Difference between revisions of "User:Babcock"

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='''Project Description'''=
 
='''Project Description'''=
−
I am conducting research on [http://reu.mscs.mu.edu/index.php/(i,j)-step_competition_graphs ''(i,j)-step competition graphs''] in the ten week long Marquette MSCS REU. The mentor that I am working with is [http://www.marquette.edu/mscs/facstaff-factor.shtml Dr. Kim A.S. Factor]. For the beginning part of this REU, I will be doing background research with Max Black and then I will work on my own research. The work I do each week can be seen below.
+
I am conducting research on [http://reu.mscs.mu.edu/index.php/(i,j)-step_competition_graphs ''(i,j)-step competition graphs''] in the ten week long Marquette MSCS REU. The mentor that I am working with is [http://www.marquette.edu/mscs/facstaff-factor.shtml Dr. Kim A.S. Factor]. For the beginning part of this REU, I will be doing background research with Max Black and then I will work on my own research. I am focusing on answering a previous research question proposed by Drs. Factor, Merz, and Sano in their paper The (1,2)-step competition number of a graph. I am working on finding other graphs in which the competition number is greater than the (1,2)-step competition number. My focus will be on unions of 4-cycle graphs and 4-cycle graphs with pendants. The work I do each week can be seen below.
  
 
='''Background Readings'''=
 
='''Background Readings'''=
Line 119: Line 119:
  
 
==='''Day 5 (6/23/17)'''===
 
==='''Day 5 (6/23/17)'''===
 +
Worked from home.
 +
*Worked on Competition Numbers practice (about eight hours)
  
 
==='''Reflection: End of Week 4'''===
 
==='''Reflection: End of Week 4'''===
 +
I feel that I am starting to get an idea of where I will be taking this research. I am working on actual applications instead of just reading, which I enjoy. This week I worked on exploring different topics where I looked at food webs and competition numbers. This was a struggle at first since I wasn't sure where to start with the competition number, but after working with Dr. Factor, I feel much more confident with that I am working on. I am looking forward to continuing my work with this idea and presenting my findings in the mini presentations next week. I feel that I met all of my goals for the week, and this seemed to be a successful week.
  
 
=='''Week 5 (6/26/17-6/30/17)'''==
 
=='''Week 5 (6/26/17-6/30/17)'''==
Line 126: Line 129:
  
 
==='''Day 1 (6/26/17)'''===
 
==='''Day 1 (6/26/17)'''===
 +
*Worked on Competition Number Practice (about three hours)
 +
*Attended talk on giving a good research presentation (about two hours)
 +
*Worked on mini presentation (about two hours)
  
 
==='''Day 2 (6/27/17)'''===
 
==='''Day 2 (6/27/17)'''===
 +
*Worked on mini presentation for about eight hours
 +
*Practiced mini presentation at home for about an hour
  
 
==='''Day 3 (6/28/17)'''===
 
==='''Day 3 (6/28/17)'''===
 +
* Worked on mini presentation for about eight hours
 +
* Practiced mini presentation at home for about an hour
  
 
==='''Day 4 (6/29/17)'''===
 
==='''Day 4 (6/29/17)'''===
 +
*Practiced mini presentation at home for about an hour
 +
*Practiced mini presentation on campus for about two hours
 +
*Attended mini presentations for about 2.5 hours
 +
*Continued work on Competition Numbers (worked on C4 union C4 union C4) for about two hours
  
 
==='''Day 5 (6/30/17)'''===
 
==='''Day 5 (6/30/17)'''===
 +
*Continued work on Competition numbers for about eight hours (worked from home)
  
 
==='''Reflection: End of Week 5'''===
 
==='''Reflection: End of Week 5'''===
−
 
+
During this week I completed many goals. I feel that I did well on my mini presentation. I know I still need improvement, but I don't think it went horribly. I have also completed a lot with my research involving the competition numbers. I have been figuring out a lot with the competition numbers, and I am excited to see what else I figure out. I am hoping to continue to learn more about this topic and improve what I already know in the upcoming weeks.
−
 
+
  
 
=='''Week 6 (7/3/17-7/7/17)'''==
 
=='''Week 6 (7/3/17-7/7/17)'''==
Line 147: Line 161:
  
