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Comment by oscarlevin | Hacker News Reader

Author here. For what it'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.

Anyway, hope you find the resource helpful.

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I appreciate you taking the time to respond.

The one part of your comment though I do have further questions about is:

> 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.

I would imagine if a professor could answer the problems in your book correctly without needing the solutions, then I would imagine said professors are also perfectly capable of creating their own problems with solutions. I imagine many professors probably do use the problems in back of the book for assignments, and I feel like that says a lot about the state of mathematical education.

However, I do appreciate all the effort you have put in to this textbook. I will most definitely be using it in the very near future, and I think your book is the one I am going to start with. It takes a pretty selfless person to release something of this value for free, so thank you very much.

Exercises without detailed solutions are useless. If I don't have direct access to a tutor I need solutions, otherwise there's no point - I can never check whether I'm right, I'm stuck, or I'm making mistakes that are invisible to me. This invalidates the whole point of a textbook, it's your entry to a field without access to a teacher.

They may be useless to you (although I think even seeing examples of types of questions that can be asked serves a purpose), but the book was not written only for you. I think it is reasonable for books to have features that are useful for students in courses that assign a grade, as well as other features that are useful for students using it for self study.

It is also worth pointing out, that at least for math textbooks, there is never an expectation that a student should solve all the exercises. If you solve those that do have a solution, then you will hopefully still have a good experience and learn lots.

I've been using textbooks to learn things for over 50 years and during my development writing code many (most?) of those times was not in the context of a classroom but in the context of needing to understand something so I could write code to do it. For folks in this situation having answers, especially to some complex problems, is a huge benefit in terms of gaining understanding and saving time.

I don't think I'm alone here when I say I frequently gain understanding of things by writing code to model them. I know I understand something when I can write it in code. So after ingesting the lesson about a topic I'll see if I can write code to do what I just learned. I have spent a lot of hours stuck at a juncture of not being entirely sure my code, which works on the simple examples, is also working in the complex ones. The difference in results may not be evident. Am I troubleshooting my understanding or my code? I need a known result to actually know.

This is one place being able to copy something from your textbook, for example, paste it into ChatGPT and ask questions is a huge benefit. ChatGippity doesn't always get it right but usually the interchange is much more useful than being stuck.

I find that exercises without answer help me to build confidence. It requires me to be sure of every step, and the actual answer is less relevant.

Of course this all depends on the type of exercise. For some, you can easily check the answer yourself after you have found a solution.

Also, in the real world, most assignments don't have an answer either, and it seems like a good idea to be prepared for that.

In the "real world" all assignments I had had answers. To quote a mathematics professor, "how else could I expect you to understand the material on your own, outside of my lecture".

It will help greatly if authors annotate unsolved problems with difficulty levels to let unmentored readers know what they are up against. Yes, its painstaking for authors to provide solutions to all problems so why not let readers contribute and post their solutions ? The link to such a forum can be part of the book text. And thank you for the superb book.

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