Projects
Overview
This page provides details on projects I have run in the past, with
links to project reports or posters where available.
The projects fall under four general themes:
Some projects (such as most of the projects under the latter four themes)
are conducted under the framework of the Illinois Geometry Lab (IGL),
and require formal applications through the IGL. Others are run
as independent projects in small groups of two or three students, and
arranged directly with the students, with the option (but no requirement)
of earning course credit in
Math 492 (Undergraduate Research in Mathematics) or
Math 390 (Guided Individual Study). The latter format
allows greater flexibility in terms of deadlines, time commitment,
and team composition. These projects can in principle be arranged at any
time, but are usually finalized at/near the beginning of the semester.
If you are interested in such a project, just contact me directly (email
ajh@illinois.edu, attach your cv and transcript).
For upcoming projects and research opportunities see my Undergraduate
Research Page.
 General description:
This project is the outgrowth of the Campus Honors (CHP) courses,
Math
199 CHP: Probability and the Real World, and
Math
199 CHP: Mathematics of Games, Sports, and Gambling,
that I have been teaching for the past several years. Its goal is to
seek out and explore interesting realworld problems of statistical
flavor in sports, finance, society, and everyday life.

Qualifications:
The specific background and skills required depend on the particular
project, but the projects typically require at least one of the following
qualifications: (1) advanced statistical background (with multiple 400
level courses); (2) a high level of experience with data mining and
machine learning through projects and/or courses; (3)
expertlevel programming skills in R or Python; (4) experience working in
a Unix/Linux commandline environment and writing shell scripts.
 Past projects:
Click on titles for links to posters.

Data Mining MSFE Program Admissions (Spring 2019).
(Danjing Jiang, Peiyun Zhu)

Comparing University Rankings (Summer 2018).
(Weiru Chen, Qianqian Li)

Data Mining Math Graduate Admissions (2017  2018).
(Jianqiu Kong, Jiahao Zhu, Ruorong Yin, Hao Qiu, Pengyu Chen)

Analysis of AP College Football and Basketball Polls (Summer/Fall 2018).
(Sam Guo, Qingqing Yang, Carson Zhang)

Distinguishing Cause and Effect (2017  2018).
(Xinying Fang, Shuyu Wang; Eli Yu, Yuxuan Ren, David Zhang)

Statistical analysis of weather forecasts (2016  2017).
(Mario Cannamela, Yajie Chu, Sijia Huo, Yantong Zheng,
David Zhang, Yayu Zhou)

Zipf's Law (Summer 2016).
(Daniyar Omarov, Khoa Tran, Laila Zhexembay)

Knowledge Spaces (coadvised by Dr. Michael Santana)
(Summer 2016).
(Qingci An, Madina Bolat, Jose Sanchez)

Statistical analysis of Daily Illini College Football Predictions
(Fall 2015).
(Qing Ma, Yayu Zhou)

Detecting nonrandomness (2015  2017).
(Tong Li, Jiarui Xu, Xusheng Zhang Victor Sui)

Benford's Law (Summer 2015).
(Narken Aimambet, Chingis Matayev, Alisher Urazbekov)

The Fake Randomness Project (2014).
(Jiachun Chen, Chad Franzen, Rishabh Marya, Robert Weber, Xin Wei)
 General description.
The goal of these projects is to create interactive Mathematicabased
visualizations of interesting mathematical topics and make these
available to a broader audience through publication at the
Wolfram Demonstrations website,
http://www.demonstrations.wolfram.com.
Topics will be
chosen based on the backgrounds and interests of the participants, and will
typically be at an advanced undergraduate or honors level. Past projects
have covered topics such as
the Coupon Collector Problem, the Ballot Problem,
Lagrange Multipliers, Harmonic Functions, Random Walks based on digits of
Pi and similar famous numbers, and Random Walk Solutions to PDEs.
See the links below for projects reports and demonstrations created in
past projects.
 Qualifications.
Prior experience with Mathematica, or evidence of strong general coding
skills, is highly desirable. Students are expected to be comfortable
with using Mathematica by the start of the project. Students should also
have a solid mathematics background, at the level of an A grade or
better in Calculus III.
 Past projects.
Click on titles for project reports.

Wolfram Demonstrations created in past projects.
 General Description.
The projects under this theme deal with mathematical questions arising in
game theory, voting theory, and related areas at the interface of
mathematics and economics.
 Qualifications.
A strong mathematical background is essential, and additional background
in economics, and especially game theory, is desirable. The projects
are particularly aimed at students who are double majors in Math and Econ
or Statistics and Econ. For many of the projects, strong coding skills
in Python or R or Mathematica are also required.
 Past projects:
Click on titles for project reports or posters.

