Does there exist a good book with a solution manual?

Question

Does there exist a good book with a solution manual ?

I am preparing for an entrance exam and hence I want to practice a lot of questions on Measure Theory,Functional Analysis.

Though I am reading from Royden's Real Analysis ,it does not contain any solutions to the exercises nor any hints.

How can I verify my work?It is quite difficult to type each and every question here as I have only $4-5$ months left

Do there exist any alternative textbook on the same with a solution manual written by the author?

Please help

Answer 1

At this level of sophistication, most textbooks do not have solution manuals written by the author. You may be able to find solutions written by readers, especially for textbooks that have seen long-term and widespread use. For example, a simple search should lead you to several reader-written solution manuals to Rudin's Real and Complex Analysis.

You'll probably have trouble finding complete solutions for newer textbooks (e.g. Stein & Shakarchi's Real Analysis), simply by virtue of the fact that students have not been using these for as long as Rudin's books. But you can probably cobble together a decent list of solutions still.

Answer 2

I warn you to proceed with caution. The pedagogy in advanced mathematics centers around students solving problems themselves, with no solutions manual anywhere in sight.

In particular, you should be able to verify your own proofs yourself by this point.

I would suggest being resourceful, up to and not including the point of having access to solutions. Even asking help from a peer is a lot more likely to elicit someone giving a constructive hint instead of a less constructive solution.

Post a few proofs here as needed to verify that you are on the right track with your proof writing ability. But you should be mostly self-sufficient.