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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. The same is the case with Mathematical Analysis by Rudin.

Why is this?

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 if I have solved an exercise, there is always a doubt regarding the correctness of the process or answer.

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    $\begingroup$ A lot of the time I think this is because the book is used for teaching and if all the answers were there the problems couldn't be assigned by the professor. $\endgroup$ – ruler501 Apr 9 '14 at 18:00
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    $\begingroup$ I feel like the answers to the problems in these books are not the important part. For writing proofs is the journey not the destination that's more important. $\endgroup$ – Andrew Sanfratello Apr 9 '14 at 19:21
  • $\begingroup$ I agree that nowadays this is more of a problem. Related discussion here: matheducators.stackexchange.com/q/6/61 $\endgroup$ – András Bátkai Apr 9 '14 at 22:39
  • $\begingroup$ Also asked at meta.math.stackexchange.com/q/13346/18398 $\endgroup$ – Joel Reyes Noche Apr 11 '14 at 22:12
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    $\begingroup$ It's mostly a commercial decision. Professors prefer if the answers are not given. Of course for self studiers, this is a killer. $\endgroup$ – Person Jun 11 '17 at 12:58
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For a little historical perspective, which at least explains why older books on non-elementary mathematics rarely have "solutions":

Imagine first that there's no internet, that long-distance phone calls are prohibitively expensive, and that photocopying is not only expensive but mostly inaccessible to students. Imagine also that people use the same homework and exam questions over-and-over. The only step needed to prevent gaming the system is to not put solutions in the book (or in the library, either). Done.

In combination with that immobility of information, there was a sort of macho culture of not telling anyone who couldn't already do a problem how to do it. This is perverse from an educational or scientific viewpoint, of course, but that doesn't mean that humans won't do it. That is, homeworks and exams would be graded, and points subtracted, and things marked "nonsense", without any "approved solution" being given, much less "published".

The common student complaint that they can't tell whether their own "solution/proof/computation" is correct... raises a different point, namely, that students should be very strongly encouraged to develop exactly the sensibilities to know at least roughly whether they're doing the right thing. (The culture of math as rules imposed by an ineffable external authority doesn't help.)

Ignoring that misguided complaint, my complaint is that there are many important, useful, traditional questions/issues with essentially no expert-written treatments... because they're always assigned as exercises... but/and crappy very-inexpert solutions or pseudo-solutions or non-solutions do circulate, thus misleading, certainly not helping, myriad yet-more-junior students.

Thus, by now, given the mobility of information, I think good, that is, "expert", solutions should be available. Yes, this does entail that "assessment" methods have to change. So be it. Also, people can read and write.

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    $\begingroup$ I have at least intermittently tried to act on this, including in my on-line algebra notes "worked examples" of all iconic questions, e.g., questions which I'd ask on prelim exams. No secrets... um, considering that it's supposed to be education, not a contest? :) $\endgroup$ – paul garrett Apr 9 '14 at 23:26
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    $\begingroup$ I wish I could upvote this a non-countable number of times. $\endgroup$ – Mark Fantini Apr 10 '14 at 1:56
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    $\begingroup$ @Fantini You could always assign a bounty (countable, but shows appreciation). $\endgroup$ – dtldarek Apr 10 '14 at 12:08
  • $\begingroup$ I'm sorry but the first part unless meant sarcastically is utter nonsense as really is the end. The reason HW's aren't worked out isn't that there is some secret cabal of professors that doesn't want students to learn things or can't come up with hw/exam questions. The main reason is that many students are too lazy to do the hw and will copy answers if it's easy. Most professors would love not having to grade hw and just assign problems with worked out solutions so students can practice on their own. $\endgroup$ – DRF Jun 12 '17 at 18:30
  • $\begingroup$ As for exam grading/assessment methods it is trivial to make up problems for exams in general. I've never used problems from the book for exams and the time I spent on making exams was spent balancing the problems properly rather than thinking them up. $\endgroup$ – DRF Jun 12 '17 at 18:33
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In my experience whenever answers are provided a huge majority of students will rush for the answers before even giving it a try. Unfortunately the best you learn from an exercise, especially a non routine one, sits in the gloomy time during which you're trying to figure out what to do and have no clues...

I think giving immediately all solutions to students is enforcing a bad habit. It is a fact that when a problem is difficult it is human to face some form of lazyness. Not providing solutions is a way to stimulate people to overcome this laziness. You do not learn much from reading a solution if you did not REALLY try to solve the problem yourself.

I think it ios for this reason that at times solution are provided in a separate form. Personally (i.e. undergrad level) whenever I put some exercises on line from my students I postpone providing solutions of a certain amount of time...

@paul garrett Nowadays with internet and all the likes gaming the sistem is impossibile due to the mobility of informations... my students are much less proficient than I am in finding solved exercises online.

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    $\begingroup$ Nicola, welcome to the site! I like your answer and look forward to seeing you around more. One small suggestion -- your note to Paul Garrett will not be delivered to him unless you move it from your answer to a comment on his answer. Maybe you already know this, in which case I apologize! $\endgroup$ – Chris Cunningham Apr 11 '14 at 14:48

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