Customer Reviews

Basic Real Analysis and Advanced Real Analysis Set (Cornerstones)

5 star:		(2)
4 star:		(0)
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1 star:		(1)

 

 

This is a fabulous book for learning real analysis. I've never taken a course in the subject (High school doesn't have one) but I have used the book for an independent study. After a fair study of point-set topology, this book can take you in and out of real analysis with ease. It's comprehensive and provides interesting insight into fields you thought you knew. It first tackles the problem of axiomatizing basic calculus, then it gives some background on metric spaces before hitting calculus of several variables and ordinary differential equations. The chapter on metric spaces was far more comprehensive than any I've read, and I've never seen a book that develops the theory of differential equations from an abstract perspective (none to this degree at least).

After this, it hits the meat of real analysis: Measure theory (and Lebesgue integration). Again, the author does an excellent job explaining and elaborating on this powerful theory. Euclidean spaces, topological spaces, L^p spaces, and Hilbert/Banach spaces take up the rest of this book. It even includes a very interesting chapter on Fourier transforms for Euclidean spaces. Overall, it's definitely worth the buy.

The kindle edition has many unreadable equations in it.

I don't know the root cause (translation to kindle format, etc.)

The bottom line is some of the equations are worthless.

Don't buy this book in this format.

I have only scanned the book very quickly but the book appears to be well written which is why i purchased the books. They appear very clear and easy to follow for self study. I like the fact that everything is explained including "standard" notation. Unfortunately, I have only scratched the surface in each book; however, they seem perfectly suited for a non mathematician interested in becoming one.