 
==='''Day 3 (7/5/17)'''===
 
==='''Day 3 (7/5/17)'''===
 +
*Worked on typing up findings with the competition numbers (about four hours)
 +
*Continued research with competition numbers (about six hours)
  
 
==='''Day 4 (7/6/17)'''===
 
==='''Day 4 (7/6/17)'''===
 +
*Met with Dr. Factor and went over my findings (about an hour)
 +
*Attended working lunch and attended presentation about having a good poster (about two hours)
 +
*Worked on competition number research (about five hours)
  
 
==='''Day 5 (7/7/17)'''===
 
==='''Day 5 (7/7/17)'''===
 +
*Worked on abstract for conference (about an hour)
 +
*Worked on competition number research (about five hours)
 +
*Worked on typing up findings (about three hours)
  
−
==='''Reflection: End of Week 6'''===
+
==='''Worked over Weekend (7/9/17)'''===
 +
*Worked on abstract for conference (researching how to do abstract/ typing it) (about three hours)
  
 +
==='''Reflection: End of Week 6'''===
 +
This week I feel that I completed my goals. I started applying for the conference, and am coming to a place where I can start writing proofs for my findings. I realized that what I was working on had to be changed since there were smaller competition numbers than what I was finding, but I was able to improve my work and can go on to writing proofs from there. In the next few weeks, I will be working on exploring other graph families, writing proofs, and preparing my presentations for the upcoming weeks.
  
 
=='''Week 7 (7/10/17-7/14/17)'''==
 
=='''Week 7 (7/10/17-7/14/17)'''==
Line 159: Line 184:
  
 
==='''Day 1 (7/10/17)'''===
 
==='''Day 1 (7/10/17)'''===
 +
* Continued research on competition numbers (two hours)
 +
*Worked on editing abstract (one hour)
 +
*Worked on finishing the type ups of my findings (four hours)
  
 
==='''Day 2 (7/11/17)'''===
 
==='''Day 2 (7/11/17)'''===
 +
*Typed up abstract in latex and edited it more (three hours)
 +
*Worked on creating paper outline (one hour)
 +
*Worked on C4 graph research (three hours)
  
 
==='''Day 3 (7/12/17)'''===
 
==='''Day 3 (7/12/17)'''===
 +
*Finished up abstract and submitted application for conference (one hour)
 +
*Worked on C4 graph research (six hours)
  
 
==='''Day 4 (7/13/17)'''===
 
==='''Day 4 (7/13/17)'''===
 +
*Typed up findings to give to Dr. Factor (one hour)
 +
*Met with Dr. Factor (one hour)
 +
*Working lunch (one hour)
 +
*Worked on paper outline (one hour)
 +
*Continued competition number research (four hours)
  
 
==='''Day 5 (7/14/17)'''===
 
==='''Day 5 (7/14/17)'''===
 +
*Finished working on outline for paper and emailed it to Dr. Factor (one hour)
 +
*Continued competition number research (seven hours)
  
 
==='''Reflection: End of Week 7'''===
 
==='''Reflection: End of Week 7'''===
−
 
+
This week was very successful. I made a lot of progress in my research. In addition, I completed my goals of meeting with my mentor and presenting her with my outline for my paper. I am prepared to get started on my paper and to start working on writing up proofs for my research findings. I will work on those in the weeks to come.
  
 
=='''Week 8 (7/17/17-7/21/17)'''==
 
=='''Week 8 (7/17/17-7/21/17)'''==
Line 175: Line 215:
  
 
==='''Day 1 (7/17/17)'''===
 
==='''Day 1 (7/17/17)'''===
 +
*Begin work on proof for research findings (8 hours)
  
 
==='''Day 2 (7/18/17)'''===
 
==='''Day 2 (7/18/17)'''===
 +
*Finalize proof write-up (8 hours)
  
 
==='''Day 3 (7/19/17)'''===
 
==='''Day 3 (7/19/17)'''===
 +
*Work on poster draft (four hours)
 +
*Write up findings for meeting (four hours)
  
 
==='''Day 4 (7/20/17)'''===
 
==='''Day 4 (7/20/17)'''===
 +
*Finish poster draft (two hours)
 +
*Met with Dr. Factor (one hour)
 +
*Working lunch (one hour)
 +
*Work on fixing proof (four hours)
  
 
==='''Day 5 (7/21/17)'''===
 
==='''Day 5 (7/21/17)'''===
 +
*Work on fixing proofs (four hours)
 +
*Work on fixing poster (four hours)
  
