I have been been part of the VSRP program for about 10 days. I have solved some problems from Atiyah-Macdonald and some from a couple of other books. I have also brushed a little of topology and other parts of Algebra.
In spite of having solved problems on prime ideals and the Zariski Topology, there is nothing that I am taking away from doing these exercises. I only have a vague picture of the underlying mathematical structure, but nothing much more. Hence unless I am really intellectually handicapped, I feel the practice (followed by most places across the world) of teaching Mathematics by solving problems is inherently flawed. The focus I feel is more on somehow being able to solve the problem, and then moving on to the next one. There is little reward to maybe generalize the problem and think about the motivation behind the problem- the generality that the problem is hiding in the form of a “trick”. I don’t think I am a big fan of this method.
I think being able to describe a mathematical structure in words is an important component of the learning process. Hence, I will continue blogging.