Customer Reviews

Problems and Solutions for Undergraduate Analysis (Undergraduate Texts in Mathematics)

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4 star:		(1)
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This collection of problems is really quite good. First, the problem is spelled out entirely, so you don't need to refer to the text. It is self-contained, for the most part. Each of the solutions is worked out with generous detail and the problems are chosen to accentuate certain basic results that are easy to take for granted unless you see the difficulties that arise in their absence. I recommend this text for self-study as a running start to Polya and Szego's more difficult problem book.

This book is not just a "solutions manual." There are detailed proofs for all of the problems in the book. This book is essential if you want to truly learn real analysis.

The only way to study mathematics is by solving a large number of problems: this book permits the eager student to challenge his acquired knowledge. A must to all the students wanting to really master undergraduate analysis.

I agree that learning math is about working problems till you puke, then wiping off the puke and working some more (as a friend who was also a Marine Corps veteran used to say). This book is perfect for that. I wish my school would've used the textbook related to this solutions manual rather than the textbook we did use, which had no solutions manual :(

A wonderful volume to complement Lang's Second Edition of Undergraduate Analysis. Feel confident, AFTER carefully studying and FULLY understanding any section of the textbook (having previously read a logical and sequential order of topics that will permit you to accomplish this, besides MAYBE having the opportunity to discuss what you learned with any "down-to-earth", yet knowledgable university professor) to consult the Solutions Manual to the textbook ONLY AFTER YOU'VE COME UP WITH YOUR OWN COMPLETE/PARTIAL SOLUTION TO A PROBLEM in order to address any kind of difficulty related to your solution or to assist you in any doubts you may have.

Even the smartest students out there (yes, I mean YOU... and don't tell me you don't need it because I don't believe you) will benefit tremendously from this manual, IF YOU REALLY KNOW HOW TO USE IT AND TAKE ADVANTAGE OF IT. This Solutions Manual will save you some time and enlighten your learning experience. It is NOT meant for cheating or learning any quicker than you possibly can.

Good luck and thanks for taking the time to read this review!

I have been using this for self-study with Lang's text and it is truly invaluable. It is refreshing to be able to immediately check proofs after attempting them, and then often read a better way of doing them, or to get insight into any gaps in my understanding. It's also fairly thorough as evidenced by the total number of pages.

The only gripe I have so far with this book is as follows. After attempting a proof on lim sups in the section on sequences, I checked Shakarchi's solution. He utilized a method that I once glossed over in another book involving open balls and radii. Nowhere in Lang's Analysis is this method discussed that I have read up to this point. That's not to say that it couldn't be used, but Shakarchi clearly was not using anything thus far presented in the text. It makes me wonder if he just proved the theorems without looking through the text.

Regardless, this is one of the only times that I've had trouble understanding Shakarchi's proofs so far, which is says a lot to his credit. 4.5stars. (I round down since most round up; it would be nice if amazon offered something remotely resembling a continuum in the rating system)