I offer a couple of Free texts, one of which is pretty popular (http://joshua.smcvt.edu/linearalgebra/). The answers, completely step-by-step solved, are available. I can give you two reasons.
1) Preparing good questions and giving answers is about half the work. On my page you'll see that the book is 500 pages and the answers are 400 pages.
And it is not the half that is fun, or that gets you credit. I find that compiling the answers greatly increases the quality of the book because I keep going back and adjusting the presentation, etc. But others don't think that. Rather the opposite; I have been told that it is work only appropriate for grad students.
2) I have gotten a fair number of emails along the lines of "I'd like to adopt your book but since anyone can download the answers, I cannot teach out of it."
It has not in the past proven to be a fruitful strategy for me to inform the email writer that the first thing any 2018 undergrad does on getting a text asignment is to google for the answers pdf, and that those students always succeed.
So one reason to not provide answers is to get more adoptions. This ties in with (1) because my five year reviews are not impressed that random self-learners find the text useful. They ask about adoptions.
I have gotten a fair number of emails along the lines of "I'd like to adopt your book but since anyone can download the answers, I cannot teach out of it."
When we had an introductory course in linear algebra, we were not given any home assignments. Instead, we were told that if we want to train and exercise some concepts, we should find third-party materials and self-study -- and so, I used your book. I really like that approach, it allows more capable students to do whatever they like instead, and to less capable -- work on it, if needed. Thus, I don't understand the rationale of not teaching out of something that contains solved exercises, because there is no reason to assign mandatory exercises in the first place. It's enough to have tests.
And of course, such books are extremely valuable for non-mainstream (that is, not enrolled into a high school or wherever) audience, which can be smaller, but has more impact regarding feedback.
It's quite common to look down on "lesser" work like this (janitorial work, writing solutions, whaterver) as only useful for those "lower" than you, but the amount of times I asked for help from a professor only to have them struggle to comprehend how to solve the problem (from their own assignment) was too damn high. Maybe if they tried to eat their own dog food, they'd see where they could improve.
>They ask about adoptions.
Of course, because the metrics we used to use to get a gauge of where we were progressing and where we needed work turned directly into a measure of our worth as a laborer. Your worth as a professor is only proportional to how much good PR you bring to your organization, they don't care about you actually teaching students, especially not students who aren't paying for your services via your university tuition.
How much time did you put into writing? I have been wishing to write something similar (that is, math texts about linear algebra, analysis, number theory, etc.) for a long time, although I can only hope it to be of this quality. Do you have any tips for an aspiring math textbook writer? I have a graduate degree in math, but I unfortunately I don't use math in my day job, so I am afraid that the material I produce will be too low in quality to be useful for people...
But wow, that is a pretty deep investment! I was expecting a little less, but I guess it makes sense since writing is not your full-time occupation.
> I have a graduate degree in math, but I unfortunately I don't use math in my day job, so I am afraid that the material I produce will be too low in quality to be useful for people...
It is good to have feedback from real people. I work through material with my students in classes, and sometimes I've had what I thought was a great approach and it would just not work in practice.
I don't know if there are online groups of people working on writng stuff like this, either at the college level or at high school or earlier levels, but if you could find such a group, it'd be good to get in with them. (And tell me. :-) )
Publishers reps seem to me to rely on paper mail, and an address like "Math Dept, St Michael's College" does provide some kind of proof. But I sometimes get emails like "I am a student in a poor country and the only way ..." and I simply am not saying no to that.
That last sentence also answers why I don't erase half of the answers.
Free texts are a different model and there are a lot of kinks.
The folks who wrote the book this thread is based on have done something great. (I teach Discrete and I had a look to see if I could use it.) But including answers is a problem to which I am unaware of a solution. Or maybe, it is just that expectations have to change.
This does call for a rather more misanthropic attitude than you seem to have, though.
So no, I'm not doing that. :-)
If you study math for some time, you'll realize that people in math community (especially students) like to repeat math related cliches (not necessarily true) over and over again. This is that sort of folk lore.
If I were to guess the whys of not including the solutions, I'd say it is to save space as detailed answers to even half the exercises take up considerable space; also "laziness" because writing detailed, explanatory answers is no different from writing the rest of the book. Who wants to do double the work ? :
Their "work" means: Find a solution, AND then check it. So, not checking it by yourself is being lazy too.
