# Extremely hard and stimulating (undergraduate) real analysis $problems$

To put it simply: I have seen many problem books in real analysis (also on this website), but the exercises they propose seem quite standardized.

What are problem books that propose really challenging and stimulating problems (as opposed to standardized exercises)?

You could try the book "Selected problems in real analysis" by Makarov and 3 co-authors: http://www.amazon.com/Selected-Problems-Translations-Mathematical-Monographs/dp/0821845594

This is a very beautiful book, and some of the problems are quite hard.

I recommend G. H. Hardy, "A Course of Pure Mathematics", a classic with many challenging problems. http://ebookee.org/A-Course-of-Pure-Mathematics-Centenary-edition_731929.html

Here are two suggestions:

-- A link to Vaughan Jones's RA course at Berkeley. In the introductory remarks he acknowledges the difficulty of the HW problems (links on the page)

https://math.berkeley.edu/~vfr/MATH10411/index.html

-- Pugh's "Real Mathematical Analysis," a great book in its own right, has over 500 problems, with many from Berkeley qualifiers.