Picnic Party

The first part of today proceeded as normal. We had class again, and I'll highlight some of what we have learned so far.

Our primary realm of work revolves around Time Scales. Time Scales are subsets of the Reals, and I won't go into more detail than that because 1) it's complicated, and 2) I don't understand it fully yet. But with this Time Scales, we are broadening Calculus to apply in more situations, much like we did in the Complex Variables class. Today we developed the exponential function for discrete calculus and saw how it is different. That was in the morning with Dr. Peterson. In the afternoon with Tanner we were formally introduced to Discrete Difference Calculus and developed the derivative the discrete case, calles the Forward Difference Operator. The Forward Difference Operator is [f(sigma(t)) - f(t)]/[mu(t)]. Since we are working with time scales, instead of the complete set of reals, sigma(t) denotes the next number in the time scale (sort of t+1). mu(t), then, is called the Forward Distance Operator and gives the real number distance between t and t+1. So mu(t) is defined sigma(t) - t. What is gives us, if we look at [f(sigma(t)) - f(t)]/[mu(t)], is Rise/Run, or slope, much like the derivative. Well, there's your math research lesson for the day!

The rest of today we were at Antelope Park here in Lincoln, where the REU groups had a picnic (hence the title of the post). We had great food catered from a local grocery store (bbq, chicken, potato salad, pasta salad) and the local ice-cream for dessert. Afterwards we had a big group picture and then department specific pictures. We were then free to go, but everyone stuck around and played fun games like volleyball, ultimate frisbee, and such. I learned to play Bocce Ball, and it was pretty great! Now we are back at home, and just hanging out before bed.

P.S. Feel free to comment or ask questions at the bottom of posts. I will respond!