Hawaii Pictures

Not much to report, since not much has happened, but today we get our car back, in about an hour, and I'm very excited! We presented some of our individual research today, and that went well, and we sort of, but not really, got some new directions to explore. He said he needed to look into it more, but we will have some more to do soon.

So with all this free time, I have been working on the Hawaii pictures, and they are now done, commented and everything! So take a look. They are on Whitney's facebook. If you can't view them because you aren't facebook friends yet, just let one of us know (possibly through a comment on here?) or just call us or something. Oh, and there's a fire-dance video you should also check out. Very neat!

Moving Along

Things have been going well. Not much to report, actually. The car is still in the shop, but we should get it back tomorrow all fixed up! We had a very pleasant weekend. Saturday we went to the zoo in Omaha, and it was wonderful. I can see why they say it is one of the top zoos in the country. We visited the desert dome first, and after that, we felt like we had already gotten our money's worth! They had a ton of stuff there, most notably the new desert dome, the giant indoor rain-forest, and the aquarium. The creatures of the night, underneath the desert dome, was also very impressive. The had an underground swamp with alligators and beavers and everything. One thing the zoo did VERY well, was put you in the environment. You are thrown right into the habitat of the animals, not just looking from a distance. Also worth mentioning is the beautiful butterfly/insect house. I had a butterfly come and land on me =)

Sunday we went to church, relaxed, read, I sorted through some of my magic cards Chad from church (at home) gave me, and after going out to eat and shopping at Walmart, Rich and Avery came over to play Settlers of Catan. We love that game.

Today, Monday, we got a day off, because Dr. Peterson is at a conference, Tanner is still out of town looking at houses in Oklahoma where he will be moving, and we finished all our assignments. We have developed a discrete Green's function, and we have been exploring its properties. They are much the same as the discrete case, I think. We then expanded it to a general time scale. I have helped in finding the max, first and second derivatives, and I was assigned recently to generalize the Lidstone boundary value problems in the discrete case. Now that we have gotten into research and not just class all the time, I'm really enjoying it. I can see myself enjoying math research later in life. I still don't know what branch of math I would want to go into, though. But I have time! I do need to start thinking about grad schools and applications soon, though....

Hope everyone is doing well!

A Few Hectic Days...

Well, things have been pretty crazy lately. Monday night I got very sick from some unknown cause and ended up throwing up twice that night. I was out of commission all day Tuesday and was just laying in bed all day, pretty much. Yesterday, I missed morning class but felt OK enough to go to the afternoon class. By that time I was not feeling bad but was just weak. And today I woke up and felt great, but very hungry! I have been catching up today, because I felt behind, and I even got to play racquetball with my my group here.

I don't think I ever officially named my research group, here. There is Matt, Rich, Sarah, Avery, and me. Tanner Auch is our grad student who is leading most of the research goals, and Dr. Peterson is overseeing the whole adventure and is there to teach us and back us all up.

Ok, so back to chaos. In addition to being sick Monday, we also took our car into the shop Monday for what we thought was an alignment issue. We got a rental car, and Whitney has been driving that to work every day since then. Turns out the problem was not alignment, however, but was subframe corrosion. We were going to have the shop it was at fix the problem (they are very nice people, best I have seen), but my Dad, because he is awesome, found online that there had been a recall back in 2009 for exactly that problem. So after about 2 hours on the phone with the shop, the dealership, and Hyundai customer service (which was actually not bad at all!), we are getting the part and labor covered by the dealership in town here.

So that has made things a bit crazy around here recently. Poor Whitney has had to work hard all day, drive 45 minutes there and back and immediately turn around and drive about for another 30-45 minutes as we run errands and get this all figured out. But things are finally settling down, because today we got confirmation that the part will be in Monday, and the car should be fixed Monday or Tuesday. We will return our current rental car tonight, since we have extended it twice now, and we are getting a longer rent period with a better rate until Monday. Whew. I am looking forward to having our own car back!!!

