Ask HN: What are the best books with problem sets that test your understanding?
What books with end-of-chapter problems have you found most valuable for truly mastering a subject? Can be any field – computer science, math, physics, economics, etc.
Some of my best learning experiences have come from textbooks that forced me to apply concepts - attack problems directly and refer to the prose on need basis to fill the gaps.
My favourites are - 1. Problems in General Physics by I. E. Irodov 2. Concepts of Physics by H.C Verma Part I & II 3. How to Solve It by George Pólya
There are several principles for reference: 1. Exercise quality: Exercises must cover core concepts, have a reasonable difficulty level, and preferably come with answers or explanations. 2. Practice orientation: Deepen theoretical understanding and cultivate application capabilities by solving problems. 3. Classics and reputation: Give priority to books that have been recognized by the academic community or learners for a long time.
Some especially good ones
Sipser -- Theory of computation
Pinter -- Abstract algebra
Kleppner and Kolenkow -- Mechanics
Klein -- Organic Chemistry as a Second Language
+1 to Sipser. Excellent book. I'm not sure there's any real competition for CS Theory out there.
Solve real life problems from work. It's easy to solve problems, so practice being a problem spotter.
100% this. Problems from work are always realistic and they give you a push to solve them well. Side projects work too, but to a lesser extent.
I could never get through an Algorithm class (self-taught), but that didn't prevent me from learning and implementing some non-trivial algos for my side projects.
It has been a while since I worked through it, but Haskell programming from first principles had some pretty good exercises IIRC.
You could do worse than The Art of Computer Programming.