 
==='''Reflection: End of Week 8'''===
 
==='''Reflection: End of Week 8'''===
−
 
+
This was another successful week. I was able to get the draft of my poster done and submitted. I also worked on writing up a proof for one of my research findings (this was pretty exciting for me). I have a lot of changes to make on both, but I will be able to fix them in the upcoming week.
−
 
+
  
 
=='''Week 9 (7/24/17-7/28/17)'''==
 
=='''Week 9 (7/24/17-7/28/17)'''==
Line 192: Line 241:
  
 
==='''Day 1 (7/24/17)'''===
 
==='''Day 1 (7/24/17)'''===
−
 
+
*Worked on editing poster (four hours)
 +
*Worked on starting paper (four hours)
 
==='''Day 2 (7/25/17)'''===
 
==='''Day 2 (7/25/17)'''===
−
 
+
*Worked on editing poster (four hours)
 +
*worked on research (four hours)
 
==='''Day 3 (7/26/17)'''===
 
==='''Day 3 (7/26/17)'''===
 +
*Edited and submitted poster (two hours)
 +
*Worked on research (six hours)
  
 
==='''Day 4 (7/27/17)'''===
 
==='''Day 4 (7/27/17)'''===
 +
*Attended working lunch (two hours)
 +
*Worked on paper (two hours)
 +
*Worked on research (four hours)
  
 
==='''Day 5 (7/28/17)'''===
 
==='''Day 5 (7/28/17)'''===
 +
*Worked on proof/paper/research (eight hours)
  
 
==='''Reflection: End of Week 9'''===
 
==='''Reflection: End of Week 9'''===
−
 
+
This week was spent preparing to wrap everything up for the REU. I was able to submit my poster (on time) and begin to finalize all of my findings. Next week I will be finalizing my paper and preparing a presentation.
  
 
=='''Week 10 (7/31/17-8/4/17)'''==
 
=='''Week 10 (7/31/17-8/4/17)'''==
Line 208: Line 265:
  
 
==='''Day 1 (7/31/17)'''===
 
==='''Day 1 (7/31/17)'''===
 +
*Work on presentation (eight hours)
  
 
==='''Day 2 (8/1/17)'''===
 
==='''Day 2 (8/1/17)'''===
 +
*Attend poster session (two hours)
 +
*Meet with Dr. Factor (one hour)
 +
*Edit/finalize presentation (five hours)
  
 
==='''Day 3 (8/2/17)'''===
 
==='''Day 3 (8/2/17)'''===
 +
*Practice presentation (two hours)
 +
*Attend presentations (four hours)
  
 
==='''Day 4 (8/3/17)'''===
 
==='''Day 4 (8/3/17)'''===
 +
*Attend presentations (two hours)
 +
*Work on paper (two hours)
  
 
==='''Day 5 (8/4/17)'''===
 
==='''Day 5 (8/4/17)'''===
 +
*Finalize and submit paper (eight hours)
  
 
==='''Reflection: End of Week 10'''===
 
==='''Reflection: End of Week 10'''===
 +
This is the last week of the REU. I was able to accomplish a lot in the short ten weeks. I was able to partially answer a research question by finding two graphs in which the competition number was greater than the (1,2)-step competition number. This week was very busy since I had to present my poster in the poster session, give a presentation, and finish my paper. I was able to successfully get everything done, though.
 +
 +
='''Artifacts'''=
 +
*[http://reu.mscs.mu.edu/index.php/REUCarissaBabcockPaper.pdf Paper]
 +
*[http://reu.mscs.mu.edu/index.php/REUCarissaBabcockPresentation.pdf Presentation]
 +
*[http://reu.mscs.mu.edu/index.php/REUCarissaBabcockPoster.pdf Poster]

Latest revision as of 21:44, 4 August 2017

Contents

Project Description

I am conducting research on (i,j)-step competition graphs in the ten week long Marquette MSCS REU. The mentor that I am working with is Dr. Kim A.S. Factor. For the beginning part of this REU, I will be doing background research with Max Black and then I will work on my own research. I am focusing on answering a previous research question proposed by Drs. Factor, Merz, and Sano in their paper The (1,2)-step competition number of a graph. I am working on finding other graphs in which the competition number is greater than the (1,2)-step competition number. My focus will be on unions of 4-cycle graphs and 4-cycle graphs with pendants. The work I do each week can be seen below.