The Mathematics of Pokerlike Games (Fall 2018).
(Kyle Begovich, Xiangyun Cao, Philip Dohm, Mengyang Zheng, Qiaoge Zhu)

The Mathematics of Poker (Fall 2017  Spring 2018).
(Tanner Corum, Jiayin Lu, Carl Tang, Alex Wang, Ajay Dugar, Kevin
Grosman)

The Mathematics of Poker (Fall 2016  Spring 2017).
(Matt Romney (graduate student), Nick Brown, Junghyun Hwang,
Ziyang Liu, Ki Wang, Yanxuan Wang, Ruoyu Zhu)

The Mathematics of Poker (Summer 2017)
(Xinying Fang, John Haug, Sultan Muratov, Sara Rat, Blandon Su, Fan Wu,
Ruoyu Zhu)

The Geometry of Voting (Fall 2015  Spring 2016).
(Matt Romney (graduate student), Daoyu Duan, Vivek Kaushik,
Aubrey Laskowski, Zelin Li, Yukun Tan, Mengzhou Tang)
 General description:
Randomlike behavior is ubiquitous in number theory. For example, the primes,
the digits of pi or other famous constants, and the Moebius function and other
numbertheoretic functions, all appear to behave much like appropriately
defined "true" random sequences. In this ongoing project we seek to explore
such random features experimentallyfor example, via large scale
computations and geometric visualizations as random walksand possibly also
theoretically.
 Qualifications: The desired background depends on the
specific project. For projects that fall mainly on the experimental side,
strong coding skills in Python and/or C/C++ and/or Mathematica are essential.
Experience with solving coding challenges from Project Euler would be a plus. For
more theoretically oriented projects, students should have a strong
general math background with A grades in key math courses, including Math
453 (Elementary Number Theory).
 Past projects:
Click on titles for links to project reports or posters.

Experimental Number Theory (2016  2018).
Mini projects at the interface of Number Theory and
Computation, in the spirit of Project Euler.
(Phillip Harris, Xinwei He, Thien Le, Yuchen Li, Zihe Wang, Yunyi Zhang,
David Zhang)

Beatty Sequences, Exotic Number Systems, and Partitions of the Integers
(joint with Prof. Ken Stolarsky) (Fall 2017  Spring 2018).
(Junxian Li (graduate student); Mark Cao, Weiru Chen, Xinxin Chen,
Jared Krandel, Stephen Fan, Matthew Cho, Jared Krandel, Xiaomin Li, Yun Xie)

Randomness in leading digits of numbertheoretic sequences (Fall 2015 
Spring 2016).
(Junxian Li (graduate student), Zhaodong Cai, Yewen Fan, Matthew Faust,
Kevin Kwan, Yuda Wang, Shunping Xie, Yuan Zhang)

NumberTheoretic Fourier Series (Spring 2015)
(Junxian Li (graduate student);
Yu Fu, Ryan Grady, Yuda Wang, Jia Yu)

Power series with numbertheoretic coefficients (2014  2015).
(M. Tip Phaovibul (graduate student), Yiwang Chen, Keran Huang)

Randomness in Number Theory:
The Moebius Case (2013  2014).
(M. Tip Phaovibul (graduate student), Yiwang Chen,
Daniel Hirsbrunner, Dylan Yang, Tong Zhang)

Numbertheoretic Random Walks
(Spring 2013).
(M. Tip Phaovibul (graduate student), Yiwang Chen,
Wenmian Hua, Natawut Monaikul, Tong Zhang; Spring 2013)

The Quadratic Residue Random Walk
(Fall 2012).
(M. Tip Phaovibul (graduate student), Yiwang Chen, Yusheng Feng, Mateusz
Wala)
 General description:
In this project we seek out
and explore interesting problems in ndimensional space that
are accessible at the calculus level, but rarely covered in standard
calculus courses. Such problems are often motivated by applications to
probability and statistics or other areas. They tend to have a broad
appeal and make for ideal topics to present at outreach events.
They also lend themselves naturally to geometric visualizations, and
can make excellent candidates for creating interactive Mathematicabased
visualizations.

Qualifications:
Students should have taken Math 241, preferably in the honors version,
with a grade of A or better, or be concurrently enrolled in an honors
section of Math 241. Beyond strong calculus skills, there are no formal
prerequisites, and the project can accommodate a broad range of
interests, backgrounds, and majors. Experience with Mathematica
visualizations is helpful, but not required.
 Past projects.
Click on titles for project reports.

The Broken Stick Problem in Higher Dimensions (2014  2015).
(Josh Adkins, Alex Page, Aditya Patel, Yuliya Semibratova,
Yao Xiao, Yi Xuan, Rui Zhang)

Random Triangles (Fall 2013).
(Zehan Chao, Liran Chen, Hao Gao, Mianfeng Liu, Gilad Margalit)

Intersecting Cylinders in n Dimensions (2012  2013).
(Lingyi Kong, Luvsandondov Lkhamsuren, Abigail Turner, Ananya Uppal)

The Broken Stick Problem with n Pieces (2012  2013).
(Lingyi Kong, Luvsandondov Lkhamsuren, Abigail Turner, Ananya Uppal)
Back to Undergraduate Research Group Page
Last modified: Sat 01 Jun 2019 12:08:15 PM CDT
A.J. Hildebrand