I don’t have a wonderful example of this insta-feedback (which definitely sounds ideal for learning), but I’ve gotten annoyed lately with any math book that doesn’t have exercises. Some of the books on MIRI’s Research Guide list are like this, and it really boggles my mind how anyone could learn math from a book when they don’t have anything to practice with. So I’m getting more selective.
Even some books with exercises are super hard, and really don’t have any kind of walkthrough process. AI: A Modern Approach is a critically-acclaimed textbook, but has little to no build up in the difficulty of its exercises, and little to help you if you get lost. Right now I’m reading How to Prove It, which is *super* good. The whole book is one big walkthrough on mathematical proof, down to how to organize your scratch work. It has tons of exercises with varying difficulty, with some answers and hints. It’s much better feedback, and is helping me a lot more, although the material is comparatively simple.
I don’t have a wonderful example of this insta-feedback (which definitely sounds ideal for learning), but I’ve gotten annoyed lately with any math book that doesn’t have exercises. Some of the books on MIRI’s Research Guide list are like this, and it really boggles my mind how anyone could learn math from a book when they don’t have anything to practice with. So I’m getting more selective.
Even some books with exercises are super hard, and really don’t have any kind of walkthrough process. AI: A Modern Approach is a critically-acclaimed textbook, but has little to no build up in the difficulty of its exercises, and little to help you if you get lost. Right now I’m reading How to Prove It, which is *super* good. The whole book is one big walkthrough on mathematical proof, down to how to organize your scratch work. It has tons of exercises with varying difficulty, with some answers and hints. It’s much better feedback, and is helping me a lot more, although the material is comparatively simple.