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Lately I've been reading lots of statistics books. Many of them have exercises after each chapter that I'm eager to solve, but I'm a beginner and can't solve most of them, and those that I think I can solve I can't check because there are no solutions and no solution manuals available.

I think the point in providing exercises without solutions is that this way the book can be used in class, where the teacher can use them as homework assignments. However, I'm self-learning and have no teacher to ask/to correct my work.

This frustrates me. I like solving stuff, but without knowing even if my solutions are correct (left alone anything beyond that) it's no fun.

What is the best way to deal with this? Are there any resources on the internet where solutions for the more popular books could be found maybe? Should I trust that trying to solve them is the most instructional part anyway and let go of my childish craving for seeing my and the book's answer are identical?

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    I think the point in providing exercises without solutions is that this way the book can be used in class, where the teacher can use them as homework assignments. — Or maybe the author doesn't want to rob the readers of the fun/experience/torture of figuring stuff out for themselves. Remember: The goal is not to answer the exercises, but to figure out how to answer the exercises.
    – JeffE
    Commented Oct 3, 2012 at 16:49
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    I don't see that: I'd be happier with having the fun/experience/torture of figuring stuff out for myself PLUS afterwards the security that my reasoning is correct. It would give me more confidence in the acquired knowledge/skills.
    – miura
    Commented Oct 4, 2012 at 7:10
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    @miura: There are psychological difficulties: if you provide solutions, then some (many?) students will give up and look at the solutions much earlier than they would have otherwise.
    – Anonymous Mathematician
    Commented Oct 4, 2012 at 13:18
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    For self-learning, one of my more important criteria for book selection is whether there are a reasonable number of exercises with supplied answers. If not, don't buy it.
    – Patricia Shanahan
    Commented Nov 2, 2016 at 13:18
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    This practice in the text book business is old-fashioned and takes power away from student. The way to deal with it is to vote with your money, only buy textbooks that provide solutions. Alternatively, one can use free learning resources like Khan Academy that have online tests with immediate feedback.
    – Evgenii
    Commented Mar 12, 2019 at 6:58

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An inability to confidently answer the questions in a text book in general is an indication of not having mastered the material.* If you are not 100% confident that you are solving the problems correctly, go back and read the material again. You will not be able to use the skills in research unless you know the material without an answer key.

*For a graduate class I used to teach there was a problem in the textbook that I could not solve. No matter how I thought about the problem, some information was always missing. I am friends with the author so emailed him for a solution set. I was too embarrassed to admit I couldn't solve the problem and figured the answer key would be helpful anyways. The answer for the problem in question was "Not possible with supplied information."

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    Well, even if I am 100% confident in my answers, it still is not certain that they are correct. All my confidence stems from my own unproven belief in my understanding. This entails a risk of false confidence. With solutions I have the possibility of external reassurance that I have understood. I can't see how that's a bad thing.
    – miura
    Commented Oct 4, 2012 at 7:15
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    There is a complex analysis book that lists the Riemann Hypothesis (one of the most important open problems in mathematics) as an exercise. There is only a note at the end saying "if you can't solve this, ask your teacher".
    – Federico Poloni
    Commented Oct 4, 2012 at 7:25
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    The absolutely beautiful paper by J Kruger and D Dunning in 1999 called "Unskilled and unaware of it: how difficulties in recognizing one's own incompetence lead to inflated self-assessments." show s how self-assessment can be really missleading.
    – Zenon
    Commented Oct 4, 2012 at 14:58
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    True, but the purpose of textbook exercises is to help the reader learn the material. Readers who have already mastered the material have little need for exercises.
    – user134410
    Commented Jan 26, 2021 at 3:03
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What is the best way to deal with this?

The best way to deal with the uncertainty is to go through other works (textbooks, videos, examples etc) that contains the subject area for which problem you are trying to solve. Make certain that these works does have answer sets that you can compare your work to. Then, once you have gained the confidence and more experience in solving the problem set, go to the original textbook and do the questions again. In theory you should be more confident that your answers are correct/incorrect.