Background Readings

There were some background readings given to Max and I to build an understanding on the topics we will be working on. Note: if a link is missing, the reading is either from a textbook or I could not find a link.

Project Log

Week 1 (5/30/17-6/2/17)

  • Note: I was not physically present during week 1 of the REU. I completed the BioMath packet during this time.

Reflection: End of Week 1

Since I was not present, there wasn't much work that I completed this week, but I made sure to complete any readings and introduction work that I could on my own.

Week 2 (6/5/17-6/9/17)

Day 1 (6/5/17)

  • Finished BioMath packet.
  • Printed readings and materials that were emailed to me.
  • Confirmed a meeting with Max tomorrow, 6/6, for 8:00 AM before the ethics training to go over week 1.

Day 2 (6/6/17)

  • Attended meeting with Max at 8:00AM
  • Attended meeting with Petra at 8:30AM to complete paperwork.
  • Attended ethical research training at 9:00AM until about 3:00PM.
  • Began reviewing The (1,2)-step competition graph with Max at 3:15PM for about 3 hours.
  • Made note to include approximate total number of hours in end-of-week reflection
  • Estimated work for the day is about ten hours.

Day 3 (6/7/17)

  • Started reading chapter 3 about graph theory in Applied Combinatorics. Read at home for about half an hour.
  • Started to read thesis paper- Using Food Webs in Order to Determine... Read first 19 pages for about half an hour.
  • Set up WIKI page for about half an hour.
  • Continued to read and go through The (1,2)-step competition graph with Max for about an hour.
  • Practiced Overleaf/ TeX for about half an hour
  • Meeting with Dr. Factor and Max for about an hour.
  • Worked with Max on new (1,2)-step competition graph article and added definitions to Overleaf for about four hours.
  • Estimated work for the day is about eight hours.

Day 4 (6/8/17)

  • Worked on presentation for Dr. Factor with Max for about an hour.
  • Read (1,2)-step competition graph article in detail. (about five hours).

Day 5 (6/9/17)

  • Worked on presentation for Dr. Factor with Max for most of the day. (About six hours)
  • Worked on adding a picture to the background section.

Reflection: End of Week 2

I feel that my first week was very successful. I am learning a lot, and I am enjoying the work I do. I know that I have a lot more to learn, but I am continuing to try to figure out as much as I can with Max. I am nervous that I'm still not sure what I want to research on, but I know this is something I can work out with Dr. Factor. All of this is very new to me, but I know with enough hard work and time, I will be able to figure things out. Next week I am hoping to figure out a research question with Dr. Factor so I know where to focus my research, but until then, I am continuing to do the necessary background research in preparation.

I accomplished many goals this week including attending ethics training, the Thursday during lunch meeting, and a meeting with Dr. Factor. I also became familiar with the campus, Overleaf (and using Tex language), and (1,2)-step competition graphs.

Week 3 (6/12/17-6/16/17)

Day 1 (6/12/17)

  • Finished up presentation for Dr. Factor (about four hours)
  • Revised hand out for presentation with Dr. Factor tomorrow (one hour)
  • Worked on finishing up readings (about two hours)

Day 2 (6/13/17)

  • Worked on background research to try to find a topic to study (about five hours)
  • Met with Dr. Factor and did presentation. Went over what I should be working on. (about an hour)

Day 3 (6/14/17)

  • Worked on completing the ethics training quizzes and readings (about six hours)
  • Wasn't feeling well, so left early at about 3:30.

Day 4 (6/15/17

  • Worked from home- was home sick
  • Worked on taking Food Webs and finding their (1,2)-step competition graph (about six hours)
  • Wrote up information from the Food Webs with Tex and emailed to Dr. Factor (about two hours)


Day 5 (6/16/17)

  • Worked from home- was home sick
  • Read chapter 3 from Applied Combinatorics (Roberts) (about four hours)
  • Worked on reading background information to find a topic to research (about two hours)
  • Continued work on Food Webs (about an hour)

Reflection: End of Week 3

I feel that this a difficult week. I have been struggling to try to find a topic to research since I'm not really sure what I'm interested yet. It was also difficult since I was sick, so I was doing most of my work from home. I accomplished my goals of completing a presentation with Max that showed definitions and examples from the (1,2)-step competition number of a graph (Factor, et al.) paper. After the presentation, Dr. Factor told me to start exploring Food Webs and find their (1,2)-step competition graph. I was successful in this, and I feel that it was good practice for me to complete this work. I was also given the task to look at the question found in the paper that asks if there exists a graph G, other than C4, such that k(G)> k(1,2)(G). I have been having issues going about answering that question. I'm not sure how to start, so I haven't gotten too far. I will make sure to work on it next week before I meet with Dr. Factor.

