirer's needs for depth. The discussion highlights the challenges of finding high-quality, inquiry-based materials that balance depth with an engaging learning pace.
SrVishi
Messages
75
Reaction score
15
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.
 
Physics news on Phys.org
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
 
Another thing to point out is that "inquiry based" means "slow", which usually clashes with expansive knowledge.
 
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.
 
The book is fascinating. If your education includes a typical math degree curriculum, with Lebesgue integration, functional analysis, etc, it teaches QFT with only a passing acquaintance of ordinary QM you would get at HS. However, I would read Lenny Susskind's book on QM first. Purchased a copy straight away, but it will not arrive until the end of December; however, Scribd has a PDF I am now studying. The first part introduces distribution theory (and other related concepts), which...
I've gone through the Standard turbulence textbooks such as Pope's Turbulent Flows and Wilcox' Turbulent modelling for CFD which mostly Covers RANS and the closure models. I want to jump more into DNS but most of the work i've been able to come across is too "practical" and not much explanation of the theory behind it. I wonder if there is a book that takes a theoretical approach to Turbulence starting from the full Navier Stokes Equations and developing from there, instead of jumping from...

Similar threads

Replies
1
Views
2K
Replies
4
Views
4K
Replies
6
Views
2K
Replies
6
Views
3K
Replies
8
Views
3K
Replies
1
Views
22K
Replies
5
Views
2K
Replies
7
Views
4K
Replies
20
Views
3K
Back
Top