A full year.

What a year it has been. I have enjoyed every single second living in Dublin and am excited to be back! I just barely got back into Dublin from visiting my family in Utah for a month. Between meeting the new addition (a nephew), being a bridesmaid in my brother's wedding, and traveling from city to city all over Utah, the month was an eventful one! It was wonderful seeing my family and being around them for a longer time, but I am cannot deny that I was excited to come back to Ireland.

First and foremost, I completed my Master's degree at UCD! The course work was extremely tough and I was definitely not prepared. When my course work started, I thought it was the most challenging work that I have done yet, and it pushed me to my limits.  Don't get me wrong. This was a good thing. And I wouldn't be lying if I said I would have it any other way. But I cannot deny that my self-esteem wasn't affected. Truth is, I am grateful that I was pushed so much and that I struggled through the year. I failed courses and got the lowest scores that I have ever had in my life, but I also didn't let that stop me. I took that failure and disappointment with myself and just worked harder. I wouldn't let that stop me from doing what I set out to do. It wasn't easy and I had my doubts. But I let my strengths work to my advantage, and everything worked out in my favor.

I did the bulk of my work within Matrix Theory, collaborating solely with Dr. Helena Smigoc. I concentrated on the Nonnegative Inverse Eigenvalue Problem (NIEP) writing an expository thesis on majority of the work already completed within the problem. I concentrated on the Real NIEP, only mentioning the Symmetric and Complex cases.

The NIEP was first posed by Suliemanova in 1949 when she asked 'given a list of real numbers where one of the numbers is positive, the remaining are negative and the sum of the entire list is positive, can we obtain a nonnegative matrix where the list turns out to be the spectrum of the matrix?' Work had been done within the NIEP but it wasn't until 1956 when Perfect and Friedland properly proved Suliemanova's question using the companion matrix of a polynomial and Descartes' Rule of Signs. In my thesis, I looked at three different methods applied to the NIEP; the use of the companion matrix presented by Perfect and Friedland, Brauer’s theorem, and Fiedler’s construction for nonnegative symmetric matrices. Each one of these methods gives us a different proof of Suleimanova’s result. 

I am very happy with how my paper turned out and was even happier with my presentation. I was so worried prior to the day I had to defend because of potential questions that may be asked. I had no clue what to expect and the uncertainty made me very nervous. It turns out that I had nothing to worry about; there were no questions. Everybody seemed to understand the material. What an experience! I was so grateful when it was over but at the same time I was really sad to be done. If you would like to see the paper I will upload it here. 

I presented my work on a Wednesday then I moved out of my place in Windy Arbour to a place in the City Centre near the Guinness Brewery that Saturday/Sunday. Once I moved, I flew back to Utah the next Tuesday. Needless to say that was a very, very busy week!! Which led into a busy month of family get-togethers. 

This past year has been crazy fun! I have had the opportunity to travel to different parts of Ireland, Scotland, England, and Germany. I am excited to keep the adventure going as I am now looking into different job positions as well as a variety of PhD programs all over the world. I hope to land something soon! Wish me luck!