where

is the number of ways to cover a 3xn board and is the number of ways to cover a 3xn board with one more square appended.]]>Contributed by: Karl Scherer

]]>1. He said that 99% of mathematicians can't program non-trivially. I am sure he means mathematics majors or graduate students, because most mathematicians in the industry or academia can probably program pretty well. As for mathematics students, especially at the top universities, they are required to program efficiently and well. I do understand his perspective that at many universities, students are merely taught to code (that is, just learn the syntax and create trivial programs).

2. He said that programming mathematics is the best way to learn. I have used that method several times and have found it to be very effective and it is probably one of the best methods of learning or practising mathematics. However, methods such as teaching it, doing problems/proofs etc are very effective as well and I do not know how to quantify effectiveness of learning. Therefore, I wouldn't say it is the most effective way.

3. He also said that programs are better than the usual proofs. I think programs are a good way to prove something, but I wouldn't go as far to say they are a better method than standard proofs because once again, I do not know how to quantify it.

Sorry if I sound like I am too exacting.

]]>I am sorry but I am unable to find any of the links of the original paper.

]]>I am sorry, where did we leave off?

]]>I am only curious

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