Customer Reviews

Basic Real Analysis

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I first learned analysis using (baby) Rudin. I had the worst instructor and had a hard time making the leap from calculus courses to mature mathematical topics.

Now that I'm in graduate school I need to have a solid background in analysis and fill in the gaps, and I needed a book on analysis that I could study on my own. This book is perfect! It assumes no real mathematical maturity (though perhaps I am biased since by now I have developed some) and takes INCREMENTAL STEPS to introducing new material.

Let me repeat. INCREMENTAL STEPS. It doesn't just throw you into a proof like Rudin without any examples and without any intuition. Most of the theorems and new definitions are complemented with concrete examples, most of which appeal to the real line and baby calculus concepts.

The other important aspect of the book is its breadth. Rudin is a great reference for the main results in analysis, but this book has a breadth of topics that I haven't seen anywhere else, and I've looked! It is very THOROUGH.

It also includes a few chapters on measure theory and probability, which is a definite plus.

If you're looking for an analysis textbook that is self-explanatory or even a reference book (I've used it for that too!) then this is it! I wish they had used this textbook in my undergraduate courses.

(My excitement over this book is after having spent quite a lot of time studying different analysis texts and not really "getting it." I'm finally starting to get it after reading this book. Thank you Sohrab for writing it!)