Week 3

June 21, 2009

A whole week has gone by since I wrote! The time is just flying by! This week we spent most of our time analyzing the catalog that we made last week. First we started out looking at theorems that have already been proved for normal energy to see if any of them held for distance, Laplacian or signless Laplacian, which we calculated and cataloged last week. We do not have any proofs for those yet but we have found many theorems that do hold for all or some of the other types of energy. Also, I found a pattern for the maximum distance energy but I have not figured out how to prove it. The professor who is working on the project with us came up with a proof for a theorem. He adapted an inequality for energy that was proved for Laplacian energy and proved it. We all checked it and tried to figure out when the equality cases held. I had an idea for how to do the proof but I knew it wasn’t all correct but I put it on the board and explained to the group what I was thinking and to see if they could see how to fix that parts that I didn’t think were correct. It was at the end of our time on Friday and no one else could see how to fix the problem areas. Oh well, the professor thanked me for sharing my idea. He said sometimes people aren’t willing to go to the board and share ideas/proofs that are not 100% correct.

There was some turbulence this week in our group. The guy in our group, Duy, has been doing the programming that helped us quicken the cataloging process. However, since he did the programming, he felt that he didn’t have to do any of the calculations for the catalog. It wasn’t hard to do the calculations since we used a computer software called Maple to do the actual calculations based on our inputs but it was monotonous since we had to do the calculations for 208 graphs. The rest of us, particularly Kate and I, did not agree with his idea of not doing any calculation. We all understand that programming takes time but we were working the whole time he was programming, fixing errors in the old numbers, so it wasn’t like we were taking a break while he worked his butt off. He didn’t understand our side of the argument and as hard as we tried to convince him, he didn’t think we understood him. We did come to an agreement (or so we thought!) that Duy would calculate half as many numbers as the rest of us because he wrote the program. The next morning when we were in the computer lab to do the calculations, he wouldn’t do any. This really hit a nerve with Kate. Duy and Kate ended up arguing again. That was early in the week and we have all moved past it but group work can really be challenging!!

For fun this week we did several things. On Tuesday night most of us went to the movie theater and saw “The Hangover”. It was funny but kind of stupid but not so stupid that it was bad. On Wednesday, it was one of the guys birthday so we had a big pot luck dinner and then a dance party. On Friday we all went out to dinner with two of the professors at a local restaurant called “Mountaintown Staton”. I wasn’t feeling adventurous so I had a chicken caesar warp and fries. That night we played apples to apples and hung out. It started raining (we were all excited for a thunderstorm!) and several of us went out and played in the rain, splashing in the puddles and watching the lightening. The rain was very refreshing. Yesterday I biked around Mount Pleasant and looked in a bunch of stores but didn’t buy anything except for a few food items. It was a nice relaxing day and I spent awhile knitting and reading “A Thousand Splendid Suns”. I also vacuumed our apartment for the first time since we got here! It was in desperate need of a cleaning!! Today I spent some time reading math books and other useful information. I also went to church and it was a normal mass this time, no incense or procession.

Below are a few pictures of my room and the CMU campus.

My bed and desk
My dresser

Behind the trees is Pearce Hall, where we work.

The Library

Sunday-June 14th

The rest of the week we worked on the catalog and going over different theorems, proofs and papers written on the topic of Laplacian energy or energy of graphs in general. There are only a few papers on the topic because it has not been studied very much.

On Friday we FINISHED the catalog! Well, at least the first “edition”. Right after we printed a copy for each of us we found a handful of numbers that seemed off. So this afternoon I went back and recalculated everything we need for the graphs that had seemingly incorrect numbers and found the correct numbers. Also, we need to do random checks to check the overall accuracy so we will do that this coming week. But we were very excited to be done-especially Kate and I who put in the most work on the catalog out of the 4 of us working on the project.

This weekend was really fun! On Friday afternoon I went to the gym after we were done working and then made myself dinner. I had no idea what I wanted to do but someone suggested we all walk to 7-11 to get Slurpees or ice cream. So about 7 of us walked to 7-11 and got our desired treat and we walked back and sat outside enjoying our summer treats! We were all a little hyper after consuming so much sugar so we went to the playground and had a good time playing until the bugs came out. It was still pretty early so we put in Pirates 1 and then called it a night.

