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On the usenet group sci.math, a grad student studying algebra posed the question "Should I solve every exercise of each textbook?" A professor responded that students don't realistically have time to solve every problem in the textbooks. While this may be true, I think that grad students should at least attempt to solve every problem in the textbooks (or at least every problem that pertains to the assigned readings). IMO, this is a good argument for not taking as many classes as a grad student as you would as an undergrad, because it allows more time for focused problem solving. (As an aside, some prelim or oral exam committees feel free to ask you anything that is covered in any of the subjects in your major and minor areas of study.)

Some people like to load up on classes (five or more per quarter or semester). Five was my limit. I never attempted more. Four was usually my comfort level. I felt uneasy when I didn't have enough time to do focused problem solving, even as an undergrad.

On a related note, I remember feeling uneasy about my last quiz in multivariable calculus during freshman year. I wasn't sure if I passed, so I figured while I was still geared up to take a test, I would go to the math office and take one of the tutored exams. (These were given by tutors in the math dept in case you wanted to test out of a unit early or you failed the in-class quiz. They were generally more difficult than in-class quizzes.) So I took the tutored exam and flunked it. A day later I found out that I had passed the in-class exam by a reasonable margin. So, which test was the better measure of my understanding?

I haven't been working on puzzles lately because I've gotten interested in some other things, plus have been generally busy. I'm starting to wonder how useful solving puzzles is going to be in finding a new job. None of the interviews I've had recently has featured any puzzles. They have required problem solving, but it is generally pertinent to the job in question, rather than being of the IQ type.

Furthermore, I'm starting to think that in focusing on puzzles, I was overcompensating for a weakness and possibly becoming weaker in more pertinent areas. I think I should be spending more time studying the protocols and algorithms that I want to work on. I remember in my first quarter of grad school, I was concerned about one class, so I spent a lot of time studying for it (including doing a lot of extra practice problems) to the exclusion of another class where I had a stronger background. But I wound up doing much worse in the latter class than I thought I was capable of, because I didn't have the "quickness" to solve its problems. I attributed my low grade to rustiness in calculus, but I could have easily remedied that with some extra practice.

I borrowed a copy of Raymond Smullyan's Forever Undecided from the Mtn View library last month, but haven't read much of it. The puzzles in that book lead the reader to Gödel's Incompleteness Theorem and other related results. It's due back in a few days, and given my current thinking about puzzles, I may not renew it. We'll see.