Current and Past Undergraduate Research Projects

Rational Numbers for which the Generating Function of a Sequence is Integer Valued

Mentor: Dr. Andrew Bulawa

Student: Danial Mohktari

Abstract: The generating function of a sequence is the power series having that sequence as its coefficients.  It has been proven that, for the Fibonacci sequence {f_n}, any rational number x for which F(x) is an integer, is expressible as a quotient of consecutive terms in the sequence, i.e., x = f_n/f_(n+1) (Bulawa-Lee, 2017).  In this project we explore what other sequences have this property.

The Eigenvalues of Markov Transition Matrix

Mentor: Dr. Haishen Yao

Student: Jiawei Ren

Efficient Class Scheduling System Using Innovative Web Technologies (React)

Mentor: Dr. Kwang Kim

Student: Brian Ryu

Abstract: This project is based on a real problem we have in the Mathematics and Computer Science department here at Queensborough Community College. The Math & CS department has over 120 members in the faculty and offers more than 250 classes. However, we have a limited number of class rooms and managing class schedules is difficult. The Math & CS department currently uses an Excel spreadsheet to manually generate schedules and it is difficult to create schedules manually that match with the schedules of the respective faculty. In this project, we investigate a possible algorithm which generates class schedules taking into account faculty members’ preferences. It may require building combinatorial data structures and finding ways to optimize such structures. The student will test some well-known data structures with existing schedules to find the best possible structure. He will also make a valuation method to measure the efficiency of the generated schedules.

Big Data Information Inference on the Infinite Communication Tree Network of DNA Evolution

Mentor: Dr. Wenjian Liu

Student: Jiayao Sun

Abstract: The big data information reconstruction problem on the infinite communication tree network, is to collect and analyze massive samples at the n-th level of the phylogenetic tree to identify whether there is non-vanishing information of the root, as n goes to infinity. Although it has been studied in numerous contexts such as information theory, genetics and statistical physics, the existing literatures with rigorous reconstruction thresholds established are very limited. In this project, we focus on the form of signals' probability transition matrix corresponding to a classical DNA evolution model which allows the existence of a guanine-cytosine content bias. The corresponding information reconstruction problem in molecular phylogenetics will be explored, by means of the refined analysis of moment recursion on a weighted version of the magnetization, concentration investigation and in-depth investigation on the resulting nonlinear second order dynamical system. Our purpose is to figure out under what condition of the base frequencies of adenine and thymine is the reconstruction solvable.

Noncommutative Geometry of Finite Sets

Mentor: Dr. David Pham

Student: Gurpal Singh

Abstract: The notion of differentiation is central to calculus. An interesting problem is whether the idea of differentiation can be extended to functions on a finite set X. The subject of noncommutative geometry provides a solution to this question with the idea of a first order differential calculus (FODC). My research project is to study certain properties of FODCs as they pertain to group actions on X. Due to the severe time constraint, my talk will focus exclusively on introducing and motivating the idea of FODCs over F(X), where the latter is the algebra of functioins on X.

Application of Principal Component Analysis on a Business Data

Mentor: Dr. Yusuf Danisman

Student: Diya Patel

Abstract: Principal Component Analysis (PCA) is one the most common dimension reduction techniques that can be used to reduce the dimension of a given large data without losing too much information. It can be also thought as finding the hidden structures of a large data.  In this project PCA will be applied to some public data to (1) reduce the dimension of the data; (2) visualize the data; (3) do some estimations about the data by using some regression methods.  For the accomplishment of the project, the mathematical background of PCA should be understand well and also to apply PCA as a programming language Matlab or Python will be needed. 

A Numerical Investigation of the Schrodinger Equation

Mentor: Dr. Andrew Bulawa

Student: Arthur Rozario

Abstract: We study solutions to the Schrodinger equation, an equation which describes the behavior of atomic and subatomic particles/systems.  This involved research on partial differential equations, numerical analysis, and quantum mechanics.  The Maple mathematics software was used to generate approximate numerical solutions and animate their evolution over time.  The student created and presented a poster midway through the semester and presented his research at the honors conference at the semester's end.

Turing machine to determine the winner of a tic-tac-toe game

Mentor: Dr. Whan Ki Lee

Student: Nitika Pandey

Abstract: Build a Turing machine that determines the winner of a tic-tac-toe game: an input is a tic-tac-toe game which is already played and represented in a sequence of O, X, and B (blank), and the Turing machine will tell who wins the game.  The student researched Turing machines and built the required Turing machine.  She presented her research at the honors conference.

A look at Class, Race, and Policing in Our Communities - A statistics project

Mentor: Dr. Mercedes Franco

Student: Tiana Freeman (Criminal Justice major)

Abstract: We are interested in policing practices in NYC and looked at some of the “best” and “worst” public schools in NYC, the communities they serve and their interactions with police. The student worked with data from the NYC Public Schools reports and the NYPD Stop-Question-and-Frisk Activity reports and used Excel to organize and analyze data, identifying and testing the significance of correlations among some of the variables of interest. As part of the research experience, my student completed training in the Responsible Conduct of Research (RCR) and attended a QCC Library Information Literacy workshop. She attended several events on campus on related topics such as a presentation by the NYC Civilian Complaint Review Board and also interviewed a police officer.  She also presented her work at the honors conference at QCC.

Tiling by geometrical shapes

Mentor: Dr. Azita Mayeli

Student: TingWei Zhao

Abstract: We studied tiling properties of two kinds of shapes with which a complex plane (xy-plane) can be tiled using finitely many matrix operations.  For example, see the mosaic floor in your classroom!  Mosaics have square shape and by lifting them up and down or left and right we can cover the entire classroom. A non-trivial example is a triangle. How can one fill in the floor of the class room only with triangles?  This is the question that TingWei answered in his project.  The project was funded by the MSEIP program from the Biology department. And the student presented his work at the Honors Conference.