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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

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  • $\begingroup$ You should be able to verify your own proofs at this point. Post specific questions in a forum like this for assistance as needed. $\endgroup$
    – djechlin
    Commented Nov 16, 2016 at 3:24
  • $\begingroup$ Relevant : math.stackexchange.com/a/750821/120540 $\endgroup$
    – pjs36
    Commented Nov 16, 2016 at 3:49
  • $\begingroup$ How to verify my own proof? $\endgroup$
    – Learnmore
    Commented Nov 16, 2016 at 3:49

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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.

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  • $\begingroup$ But you will always find your own work correct.And that's where we need someone to make sure we are on the right track $\endgroup$
    – Learnmore
    Commented Nov 16, 2016 at 3:49
  • $\begingroup$ @BenStokes If you always think your own work is correct then you do not have a wide enough library of examples and counterexamples. You should be in the habit of casting doubt on everything you claim. It's important that you be able to do this for yourself. If you become reliant on someone else to verify your proofs you will run into a wall when the proofs become too hard for someone to verify easily. (And let's not even bother with research...) $\endgroup$
    – Gyu Eun Lee
    Commented Nov 16, 2016 at 4:48
  • $\begingroup$ @BenStokes I was a math major with a bit of 1st-2nd year grad coursework. By that point, I had enough mathematical maturity to not need reliance on someone to check my proofs as a matter of course. $\endgroup$
    – djechlin
    Commented Nov 16, 2016 at 5:44
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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.

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  • $\begingroup$ But how to make sure that the solutions are correct in those reader written manuals $\endgroup$
    – Learnmore
    Commented Nov 16, 2016 at 3:47
  • $\begingroup$ @BenStokes That's your job. Being able to discern whether a proposed proof is correct or not is also a skill you need to develop. Also, it's not as if author-provided solution manuals (if/when they exist) are immune from errors. Heck, even the textbooks themselves aren't even immune from errors. $\endgroup$
    – Gyu Eun Lee
    Commented Nov 16, 2016 at 4:47

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