Yesterday I slept in until almost noon! Oops! I LOVE sleeping in but then half the day is gone!! I biked to Target to get a few things I needed and to explore the town a little bit. It was a nice and super easy bike ride! Not nearly as many hills as by my house! Then 5 of us headed down to the river for a bit. I checked out “A Thousand Splendid Suns” from the library so I enjoyed the sun and read my book. I put my feet in but didn’t actually go swimming. After dinner we were going to go to a malt shop at the edge of campus and get malts. Unfortunately, when we got there the malt shop was closed but luckily Dairy Queen was about 6 blocks away so we just went there instead! Yum! One of the girls had never been to a Dairy Queen before and she really liked it! The bikes have really come in handy! I’m so glad we were able to borrow them!!

Today I got up late again and bummed around doing things around here like laundry, taking out the garbage and recycling, fixing some numbers on the table, checking out some books from the library and going to church. The church I went to was on the CMU campus and was small so I expected it to be a normal hour long mass but it ended up lasting an hour and a half! And it included a procession around the block with the host in the monstrance as well as incense numerous times throughout mass! I was shocked! This was the first time I went to this church so I’ll see what it is like next week! It may just be a really conservative parish or today may have been a special day, time will tell! The good thing is that mass is at 6pm which works well with my tendency to sleep in! Overall, it was a nice day and went way too fast!!

More about this week and my project

June 10, 2009

So let’s see, what has happened in the last few days? My group has basically been working on making a big catalog. I think I need to explain a little more about my project. I will do my best to explain it so you at least get an idea. We start with a graph, a simple graph (one that does not have any loops or double edges) and we make a matrix from it. There are lots of different types of matrices you can make. One matrix we made for each graph was an adjacency matrix.
(I couldn't get the graph to paste here so use the link to look at it)
http://en.wikipedia.org/wiki/File:6n-graf.svg

For a graph, each of the dots is called a vertex and the line connecting the dots is called an edge. For an adjacency matrix, if there is an edge connecting two vertices, you put a 1 in the matrix, if there is no edge connecting the two vertices, you put a zero. Below is the matrix for this graph.

0 1 0 0 1 0
1 0 1 0 1 0
0 1 0 1 0 0
0 0 1 0 1 1
1 1 0 1 1 0
0 0 0 1 0 0

I’ll explain the first row. There is a one in the 2nd column and the 5th column because vertex one is connected to vertex 2 and vertex 5 by an edge.
One of my group members made a computer program to make the adjacency matrix so we only had to input the edges and the program made the matrix for us. Once we have the matrix, we used a math software called Maple to find the eigenvalues of the matrix. I’m not sure how to explain an eigenvalue. Once we have the eigenvalues, we take the absolute value of each and add them up which gives us the energy. Does that help?

So the last few days we have been calculating the eigenvalues and energy for the adjacency, Laplacian and distance matrices for 208 graphs, all the graphs with 1 to 6 vertices. We have a catalog that pictures all these graphs and all the graphs with 7 vertices but there are a TON of graphs with 7 vertices, over 1000, so we are starting with just the graphs with 6 or fewer vertices and eventually we hope to catalog the graphs with 7 vertices as well. Once we have all the data we will be looking for patterns, making conjectures and hopefully proving them! We will be looking at things like what happens to the energy if you add/delete an edge? It is taken longer than I expected to finish the catalog/database for the first 208 graph but I think we will finish tomorrow!

Other than that, I’ve been watching TV/movies, reading (just finished “Three Cups of Tea”), knitting, hanging out and getting to know everyone better.

