"Some teachers may be displeased with me for including fairly detailed solutions to the problems, but I remain unrepentant [...] In my view any author of a mathematical textbook should be

*required*by the editor to produce detailed solutions for all the problems set, and these should be included where space permits."

By the way, Jones was writing this in 1979; presumably if space does

*not*permit, in the present day solutions can be posted on the author's web site. (This will pose a problem if websites move, though; perhaps an arXiv-like electronic repository of solutions would be a good idea?) A reviewer at Amazon points out that the inclusion of solutions to problems might be an issue for those choosing to assign the textbook in a course where homework is collected and graded. Jones has a PhD from Cambridge and as far I can tell was at Imperial College, London at the time of writing; the willingness to include solutions may have something to do with the difference between the British and American educational systems.

I've seen frustration about the lack of provided solutions in textbooks on the part of my more conscientious students. (This isn't with regard to this text - I'm not currently teaching game theory - but with regard to other texts I've used in other courses.) They want to do as many problems as they can, which is good. This practice of leaving out the solutions is perhaps aimed at the median student - in my experience the median student does all of the homework problems but would never consider trying anything that's not explicitly assigned. (And although I don't know for sure, the student who goes out of their way to get a bootleg solutions manual is probably

*not*the conscientious student I'm referring to.)

## 7 comments:

My undergraduate topology textbook had solutions to most of the exercises in the back. Unfortunately, my classmates and I were unable to make heads nor tails of the most solutions, such was the gap between our understanding of the material and the expositional level of the solutions. Our professor eventually decided that the presence of the solutions was a hinderance to our learning, so he confiscated all of our textbooks, and taught the remainder of the course by Moore method.

First reference to "Moore method" I've heard in many years. My mom took classes from him at UT, Austin. And I had a topology class at NMT that was sort of similar to Moore method in that the class was almost entirely grad students giving proofs on the blackboard. A difference was that Dr. Arterburn assigned specific problems to the different students. He gave the better students harder problems. The text was Dugundji, "Topology".

*raises hand* I'm guilty of trying to find a bootleg solutions manual...though unsuccessfully. I am an undergraduate and all throughout high school (and even this year because my college doesn't have a very strong math department), I worked through various texts in linear algebra, group theory, dynamics, number theory, and topology, and having solutions to problems is useful when I get really stuck, but books rarely had them.

Just to clarify, Sachi, I didn't mean that you shouldn't be trying to find bootleg solutions manuals. (I'm ignoring copyright issues here.) I meant that the student

taking a classwho looks for such things is often the one trying to avoid doing homework.I couldn't agree more on providing solutions along with representative problems if the purpose of the text is education.

If solutions "are left as an exercise to the reader" then maybe the ratio of "new concepts" (from the perspective of the student) to "available pages" is excessive and it is expected from the student to have the same drive and passion about a subject as the author.

But books are written by people who are at a different mind set than students. The author is trying to compartmentalize, organise, provide structure, while the student is more like "OK, here are N different new concepts, how do they work with each other? What do they really mean? How can i make use of them? How do they fit with the bigger picture?"

So, worked out problems and engaging unsolved ones of course, are a sort of playground where you can familiarize yourself with the subject and hopefully at some point feel confident to tackle never before seen problems.

In my experience, the most frequent feedback from students about courses in general is that they wish the prof would have provided more examples in class. Similarly, the most frequent complaints about textbooks involve those that have no answers to exercises.

I think that solved problems (or worked examples) in textbooks are very useful to almost all students, but failing that, at least provide answers to all exercises.

That full solutions and answers to all exercises are typically not included is purely to support our current (broken and inhumane) system of evaluating students.

I can understand why some people might not put solutions to all the problems in their books. However, as a student I would find this rather helpful, especially when first learning a topic.

If providing solutions is out of the question, I would propose a system similar to that used by The Art and Craft of Problem Solving. Here the author provides hints to the solution, and the usefulness of the hint depends greatly on how well you understand the material.

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