> The common answer I get is solutions "rob" the student of learning.
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 ? :
Studying math is the most direct and easiest route to get the human tendency to believe what's psychologically expedient beaten out of you. Any rigorous intro to math (abstract algebra, analysis, topology, whatever) book will do. But the easiest, most varied and funnest would be intro to discrete math or the so called "transition" books. For example, check out [1] Discrete Math by Susanna Epp, [2] Transition to Advanced Math by Gary Chartrand et al, [3] How to Think about Analysis by Lara Alcock, [4] Learning to Reason by Nancy Rodgers
I've been doing the book of proof front-to-back, all the odd problems and finished like 30% of it. Been doing it for about 1.5 months so far before I go to sleep.
Its made me realize that critical thinking is just breaking down logic to its smallest component form. And having some means of expressing different ways of organizing those components. Logic applies to all things, so time spent learning math is always useful.
I'm trying to make math derivations / critical thinking something I can do without trying, so its easier for me to pick up more complex topics and actually understand what's going on.
Looks like this book heavily intersects with "Probability and Computing: Randomization and Probabilistic Techniques in Algorithms and Data Analysis" by Mitzenmacher/Upfal [0].
[0] https://soundcloud.com/anninops/tzusing-met-byhzz-hol
[1] https://www.youtube.com/watch?v=Y0mM-J6wisU