June 4th
Thursday morning we all went in and the first thing was to see who was in which group for the projects. Almost everyone got their first choice which was good. One of the guys who got his second choice decided Wednesday night that he actually wanted his second choice more than his first choice so it worked out! I got my first choice-“The Energy of Graphs and Matrices”. I think it is kind of funny that this ended up as my first choice and the project I got because my mom kept saying that this was the name of my project when people asked because it was the only project she saw the title of, even though there were four choices. A lot of people wanted the project I put as my first choice so we ended up with 4 people in our group, me, Kate, Amalia and Duy. Amalia and Duy are international students and are funded by their universities not the NSF like the rest of us. It is a big group so it will be interesting to see how things go. We decided to all look at the same question for a few days and see how it goes. I think we will need to split up into groups of two but we will see. We got some packets to read and some other packets with useful information that will help make our lives a lot easier. I think it is going to be a fun project and I think we will be able to come to some good conclusions. In the morning after we got our groups, we went outside and took a REU & LURE group picture. The LURE students are Central Michigan University students who work with professors for two summers on projects, there are 6 of them- 3 rising sophomores and 3 rising juniors. Also, my group got an intro to a math software called Maple that will be helpful for our project. In the afternoon we started coming up with ideas and then decided we needed to take a step back and make a database with a bunch of information so that when we come up with a conjecture it will be a lot easier to check if our idea is solid instead of having to do all the calculation when you have a million thoughts racing through your mind. So we split up the work and plan to make a spreadsheet Monday.

Oh, so after I found out I got my first choice project I was pretty excited but it didn’t stop there. Dr. Narayan, who is in charge of the program and also my project, said that there are bikes we could have for the summer if we wanted! I was so excited!! A couple people had bikes they brought and I was thinking how nice it would be to have a bike as well! So before I went back to eat lunch, one of the guys and I went and found where we could get bikes and excitedly road our bikes home. My bike is purple and it is by no means a great bike but it gets me from point A to point B, and a lot faster than walking. The bike came with a lock too which was great.

A bunch of people got bikes in the afternoon and we found out where a nice little beach/river was and took a trip there. The water was freezing! I didn’t swim but a couple people did and there were a bunch of people tubing already! I want to go tubing when it warms up, I would prefer not to freeze!

June 5th
We had to get up early! We left at 7:15 for Mackinac Island. We took the 10:30 ferry to the island and had free time until 4 when we met up as a group for dinner at an Irish restaurant and pub-although they didn’t seem to have many Irish dishes on the menu. The weather was amazing!!! We were all worried because during the week it was forecasted to rain and be chilly but it turned out to be a great day! It rained for the last half hour or so but other than that is was nice and sunny! I forgot to bring sunscreen with me so my nose got burnt. Oops. Originally some of us had planned to rent bikes and bike around the island. Then we saw it cost $7 an hour and that was too steep for most people. I would have gone for it but no one else really wanted to so we just walked. Of course that meant we didn’t go around the island since it is 8 miles around and we didn’t have that much time. We went into the visitor’s center and decided to walk to Arch Rock which was only about a mile away. I enjoyed the walk, especially the part that was through the woods! After we saw the cool rock, we were all starving so we headed back to town and got a quick lunch since we were going to have dinner in about 3 hours. Since Mackinac Island is famous for fudge, we decided to look into it. There are a TON of fudge shops on the main street by where the ferry came in. So we went into probably 10 different shops and sampled fudge as we made our way down the street. Not a bad way to spend the afternoon! We keep walking and were going to try to find the Grand Hotel but never made it; it was further than we thought it would be. Instead we sat at a beach for awhile, played on a playground and then headed back to make our fudge purchases before we had to meet for early dinner. I know I didn’t see much of the island but it was still an enjoyable day. It is hard going places with a group, especially when no one really knew what they wanted to see. The group did split up but I ended up with a fairly large group. I should have looked up more about Mackinac Island before I went and had an idea of what to do. After successfully purchasing our fudge, a half pound slice of chocolate peanut butter fudge for me, we made our way to the restaurant and order. Of course, they were out of the item I wanted-darn! Oh well, I chose a different item instead. An interesting fact is that there are no vehicles allowed on Mackinac Island instead they have a lot of horse drawn carriages. We ducked in and out of a few tourist shops as we waited to take the 6:00 ferry back to Mackinaw City. After a 2.5 hour car ride we were back in Mount Pleasant.

I can’t believe the first week is over!

