Understanding what sections of your paper are graded and how they are graded is crucial to the development of your paper. ** This rubric is for 2015 ONLY.
This paper demonstrates a sufficient understanding of the first contest problem, but the competitors need to further enhance their math skills in order to develop an effective model for this problem.
Using normal distribution, this model solves the problem in an easily understandable manner, but lacks proper analysis. Better explanation and organization could largely improve this paper.
The first AoCMM competition hosted 111 teams from 13 different countries, and a variety of backgrounds. Most of the teams have never participated in any math modeling competitions before, making AoCMM their first exposure in the field. AoCMM primarily focuses on bringing math modeling to those who have never been exposed to this fascinating field before, so we are glad to see so many students interested in math modeling! Most of our competitors are high school students, a group that is hugely underrepresented in the field of math modeling.
Unlike most other competitions, AoCMM gives competitors the option to solve two problems of different types, as well as not requiring that both problems be completed. Competitors could choose either one or both to complete. We believe that this ensures the teams have the chance to demonstrate a more thorough understanding of math modeling through their reports, allowing judges to provide more detailed feedback on every aspect of their abilities.
|Type||# of Winners||Percentile||Award|
|Grand Prize||1||Top 1%||$4392|
|Alpha Prize||2||Top 3%||$300|
|Beta Prize||5||Top 8%||$100|
|Gamma Prize||8||Top 15%||None|
The math modelers were given 72 hours to model and report on the following two problems with their teams:
1. How should a professor distribute the difficulty of problems on a test to ensure that a group of students, with varying abilities, will form an ideal distribution?
2. We would like to position N GPS satellites, making sure that at least 90% of the world's population can get their location using the GPS system accurately at least 95% of the time. What is N and what is the constellation needed to achieve it?
- Keep in mind that a minimum of 4 satellites are needed to get a solution (time difference is also an unknown).
- You may "place" your satellites in any orbit you like (i.e., the altitude need not be the one used by GPS systems today).
- Background on the GPS systems:
- Laws and Policies:
"The first annual AoCMM competition was a great experience for our entire team. None of us had ever done any modeling competitions before so the entire ordeal was new to us. The four of us came into the competition with varying levels of experience but we all gained something from participating.
For future competitors, some things to keep in mind are manage your time well, bring your enthusiasm, and be ready for an intellectual marathon! It is important to plan out exactly what you want to accomplish and set goals for your group to avoid cramming and stressing an hour before the submission deadline. Be sure to clear your weekend and set aside more time than you think necessary as some parts may take longer than expected. At the same time, schedule hour long breaks and get enough sleep to let your mind rest, recuperate, and work more efficiently.
Overall the competition was a great way for us to improve in a variety of skills including modeling and teamwork. We would recommend AoCMM to anyone!"
Team members: Charlin Duff, Audrey Kurz, Ethan Kurz, and Dimitriye Danilovic
Award: Best Composite Score and Thinktank Learning Prize winner ($500 cash + $4399 Thinktank Credit)
Team members: Zihong Chen and Zhengzhi Liang
Award: Best Problem 2 Score and π Prize winner! ($314 cash)
"AoCMM 2015 is my first math modeling contest-----it was really fun and intriguing! The problems were really challenging, especially the second one, since the functioning GPS was something that my friend and I were totally unfamiliar with. And the hard part lies in the limited time, during which we needed to pore over background information, form our ideas, write the solution and computer programming....
Since we had only two people in the team, there indeed ain't enough time for us to track all these issues, so we decided to focus more on building the model and analyze the approach we use than programming and seeking numerical result (Another reason was because neither of us was proficient in programming).
Our models were built on our own interpretation of the problems, and we tried to make them as specific as possible. For example, we illustrated a test design depending on student profile (problem 1), and used matrices to represent the input (student profile) as well as the output (expected score). We also defined the ideal score distribution to be the normal distribution. In our solution to the second problem, we simplifies the problem by analyzing two time-independent GPS constellations. We also designed ways to test instant visibility and compute the expected visibility period of a location on earth in order to ensure the functioning of the system.
During the competition, Zhengzhi and I cracked the first problem together, and as I started to formulate down our ideas and write the solution paper, Zhengzhi set out for background information on GPS. This is just a way to save time and make efficiency. (Well, after the three-day competition, I think I would recommend coming with a team of three or four. This will make everyone more focused and less stressed.) After all, it's truly a great experience with AoCMM. Look forward to attending next year!"
"We want to thank AoCMM and all the judges for letting us compete in this competition. We felt that it was very beneficial and that we truly learned a lot."
Team members: Kevin Yang, Raman Kathuria, and Kedar Thakkar
Award: Maplesoft Prize Winner! (Maple 2015 Student Edition *2)
Team members: Guodong Zhang, Hongkai Yu, and Xuanang Xiong
"We had a wonderful experience participating in this global modeling competition, on account of which we appreciate AoCMM for organizing as well as providing us the opportunity to compete with undergraduates and teenagers around the world. By taking this challenge, we not only embraced the chance to study and practice mathematical modeling but also appraised our academic abilities. Also did we realized that, frankly, we still have a long way to go.
However, taking part in this competition really triggered our interests in exploring further and deeper in the field of modeling as well as math. Given more time, we would be able to make significant progress while confidently prepare for the next time.
We're grateful for the honorable mention and deem it an encouragement!"
|890||Grand Prize||Charlin Duff, Audrey Kurz, Ethan Kurz, and Dimitriye Danilovic||Best Composite Score and Thinktank Learning Prize winner!|
|861||Alpha Prize||Chang Zhou, Yunfan Sun, and Rui Shen||Best Problem 1 Score and π Prize winner!|
|985||Alpha Prize||Zihong Chen and Zhengzhi Liang||Best Problem 2 Score and π Prize winner!|
|862||Beta Prize||Hongxiang Jia, Yue Ying, Hua Ding, and Xuebin Gui||Second Composite Score|
|863||Beta Prize||Jianxiang Chen, Runhua Wu, Jiayun Wu, and Zhiyao Tang||None|
|868||Beta Prize||Sitan Liu, Zhicheng Kai, Yuze Li, and Wei Zhan||None|
|873||Beta Prize||Kevin Yang, Raman Kathuria, and Kedar Thakkar||Maplesoft Prize Winner!|
|928||Beta Prize||Sid Satya, Aditya Pimplaskar, Adi Menon, and Srikar Boinapally||Art of Problem Solving Prize Winner!|