All in all, things are still going well, though. We are hugely blessed that God kept us safe in a car that was deemed "not safe to drive, especially at high speeds or for long distances", especially considering we drove to Nebraska on it and then Whitney drove 45 min. each way to work a few days! So happy we are both safe! And the car, for that matter, could have been damaged a lot more.... So things are turning out alright.

I could write some more about research progress, but I think I will have more to say in a day or two, so I'll postpone that. For anyone dying to read the nitty-gritty stuff, sorry, but stay tuned!

Another Great Weekend

Sorry I have been behind on my posting! I don't really know why... maybe there just hasn't been much to post recently?

Saturday was an eventful day. We woke up and went to LaMar's to get donuts, which were great. We then took our donuts to the farmers' market downtown, which was huge. It wraps around a city block and is on both sides of the street. There is a quite a bit of produce and such, but also a lot of crafts and miscellaneous things. I got a cup of old-fashion homemade root beer, which was amazing, and Whitney got a bag of kettle corn.

After lunch we went to the capitol building. It is truly an amazing building and a work of art. It is massive from the outside, but the real beauty lies on the inside with the architecture details and the paintings/murals. Tours are every day often and free, so we took a tour which was fantastic, and after the tour we went up to the top floor where they have a viewing area. You can see forever, and it's very peaceful up there. I highly recommend it to anyone who may come to Lincoln.

After the capitol building we went to Walmart, had trouble returning pepper-spray (apparently it's a non-returnable item, or something...), and then spent the night playing online with Nate and one of his friends. It was good to talk with him, again.

Sunday we went to Grace Chapel again, and we really love the church. It is such a blessing to have found a great church immediately upon arriving! Not a Sunday went by without us having a place to fellowship and worship =)

We went out to eat after church again, this time to Qdoba with not only Tanner but some of his Math friends who go to Grace also. It was a good time. After lunch we called the Dads and talked with family. Let's see... we also visited the Gameroom on the way home after dinner at the UNL dinning hall (they have tons of used games, from the beginning of time until now). We then watched the last episode of North America on the Discovery Channel. We will probably end up buying the series; it was so good!

As far as research goes, we have now covered factional sums and differences, so we have officially gotten into the "fractional calculus" part of the program. Although this is discrete fractional calculus, not continuous (but there is a continuous version for fractional stuff). So it turns out the half-integral of 1 is [2/Sqrt(Pi)]t^(1/2). The underlined power is on purpose and denotes the falling function... blah blah blah. It functions like a normal exponent, sort of.

We were also told that our project will probably consist of expanding the use of Green's Functions to some other area. I think we might be expanding their use from a simple discrete case to the general time scale.... I'll let you know when I know more =)

Two Great Days

The past two days have been wonderful! My parents have been here, and sadly they have to leave tomorrow morning. They have been eating lunch with me every day at the cafeteria. Monday we went to eat at Runza, which is a special Nebraska restaurant. Runza serves runza's, which are sort of like subs or burritos that mainly have sausage and cabbage. There are a lot of varieties, though, like the bbq runza, or the cheeseburger runza, or the spicy jack runza (my favorite). I highly recommend it (if you are ever in Nebraska)! After Runza, Whitney and I introduced my parents to Settlers of Catan, which we just got this past weekend. It is a very great game.

This morning we went to LaMar's Donuts and found the largest donuts we have ever seen! They were very good too, although no better than Donut Bank's in Evansville. After classes and after Whitney got back from work at about 4:30, we went to eat at Lazlo's brewery and grill. I had been told it was the best place to eat in Lincoln, and I don't doubt it, now that I have been there. I got the hot rost beef sandwhich; Whitney got the grilled salmon and avocado salad; Dad got the voodoo chicken; and Mom got the Greek chicken wrap. All the food was very delicious, and we got some cheesecake afterwards to finish it off, which was also amazing! Then again tonight we played Settlers of Catan. We all had a great time! We have also done quite a bit of city exploration and walking around while my parents are here, which is nice.