I am nervous about not knowing what I'm doing yet, but after meeting with Dr. Factor on Tuesday, she informed me that this is normal. I will make sure to continue to explore various readings to try to figure out what I would like to do for the rest of the REU. I am hoping to have a topic chosen soon. Since I was unable to meet with Dr. Factor on Thursday (due to me being home sick), I am hoping to meet with her early next week to go over my work so far and future work.

Week 4 (6/19/17-6/23/17)

Day 1 (6/19/17)

  • Worked on finishing Chapter three in Applied Combinatorics (Roberts) (about three hours)
  • Continued work on Food Web work (about four hours)

Day 2 (6/20/17)

  • Explored question about graphs found in The (1,2)-step competition number of a graph (Factor, et al.) paper (about two hours)
  • Met with Dr. Factor. (about an hour)
  • Fixed work with food webs (about four hours)

Day 3 (6/21/17)

  • Continued work with Food Webs (about two hours)
  • Worked on answering question about competition number (about five hours)

Day 4 (6/22/17)

  • Worked on Competition Numbers practice (about six hours (split between morning and afternoon))
  • Met with Dr. Factor (about 30 minutes)
  • (Working Lunch (about an hour)

Day 5 (6/23/17)

Worked from home.

  • Worked on Competition Numbers practice (about eight hours)

Reflection: End of Week 4

I feel that I am starting to get an idea of where I will be taking this research. I am working on actual applications instead of just reading, which I enjoy. This week I worked on exploring different topics where I looked at food webs and competition numbers. This was a struggle at first since I wasn't sure where to start with the competition number, but after working with Dr. Factor, I feel much more confident with that I am working on. I am looking forward to continuing my work with this idea and presenting my findings in the mini presentations next week. I feel that I met all of my goals for the week, and this seemed to be a successful week.

Week 5 (6/26/17-6/30/17)

Day 1 (6/26/17)

  • Worked on Competition Number Practice (about three hours)
  • Attended talk on giving a good research presentation (about two hours)
  • Worked on mini presentation (about two hours)

Day 2 (6/27/17)

  • Worked on mini presentation for about eight hours
  • Practiced mini presentation at home for about an hour

Day 3 (6/28/17)

  • Worked on mini presentation for about eight hours
  • Practiced mini presentation at home for about an hour

Day 4 (6/29/17)

  • Practiced mini presentation at home for about an hour
  • Practiced mini presentation on campus for about two hours
  • Attended mini presentations for about 2.5 hours
  • Continued work on Competition Numbers (worked on C4 union C4 union C4) for about two hours

Day 5 (6/30/17)

  • Continued work on Competition numbers for about eight hours (worked from home)

Reflection: End of Week 5

During this week I completed many goals. I feel that I did well on my mini presentation. I know I still need improvement, but I don't think it went horribly. I have also completed a lot with my research involving the competition numbers. I have been figuring out a lot with the competition numbers, and I am excited to see what else I figure out. I am hoping to continue to learn more about this topic and improve what I already know in the upcoming weeks.

Week 6 (7/3/17-7/7/17)

Day 1 (7/3/17)

Day 2 (7/4/17)

Day 3 (7/5/17)

  • Worked on typing up findings with the competition numbers (about four hours)
  • Continued research with competition numbers (about six hours)

Day 4 (7/6/17)

  • Met with Dr. Factor and went over my findings (about an hour)
  • Attended working lunch and attended presentation about having a good poster (about two hours)
  • Worked on competition number research (about five hours)

Day 5 (7/7/17)

  • Worked on abstract for conference (about an hour)
  • Worked on competition number research (about five hours)
  • Worked on typing up findings (about three hours)

Worked over Weekend (7/9/17)

  • Worked on abstract for conference (researching how to do abstract/ typing it) (about three hours)

Reflection: End of Week 6

This week I feel that I completed my goals. I started applying for the conference, and am coming to a place where I can start writing proofs for my findings. I realized that what I was working on had to be changed since there were smaller competition numbers than what I was finding, but I was able to improve my work and can go on to writing proofs from there. In the next few weeks, I will be working on exploring other graph families, writing proofs, and preparing my presentations for the upcoming weeks.

