<story><title>Discrete Mathematics – An Open Introduction, 4th edition</title><url>https://discrete.openmathbooks.org/dmoi4.html</url></story><parent_chain><item><author>hirvi74</author><text>I wish more textbooks, especially free resources like in the link, would be better about providing more solutions. A book with a lack of solutions tends to create a circular problem for me.&lt;p&gt;Knowing whether my solution is correct or not is dependent on how well I truly understand the concepts. However, if I truly understood the concepts, then I wouldn&amp;#x27;t need to solve the problem in the first place. How is one supposed to learn without feedback?</text></item></parent_chain><comment><author>oscarlevin</author><text>Author here.  For what it&amp;#x27;s worth, deciding what percentage of the exercises should have solutions is a continual challenge.  I chose to use a lot of interactive exercises (thanks to PreTeXt these are easy to embed in the text) for which students can enter their answer and get feedback on whether they are correct.  That works well for computational problems.  For proof-based or otherwise theoretical problems, I tired to provide enough examples with full solutions and a few exercises with them as well, while still giving those who would like to have a more authentic open-ended problem without solution that opportunity too.  And of course, I want other professors to find the book useful for courses they teach, and providing problems without solutions that can be graded for credit is also important.&lt;p&gt;Anyway, hope you find the resource helpful.</text></comment>
<story><title>Discrete Mathematics – An Open Introduction, 4th edition</title><url>https://discrete.openmathbooks.org/dmoi4.html</url></story><parent_chain><item><author>hirvi74</author><text>I wish more textbooks, especially free resources like in the link, would be better about providing more solutions. A book with a lack of solutions tends to create a circular problem for me.&lt;p&gt;Knowing whether my solution is correct or not is dependent on how well I truly understand the concepts. However, if I truly understood the concepts, then I wouldn&amp;#x27;t need to solve the problem in the first place. How is one supposed to learn without feedback?</text></item></parent_chain><comment><author>yshklarov</author><text>Not providing solutions is quite common in math textbooks, in part because professors (including the author!) want to be able to assign problems from the textbook to their class, and in part because making solutions is a lot of work!&lt;p&gt;Outside of a classroom setting, the way you learn from a textbook without external feedback is by engaging more actively with the material.&lt;p&gt;Treat each statement in the main text as an informal exercise. Each time you come across a proposition -- whether it&amp;#x27;s a formal theorem statement or a claim in the body of the exposition -- try proving or otherwise justifying it to yourself before reading on.&lt;p&gt;Take a look at Theorems 2.3.1 and 2.3.2 -- they are very similar. Once you have absorbed the proof of 2.3.1, you can attempt 2.3.2 on your own. If you can&amp;#x27;t finish the proof, you can read a couple of sentences from the included proof for &amp;quot;hints&amp;quot;... or, if you do finish a proof, you can compare it to the proof in the text.&lt;p&gt;If you read actively enough, you can learn the material quite well without doing &lt;i&gt;any&lt;/i&gt; problems. Many people will claim that you need to do formal problems in order to learn math, but this is untrue. Many math textbooks at the higher level don&amp;#x27;t include formal exercises or problems at all, and people learn from them just fine.&lt;p&gt;Admittedly, reading mathematics is a skill in its own right, and you shouldn&amp;#x27;t expect it to come easily right away. Of course, the best thing is to have a one-on-one teacher, but few of us are so lucky.</text></comment>