Now for the more complicated stuff =) . Dedicated readers, venture on!

Monday we had what was probably the easiest class, and it also happened to be the class that connected things for me. The lectures have been very similar, but slightly separate in subject-matter, and I have been trying to connect them. It turns out that Dr. Peterson in the morning has been teaching us Discrete Calculus which is based on a fixed number line, more like the set of integers. What Tanner has been teaching us, however, is for any Time Scale, which is any set of real numbers on a "number line", which are defined by a(t) + b. So Tanner's work covers what Dr. Peterson is teaching us, and that's what made Monday's lesson the easiest - it was all review. Today, Tuesday, we finished up the Fundamental Theorem of Discrete Calculus, and we also covered Taylor Monomials. In Peterson's class, Taylor Monomials (a term which he coined) were very easy to understand. In Tanner's class, it was some of the ugliest math I have ever seen =P

First Weekend

Sorry I have not been writing every day like I thought I would, but the weekends turn out to be my lazy time =) . Whitney starts her work tomorrow. She is working in the small town of Waco, NE at the Monsanto plant. It's about a 45 minute drive, so she has a long drive to work and back every day. But they pay her for the miles, and the hourly pay is good, so it's worth it. We are just very happy and blessed that she was able to find a job half way across the country so easily. God kind of just laid it out for us!

This has been a great weekend. We spend Friday night with Nate online, mostly, playing games. We have been reading Lord of the Rings, too (Whitney is finishing Return of the King, while I am half way through the Fellowship). Saturday we were going to go the Farmer's Market here, but ended up sleeping in and not wanting to go (or maybe that was just me. woops). We went grocery shopping on Saturday too, and forgot tons of things at Walmart that we realized almost as soon as we got home (don't you hate it when you do that!). But we managed to scrounge up ways to get them. We found a neat board game hobby store where we bought Settlers of Catan, and we have played it three times I think, in the past two days! It works with two people surprisingly well!

Today, Sunday, we went to Grace Chapel Presbyterian Church. We were invited by Tanner Auch, the grad student for my program, who goes there with his wife. We were surprised to find that it was a Presbyterian church with the name of Grace, just like our church at home in Jackson! (Once again, God's putting His signature on things =] ). Church was good. I think it is a relatively young church, and the building at least is a nice and unique blend of old/traditional and modern. The people there are nice, but were not as inviting as Grace at home (no other church is). We miss our church family at home, but this is a nice temporary place, and it's nice to know at least two people there.

My parents drove here to Lincoln all the way from Evansville, IN today! It was a long drive, about 11 hours, but they made it and we were able to hang out for a few hours together tonight. They will be here two full days (Monday and Tuesday), and they will leave Wednesday morning, I think. Tonight, after they got here, we had spaghetti that Whitney made (and was delicious!), and then we went for a walk around the UNL campus. My parents were ready to walk around after the long car ride of sitting. After dinner and the walk, we came back to our apartment here and watched the next to last episode of North America on Discovery. So sad it's the last one soon.... My parents had not heard of it, and they really enjoyed it. It was all about the deserts.

Well, tomorrow I go back to classes and learning new recently discovered things, and Whitney goes to work for the first time for real here (first time was for drug test). I look forward to awesome school cafeteria food, spending time with my parents, and learning new math! Hope you all have a great week as well.

Bowling with Nerds

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.

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!

First Day of Class

Today we had our first class sessions. Dr. Peterson is teaching in the mornings at 9:30, and Tanner Auch, the grad student who is defending his dissertation this summer, teaches in the afternoons at 1:30. The class sessions went by super fast, and we were learning quick. We have no textbook (which makes sense, since it's research), but Dr. Peterson has printed notes for us all to follow. Tanner just writes from his own notes on the board, so I found myself taking notes for the first time in a math setting! It makes it difficult to keep up and absorb things when you are rushing to write everything down....