Also, if you are learning; software like wolframalpha can help you too to check your solution. [Thanks, throwawaymath for recall this basic answer].
> I wouldn't want a beginner programmer writing "production ready" code without code review, so why should we expect a beginner math student to write error free proofs?
"Code Reviews" are for checking "how did the programmer solved that problem". On the other side; you know if some code is giving good or bad outputs by checking it with "Tests" (In the worst scenario; manually). So, you have to learn to "test" your solution. The creativity is in how you managed to get the solution and teachers should give insights about your way to solve it and present you easier or better ways to achieve the same. (Just change "teachers" for "senior devs" and now, that is code review).
> These text seem to be designed solely for a classroom where students will get assistance and feedback from TAs and professors.
Probably that's true. You have to consider those types of books as "slides"; just like a guide for the teacher and memory refresh for students.
They're to sell a crapload of books indirectly through University professors.
As for the "you should know" angle, I do believe that a lot of problems chosen for math classes are chosen because they are asymmetric. That is, getting the answer is much harder than checking the answer. For fractions or systems of equations you absolutely can check your work. It's frustrating for me that nobody appears to be teaching kids that.
If you want to get an A on a college level math test your best use of time left over at the end of the test is to check your work.
"people learn more when they discover something for themselves than they do if someone tells them about it."
The whole idea of IBL is apparently just even communicating properly what problem you're having is a better learning experience than looking at an answer. As an anecdote a few times when I've asked math.stackexchange I found the answer just by thinking about my question.
For math specifically, they all state theorems and prove them. It's good practice to try to prove a stated theorems without looking at its proof first.
> Additionally, I heard the argument that "you should know" if your solutions are correct.
Anyone who believes this has forgotten their own early struggles or never watched beginning students struggle with something comparatively basic, like induction. In fact, introductory (proof-based) math courses are particularly dangerous for not knowing whether or not your proof is sound, because you've not yet built the mathematical maturity to check your own work. In a similar vein, beginning students often have a high level mental model of why a statement is true and which "tools" are needed, but no idea how to concretely put these together in a sound proof.
This is more of an opinion that doesn't reflect reality:
> The common answer I get is solutions "rob" the student of learning.
If the presence of the solution means the student will simply refer to it instead of e.g. completing homework on their own, then the student was probably never really engaged with the material in the first place. It's one thing to laboriously complete the proof first and then use the solution to check it, but it's another thing entirely if the student is just skipping all the work. This is especially true nowadays, because students who want to get easy answers can just go on math.stackexchange for virtually any homework assignment.
These answers are parroted because there is a deep seated "trial by fire" culture in advanced math. But this doesn't have anything to do with why the solutions don't tend to be in the books. To begin with, you have to check your assumptions:
> How can a self-learner without access to a university or professor check their work?
These textbooks are (for better or worse) not designed to be used by self-learners. In fact there isn't really any mainstream publication effort in higher mathematics targeting autodidacts. Therefore that criticism - while valid - isn't really applicable to math textbooks. Ostensibly students are using these textbooks under the instruction of a professional mathematician in a classroom setting.
The other reason mostly follows from the first one. The proof of any given statement is typically significantly longer than the statement itself. As it stands, math textbooks are usually filled with sequences of axioms, definitions, propositions, theorems and lemmas. Each chapter tends to have at least six or so of those sequences, but potentially dozens. The proofs of theorems are included, which means that all but the most trivial of chapter exercises would significantly lengthen the entire enterprise. That's a lot more writing, grammatical editing, mathematical proof-reading, page binding, etc for the whole publication process.
The common answer I get is solutions "rob" the student of learning. Why should the fear of the lazy student cheat those that actually attempt their work and want to see if their solution is correct?
Additionally, I heard the argument that "you should know" if your solutions are correct. A beginner is probably prone to subtle mistakes and may think their reasoning is rational. Thus they are probably unaware of any subtle logic errors and could easily fool themselves into thinking their proofs are correct.
Is it partially laziness from the authors in creating new problems for homeworks/exams? Or do people think a literal beginner in math can be their own proof checker?
I wouldn't want a beginner programmer writing "production ready" code without code review, so why should we expect a beginner math student to write error free proofs? What is the point in not allowing solutions?
As great as these text may be, I couldn't and wouldn't recommend them for the beginner. These text seem to be designed solely for a classroom where students will get assistance and feedback from TAs and professors. They seem useless for a beginner to learn on their own without outside proof checking.