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I am currently going through the " Topics in Algebra" By I. N. Herstein. The problems are pretty good. But there are no answers on the back. Same is the case with "Mathematical Analysis" by Rudin.

I don't understand why is this so??

Even though some would argue that it robs the question of its charm, sometimes it is necessary to check out the answer just to get confirmation that what you have done is correct.

Moreover it becomes necessary in an environment where you study on your own. Even though I have solved exercises, there is always a doubt regarding the correctness of the process or answer.

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Perhaps better suited for MESE. –  Git Gud Apr 9 at 15:33
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I'd say this is in order to make you look at the definitions and theorems in the book instead of the solution when you are stuck, or to force you to communicate your question to other, which also forces you to recap. –  Thomas Apr 9 at 15:36
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Perhaps the main reason is that including solutions in a textbook would add many many pages to a book that might already be very long. Including detailed solutions also takes some effort. –  spin Apr 9 at 15:37
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And also, there is not always one solution. But the main thing is that it takes too much time to write a detailed solution and also that if there is a solution, then the reader will maybe not do the exercise. The best way is to compare with others. For example on this website? –  Jérémy Blanc Apr 9 at 15:40
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Would be nice if for each book they also make a book with solutions. They would sell more and more students would be able to check their answers. –  Integral Apr 9 at 15:40

1 Answer 1

up vote 7 down vote accepted

Several answers to this question come to my mind, some of which are already covered by the comments. Actually, if I'd ever were to write a textbook I'd do the same.

Since you cite Rudin I'd like to note in advance that many consider his books on analysis among the best, and I don't think it is a coincidence that someone writing books which do get that attention and appreciation follows this practice.

Something everyone learning mathematics (not only there) has to learn is the reality (from which you are well protected at school) that you will usually (not sometimes, usually) face problems which you cannot solve. Maybe not at all, at least not with the first attempts or with little effort. You have to find your way to the solution one way or the other, either by thinking harder and smarter, by talking to people, whatever. But you don't get it for free, in real life. Almost never. It is an experience of people who teach (not just math), that this fact has to be taught as well, unless they want to produce many many people leaving university who will then have to learn it too late the hard way.

And, no insult intended, one word of advice: if you find you really need the solutions to make your way through such books, you may want to consider whether you've really chosen the right topic for you.

And one additional remark: why do you need the solution? By working seriously on a problem you may learn more -- even if you cannot solve it -- than by looking up the answer (and, very likely, missing most of the subtleties).

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On the other hand, the deep psychological NEED to know is part of what drives all good mathematicians. We need it so badly that if the solution isn't in front of our noses then we work very hard to find it. –  Lee Mosher Apr 9 at 16:15

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