Today we went over what the trig functions would look like in the discrete case. Surprisingly, they were defined almost exactly like they were in Complex Variables, only with the discrete exponential function and such. Many of the identities were the same as well. It was very neat! We went over sin, cos, sinh, and cosh. We also were introduced to the Discrete Delta Integral. It functions as an anti-difference for the difference function (like a derivative). We were assigned to find the integration by parts equivalent for discrete calculus. I think I found it, but not sure. I looked in my old calc book, and in the continuous case, it was derived from the product rule. So I followed the same procedure with our discrete product rule (minutely different), and I hope it works.
Tonight we had an organized bowling outing for the math REU students. It was a lot of fun! Many of the students were pretty good (by normal standards), and even some of the professors. Some of them were pretty bad, though =) It was pretty funny. We all had a good time, though, and we are getting to know each other better.
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