[amalcon]

When I was In a numerical approximations course, one other student in the class and I managed to correct the professor about once a week. He wasn't deliberately lying; actually, it was because he had a very poor textbook to work with and was trusting it too much. We were just in the process of doing this again when he demonstrated that you can legitimately say O(n) when you mean O(n^2).

Come to find out, he was a math prof, and very much not an algorithms guy. There are two versions of big-oh notation: one for algorithmic complexity, and one for accuracy of approximations. They are exact opposites of each other: higher numbers are "better" for approximation accuracy, at least in the sense they were used in the course. He was unaware of the former, but both of us were unaware of the latter.

Not such a great teacher, no. Still, the last mistake was an entirely reasonable one. It's a great example of how even math students need to be on their toes.

[pmiller2]

One thing I'd like to mention is that math and science profs rarely mind being corrected when they're wrong (assuming it's done respectfully). I've seen profs in other disciplines become positively incensed when a student tried to challenge what the professor was saying, but I've never seen a math or science prof do so. Your mileage may vary (and I admit this is really nothing more than anecdotal evidence of anything), but I think it says something about the culture of science vs other disciplines.

[eru]

I can verify this for my math profs. I guess it has something to do with coming closer to `one single truth' in math than every where else.

[dbz]

Oh yes I agree. I personally am a math guy. My algebra two teacher was...well...Let's say that I sat in the back of the class the entire year and just corrected him several times a day. Almost all of the people who left that class struggled to understand concepts of their next math course because they:

1) Didn't have a solid understanding of algebra. and 2) Didn't even learn all of the algebraic concepts.

I was fine (because I could recognize the concepts even though he made a TON of mistakes) and skipped (precalc/) trig (which I learned during..) and went right on to AP calc . But the point is that the fact that the teacher made so many mistakes led to the students not being able to comprehend slightly higher level math. (and him being fired)

[eru]

It's one the big-O notation and the other the small-o notation, or so? There's also the \omikron or \Omega notation (or so) that has to be asymptotically correct (up to a factor) in both directions.