June 3

Over the last 2.5 days I took 42 pages of notes on the 4 projects that we could work on this summer! We had a series of talks and question and answer sessions with the professors we will work with on the projects on Monday, Tuesday and this morning. This afternoon by 2 pm we had to submit our top two choices for what projects we would like to work on and rank them #1 and #2. I will be interested in seeing how the groups end up. I think my first choice was a lot of people’s first choice so I’m not sure if I will get it. I also like my second choice so I won’t be too disappointed if I don’t get my first choice but obviously I would prefer my first choice. Also, there is one project that I am not sure if anyone will put as their first choice so I’m not sure how they would deal with that.

Tomorrow we will take a group picture and break into our research groups to get started! It is sunny today which is nice but it is still not that warm in my opinion.
On a sheet we got our first day, it says our work hours will be 9-12 and 1:30-4:30 each day, and this is what we have been doing the last few days. I like having the 1.5 hour lunch break! We have to walk back to our townhouses and make lunch and then walk back so there really isn’t much extra time but enough so I can check my email and sent one or two. When it is all said and done we have about 50-60 minutes to make our meal and eat it which is very reasonable. I’m glad we don’t have to bring our lunches with us and eat in half an hour, which I was kind of expecting since I have never had more than a 30 minute lunch break.

Also, for the first time in my life I have a room to myself. It is kinda strange but also nice, especially when just getting to know everyone else I am living with! My room is a nice size, has a big dresser with a mirror, a nice closed, desk and chair and a bed. I really didn’t know what to expect before I came but I like the set up and I have plenty of room for all my stuff! I am looking forward to having my own room at school next year too! I have always had roommates with different sleep schedules from me so it will be nice to finally not worry about being quiet when they were sleeping!

That’s all I can think of for now! I hope you are all having a great summer so far!!

Michigan REU

Hi!
I thought using the same blog as I used in France would be the easiest way of giving you all a little information about my summer since I’m not at home. As some of you know, I am in Mount Pleasant Michigan, at Central Michigan University for an REU (Research Experience for Undergraduates) program. One of my professors at CSB/SJU suggested I apply and since I didn’t get an internship I was happy to get into an REU program! Today was the first day of the program but I flew in on Saturday afternoon. That evening one of my housemates (we are living in townhomes just a few minutes’ walk from campus) took me to Target so I could get a few things I needed like a pillow and some hangers. On Sunday, once more people had arrived we took a big trip to the grocery store called Meijer. It is like a Super Target because it has food and everything else. I am living with two students who go to CMU (Central Michigan University) and two other students in the REU program. One of the girls in the others girls’ townhouse is also a French and Math double major but she is in the program for the CMU students. She seems really nice, as do everyone else but as usual, there are some people who I can see myself becoming better friends with than others.

Today was the first day of the program. We all met in the math building at 9 am. They provided bagels, coffee and orange juice for us. They also gave each of us a CMU mug, a 3 subject notebook, CMU folder and a note pad. I brought school supplies with me but I’m sure I will need more than one notebook anyway. After some intro information, we went and got ID cards so we can use the gym (normally a $30 fee to use in the summer but the REU program is paying it for us!!) and check out books in the library. It was misting this morning as we walked to campus so naturally my hair looked horrid in my ID picture. It looked nice when I left the townhouse but my hair is no match for the mist/rain, it instantly becomes fizzy and anything I had done to it in the morning disappears. Oh well I guess, it is only for two months. In the afternoon we had an introduction to two of the project we can work on. Tomorrow morning the other two projects will be introduced. In the afternoon tomorrow morning and the morning on Wednesday we will get some more information about all the projects and have time to ask questions. On Wednesday afternoon we have to submit our first and second choice projects with our reasons why we want to work on those particular projects. I liked the first project that was introduced today but not the second one. I’m excited to learn about the other two tomorrow! I found it funny that Pearce, the math/computer science building here at CMU is abbreviated PE which is the abbreviation used for the Peter Engel building at SJU where the math classes are held at SJU!

Thursday we start working on our projects and on Friday we are going to Mackinaw Island.

I forgot my camera cord at home so for now I don’t have any pictures but once I get it, I can post pictures of my townhouse and the campus.