Except for a few more events pertaining to all the research programs, my schedule will pretty much be the same:

Breakfast
9:30 class with Peterson
Lunch
1:30 class with Tanner
Dinner

So my posts may start to include some of the more technical things we are learning, if I find it easy enough to type. So, sorry family and your welcome school-mates/professors! Once we get a little further in and I understand the material better, I'll try to explain a little of it. For now it's all new and different and strange.

Orientation Day

This morning I had my first meal in the Selleck Dining Hall. It reminds me a lot of Cobo at Union, but the food is much better and there are a few more options. All in all, I was very impressed! After breakfast, everyone had orientation in the Multicultural Center at 9:00. After going over the things in our packet they gave us last night, we talked about a bunch of common sense logistical stuff. After the orientation, we divided into groups and went to get our Ncard, which is the student ID card. Then we had a tour of campus, which is huge! They have about 22,000 undergrads here, I believe, and UNL has many summer programs too, so the place is pretty bustling.

The Rec Center is wonderful. It has a pool, a large indoor turf field, and everything else you can think of including massages. How much I will use it, since I live off campus, I don't know yet, but if a gym can make you want to work out in it, this is the one!

After the tour we had lunch (also great) and then a break. Then at 1:15 we met in front of the dorm building everyone is staying at and divided into program specific groups. We were then shown to our lab buildings and where we would be doing our work. We met with the staff and our program mentors. I will be working under Dr. Peterson and a grad student named Tanner who is about to get his Ph.D. in August, I believe. There is another math program working on wave mechanics and partial differential equations, and both that group and my group have about 5-6 people.

After meeting the faculty and such, we were done for the day! My program group will be meeting twice a day for Monday-Friday at 9:30 and 1:30, I think. So tomorrow we will actually get some lecture. Dr. Peterson lectures in the mornings, and Tanner lectures in the afternoons. We were told the first three weeks will be a lot of learning and preparation for the problem-solving side of the research. The rest of the eight weeks will be busier then working on problems and producing work. I am excited, and the faculty as well as the students seem really nice to work with.

The Welcome Party

Today Whitney and I got back from Hawaii and, after flying to Omaha, we drove to Lincoln, Nebraska. The city here is lovely. It is a quite place with nice people and a very homey feel. After finding some dinner, we found our extended stay hotel, the Townhouse. From the outside, it doesn't look like much (doesn't look bad, though), but inside it is very nice. It is worth the price and will be a nice and comfortable place to live for the next 2 months.

After relaxing for about an hour, we headed to the Univeristy of Nebraska Lincoln (UNL) campus to get signed in. I got a packet full of information about the program, the campus, and the city of Lincoln. After getting signed in, Whitney and I went to the library for a bit to read, relax, and wait for the pizza party at 6:00.

The pizza party was in the basement of Neihardt Hall, a dorm building where most of the research students are staying. We got to meet many new people, and I can only remember a handful of their names. Let's see.... We sat with Gavin and Jay. They were both doing different science programs. Then there was another David at the table who was doing more Physics-related work. There was also a Carl who was doing virology studies on the Herpes virus. There are two programs for math, and most of the crew for the one I'm not in was there. There was an Ean (ee-an) from Montana who had a 14 hour drive, and there was a Sarah, I think, who was the only other person in my program there. Everyone was very friendly and talkative, and the Valentino's Pizza was delicious! We got to take almost an entire box home (breakfast tomorrow?). Throw in some breadsticks, salad, and Pepsi, and it was a grand and merry feast! Most people were surprised to find that I was married, but everyone seemed to think that was cool. I got a few questions about how old we were and how long we had dated, and I think we passed =) .

After watching North America on the Discovery Channel (you should watch it too, it is awesome), we are winding down. Whitney is playing Pokemon, and I decided to start this blog up to journal my research adventure and make it easier for those who wish to keep up with me to do so, so enjoy!