As an example. Lets say you are working through math textbook1, the algebra chapter. You do all the algebra questions, however textbook1 does not contain the answers for the algebra chapter hence you are not as confident that you have the correct answers. What you should do is to find math textbook2 that contains a chapter on algebra with questions that contains answers. Work through the examples in textbook2 and confirm that your answers and methods you followed to obtain the answers are correct. Once you are confident you have a proper understanding of the work, doing the questions in textbook1 should be easier and you will be in a better position to know if your answers are correct.

Another alternative would be to use software to confirm that your answers are correct. E.g. math problem? use SAGE to confirm the answer. Bear in mind that the software may only provide an answer and not the method on how to get to the answer. But this can be used to your advantage in the scenario that your answer is incorrect, hence you could deduce that the you are not following the prescribed solution method correctly.

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  • That is a reasonable approach. However, with these statistics problems, my mathematical ineptness is often not the primary problem. It is even knowing how to approach the problem or what the question really means, grasping the concepts. It is a difficult topic to self-learn, that's why solutions would be such a relief. Solutions for the math are often easily found e.g. using software/the internet.
    – miura
    Commented Oct 4, 2012 at 7:20
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    Ah, I understand where you are coming from. I chose mathematics as it was easiest to use as an example. As with learning anything new, it sounds as if you are going to have to give it the good ol' blood, sweat and tears. Perhaps emailing the book author or speaking to others who are knowledgeable on the matter. Approach a few people and clearly state your case by describing how you have interpreted the problem and explaining where your currrent dilema lies. Also make a note of all the options you have taken to solve/understand the problem.
    – Eminem
    Commented Oct 4, 2012 at 8:39
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I abandon and don't pick the book up if it does not have the answers, whether explicitly or implicitly earlier on in the text, unless the answers can be achieved through an internet search. Why? Because an important part of becoming an expert in something is having the confidence in the answers you give, and that can't be achieved if no one ever confirms your answers.

I also think that it makes learning less fun. You can get stuck and lose the drive to learn since you never understood those few questions in that book. It also wastes quite a lot of time which could be spent more wisely, or you may not even realise your mistake.

People often fail an exam due to stress which maybe partly is due to lack of confidence, rather than lack of knowledge. There is many books which would support a self-learner better than one intended for teachers who already have that confidence - at times wrongly held.

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Pick some problems that you're most interested in and attempt to write up full solutions.

Perhaps you will feel 100% confident in your answer. If so, great, and move on.

Otherwise, you will get stuck. Either you won't know how to solve the problem, or you won't know how to verify that your solution is correct.

Try to answer these: meta-questions yourself: why can't you solve the problem? why can't you verify that the answer is correct yourself?. This process will probably involve re-reading the material that was supposed to prepare you to answer the question. It will often involve convincing yourself that you understand terms fully. If you are still stuck, ask for help in a constructive way. A great way to know if you are asking for help in a good way is if you can write a good question on a StackExchange site. If there is no one around to ask, you can literally ask on a StackExchange site.

This takes a while and you'll answer less questions, but it means that you will know something more important than whether or not you are right: you will know why you're right.

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Find examples on the internet that do contain detailed solutions for the concept you're trying to understand.

This can be from pdf files of solutions posted online for a homework, other textbooks, forum posts or even youtube videos.

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Some grad students/advanced undergrads tutor for spare money. I imagine it wouldn't cost too much to convince someone to grade your "homework" for you and provide suggestions. It would even be cheaper if you can find someone already TAing a relevant class. [This works better if you are physically near a university, but could potentially be done online. Just make sure to look for someone who is advertising - academics occasionally get "I want you to tutor my child" emails that are scams.]

This would add up over time, but at $10/hr or so, it might be cheaper than buying a more popular book with well-known solutions, and it would serve as an external reference point.

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