Week 7 (7/10/17-7/14/17)

Day 1 (7/10/17)

  • Continued research on competition numbers (two hours)
  • Worked on editing abstract (one hour)
  • Worked on finishing the type ups of my findings (four hours)

Day 2 (7/11/17)

  • Typed up abstract in latex and edited it more (three hours)
  • Worked on creating paper outline (one hour)
  • Worked on C4 graph research (three hours)

Day 3 (7/12/17)

  • Finished up abstract and submitted application for conference (one hour)
  • Worked on C4 graph research (six hours)

Day 4 (7/13/17)

  • Typed up findings to give to Dr. Factor (one hour)
  • Met with Dr. Factor (one hour)
  • Working lunch (one hour)
  • Worked on paper outline (one hour)
  • Continued competition number research (four hours)

Day 5 (7/14/17)

  • Finished working on outline for paper and emailed it to Dr. Factor (one hour)
  • Continued competition number research (seven hours)

Reflection: End of Week 7

This week was very successful. I made a lot of progress in my research. In addition, I completed my goals of meeting with my mentor and presenting her with my outline for my paper. I am prepared to get started on my paper and to start working on writing up proofs for my research findings. I will work on those in the weeks to come.

Week 8 (7/17/17-7/21/17)

Day 1 (7/17/17)

  • Begin work on proof for research findings (8 hours)

Day 2 (7/18/17)

  • Finalize proof write-up (8 hours)

Day 3 (7/19/17)

  • Work on poster draft (four hours)
  • Write up findings for meeting (four hours)

Day 4 (7/20/17)

  • Finish poster draft (two hours)
  • Met with Dr. Factor (one hour)
  • Working lunch (one hour)
  • Work on fixing proof (four hours)

Day 5 (7/21/17)

  • Work on fixing proofs (four hours)
  • Work on fixing poster (four hours)

Reflection: End of Week 8

This was another successful week. I was able to get the draft of my poster done and submitted. I also worked on writing up a proof for one of my research findings (this was pretty exciting for me). I have a lot of changes to make on both, but I will be able to fix them in the upcoming week.

Week 9 (7/24/17-7/28/17)

Day 1 (7/24/17)

  • Worked on editing poster (four hours)
  • Worked on starting paper (four hours)

Day 2 (7/25/17)

  • Worked on editing poster (four hours)
  • worked on research (four hours)

Day 3 (7/26/17)

  • Edited and submitted poster (two hours)
  • Worked on research (six hours)

Day 4 (7/27/17)

  • Attended working lunch (two hours)
  • Worked on paper (two hours)
  • Worked on research (four hours)

Day 5 (7/28/17)

  • Worked on proof/paper/research (eight hours)

Reflection: End of Week 9

This week was spent preparing to wrap everything up for the REU. I was able to submit my poster (on time) and begin to finalize all of my findings. Next week I will be finalizing my paper and preparing a presentation.

Week 10 (7/31/17-8/4/17)

Day 1 (7/31/17)

  • Work on presentation (eight hours)

Day 2 (8/1/17)

  • Attend poster session (two hours)
  • Meet with Dr. Factor (one hour)
  • Edit/finalize presentation (five hours)

Day 3 (8/2/17)

  • Practice presentation (two hours)
  • Attend presentations (four hours)

Day 4 (8/3/17)

  • Attend presentations (two hours)
  • Work on paper (two hours)

Day 5 (8/4/17)

  • Finalize and submit paper (eight hours)

Reflection: End of Week 10

This is the last week of the REU. I was able to accomplish a lot in the short ten weeks. I was able to partially answer a research question by finding two graphs in which the competition number was greater than the (1,2)-step competition number. This week was very busy since I had to present my poster in the poster session, give a presentation, and finish my paper. I was able to successfully get everything done, though.

Artifacts

Retrieved from "https://reu.cs.mu.edu/index.php?title=User:Babcock&oldid=2792"