General Information
Project Information
Project Title: "Proof a Maximal Antichain is a Quantum Cover"
Abstract: In standard measure theory on finite sets requires that the measure of the union of two disjoin sets equals to the measure of their sum. However, there are real life situations, like quantum mechanic, we want to measure things that do not satisfy the condition that is mentioned above. In this case, quantum measure theory is required. However, quantum measure theory has the downside, such as that the measure of every set in a cover is zero (0), it doesn't mean that the measure of the whole set is zero (0). This is where a quantum cover is needed to for quantum measure theory. A cover is a quantum cover if it satisfies the statement: if the measure of the cover is zero (0), then the whole set has the measure of zero (0). The goal is to determine a general class of covers that is a quantum cover.
Weekly Journals
 Week 1: (May 31, 2011 to June 6, 2011)
 This is the first week of the Dimacs program. With in this week, I had two meetings with my mentor, Katy Graig. I received two of the main reading sources that I will be focus on for this research project. The basic terminologies, ideas and concepts about the quantum measure theory were introduced to me to help me to prepare for the presentation that's on June 7, 2011.
Karmen T. Yu
 Week 2: (June 7, 2011 to June 13, 2011)
 As of the second week in the Dimacs program, I met my mentor twice this week. More materials about quantum cover were exposed to me during the two meetings. I read a reading about induction, which plays an important role in this project. On the other hand, my mentor and I looked at a few examples and proofs.
Karmen T. Yu
 Week 3: (June 14, 2011 to June 20, 2011)
 This week, I was assigned with more proofs to work through by my mentor. After I tried my best to work through the proofs I then presented my work to my mentor during our second meeting of the week. Last two weeks I learned about how different theorems work (the condition and etc.), but this week we concentrated on prove them to be true. I was assigned to start proving for small cases that a maximal antichain is a quantum cover. Proving for small cases is still in progress.
Karmen T. Yu
 Week 4: (June 21, 2011 to June 27, 2011)
 As of week four, more time is spent to understand the background information. The process for me to understand background information is coming towards the end. My mentor and I had came up with different possible directions that we might want to work on regards to our research project. We decided to take the time over the weekend to do more research on the different possible directions that we are interested to work on.
Karmen T. Yu
 Week 5: (June 28, 2011 to July 4, 2011)
 For this week, my mentor and I met up twice. During these two meetings, we talked more about the direction and plan for this research. My mentor mentioned to create example under this topic. This week, we focused and will keep on focusing on doing that. For this weekend to next week I will be working on creating the "ideal" example and the "real life" example. The most important thing is that we are still aiming and moving towards our conjecture for this research.
Karmen T. Yu
 Week 6: (July 5, 2011 to July 11, 2011)
 This week I been working on modeling the single, double and triple slit experiments. With a formula that we found, I was trying to come up with some computations. I also put diagrams together that match with all possible situations for those experiments. With those computations, more analysis work will be done on them. Towards the end of this week, I've started to put together my second presentation for DIMACS which will be hold on the up coming Thursday, July 14, 2011.
Karmen T. Yu
 Week 7: (July 12, 2011 to July 18, 2011)
 The final presentation is this week's Thursday, July 14, 2011. Before the presentation, I mainly spent my time to prepare the power point for my presentation. I met up with my mentor twice this week. During these two meet up, we spent time to discuss and go over my power point presentation. After the presentation, I spent my time to work on my final report.
Karmen T. Yu
 Week 8: (July 19, 2011 to July 22, 2011)
 This is the last week of the Dimacs REU summer research program. During this week, I met up with my mentor twice to talk about future approaches for this research project. This week I mainly concentrated on writing my final report for my research.
Karmen T. Yu
Extend Research Journals
 Update 1:
 To Be Announced!!
