Mathematics

Student Research

Note: Research Projects/Presentations denoted with a "" are from the Applied and Computational Mathematics Graduate Program.

Three graduate students from Professor Chuan Li's MAT 555 Industrial Mathematics Practicum presented their research projects at the WCU Research and Creative Activities Day event on April 17, 2024. Two of them won  graduate student oral presentation awards.

Nathaniel Jones (first place winner), A Machine Learning Approach to Solve Partial Differential Equations .

Abstract: Artificial Intelligence (AI) techniques have advanced significantly and are now used to solve some of the most challenging scientific problems, such as Partial Differential Equation models in Computational Sciences. In our study, we aimed to explore the effectiveness of a specific deep-learning technique called Physics-Informed Neural Networks (PINNs) for solving partial differential equations. As part of our numerical experiment, we solved a one-dimensional Initial and Boundary Value Problem that consisted of Burger's equation, a Dirichlet Boundary condition, and an initial condition imposed at the initial time, using the PINNs. We examined the effects of network structure, learning rate, batch size, and other factors that influenced the network output and characterized the tradeoff between training speed and solution quality. In addition, we solved the problem using the standard Finite Difference method. We then compared the performance of the PINNs with the standard numerical method to gain deeper insights into the efficiency and accuracy of the PINNs.

Johnathan Makar (third place winner), Pennes Bioheat Equation .

Abstract: This research is in conjunction with Dr. Li’s research into Magnetic Fluid Hyperthermia, a cancer treatment alternative. In this research, we analyze Harry Pennes Bioheat Equation. The goal is to find the best coefficients to get the analytical and numerical solution as close as possible. For simplicity, we are starting by analyzing the 1-dimensional case before moving onto the 2-dimensional and 3-dimensional cases. If the propagation of heat can be understood and modeled accurately, this will allow us to continue further into the Magnetic Fluid Hyperthermia research. By understanding and finding the best coefficients for the Bioheat Equation, we can then begin trying to apply this to irregular domains such as tumors and see how heat would propagate throughout the mass. Ultimately, with the research done on the Bioheat Equation, we hope to give Dr. Li a leg up on his research towards modeling Magnetic Fluid Hyperthermia, ultimately leading to a better way of fighting cancer.

Benjamin Pentecost, Improved Augmented Matched Interface and Boundary (IMIB) Method for Solving Problems on Irregular 2D Domains

Abstract: A new method called Augmented Matched Interface and Boundary (AMIB) has been developed to solve partial differential equation models, such as the heat equation, over irregular two-dimensional domains. The original AMIB method features unique numerical treatments to solve problems with various boundary conditions and shapes, resulting in highly accurate and efficient numerical solutions. However, recent numerical experiments have revealed that the original AMIB method can fail when dealing with sharply curved boundaries. To address this issue, new numerical techniques have been introduced in our latest work to enhance the robustness of the AMIB method. These techniques have been numerically verified to improve the accuracy and efficiency of the AMIB method when solving various problems with sharply curved boundaries. Due to its success, we plan to use this method to simulate Magnetic Fluid Hyperthermia (MFH) cancer treatment by solving the Pennes Bioheat Equation on a domain that consists of a tumor and the surrounding healthy tissue.

Some past and current students recently gave presentations at  the Fall 2023 meeting of EPaDel held November 11, 2023 at Villanova University.

Dachao Sun is a current mathematics graduate student at West Chester University. His talk was entitled Fourier Inversion of Moment Generating Functions.

Abstract:  Moment generating functions (MGFs) are a insightful tool in probability theory and statistics, which shares the identical form of a two-sided Laplace transform. In a typical progression of the introduction MGFs, a look-up table is usually present in purpose of finding the corresponding probability distribution from which an MGF is calculated by summation or integration. Here, we will start from the definitions of integral transform and (exponential) Fourier transform, and delve into the general case of moment generating functions, and then perform a "Fourier inversion" to get back to the probability density function, using the Fourier transform as a wrapper tool.

Alexander Furia, former West Chester mathematics student, recently received his PhD in mathematics from Drexel University. He is presently Assistant Professor of Mathematics at Chestnut Hill College.  His talk was entitled The Many Pitfalls of Computers and the Ladder of Verification:

Abstract:  Numerical computation power has increased drastically over the past few decades. This numerical power has resulted in many benefits for mathematicians. However, while computers do provide an amazing resource, many pitfalls exist that make numerical results difficult to obtain. In this talk we will explore the many issues that can arise when trying to obtain numerical data in a scattering problem and a present the ladder of verification used to ensure accurate results.

Kenneth Gill, former Westchester mathematics student, is currently completing his PhD at Penn State. His talk was entitled Probabilistic automatic complexity of finite strings.

Abstract:  We define a new complexity measure A_P(x) for finite strings x using probabilistic finite-state automata (PFAs), inspired by similar existing notions that use deterministic and nondeterministic automata. AP(x) is the smallest size of a PFA for which x is the most likely string to be accepted among those of the same length. In this talk, we survey the results that have been obtained so far, including a complete classification of the binary strings with A_P(x)=2, and discuss future directions of research.

CSM Research Poster Session  12/7/2022

Evan Parker, a student of Laura Pyott,  won 3rd place in the CSM Celebrates Poster Session in December. Here is Evan's poster .

Recent Student Publication

It has been some time since we highlighted student publications.

• In Fall 2022, John Aceti (current MA student who will graduate in Fall 2022) and Professor Jeremy Brazas wrote a paper,  "Elements of higher homotopy groups undetectable by polyhedral approximation", which has been submitted for publication.
• In Fall 2021, Sarah Emery (previous student in the MA program, now graduated (having completed a thesis under the supervision of Professor Shiv Gupta) and currently teaching at Delaware County Community College) and Professor Jeremy Brazas wrote a paper,  "Free quasitopological groups", which has been submitted for publication.
• Eric Boerman (MS student in the Applied and Computational program), working with Professor Chuan Li, was a co-author of the paper "A Fast Sine Transform Accelerated High-Order Finite Difference Method for Parabolic Problems over Irregular Domains", which has been submitted to the  Journal of Scientific Computing
• Mark McGowan (former MS student in the Applied and Computational program) , working with Professor Chuan Li, was a co-author of the paper "A Newton-like iterative method implemented in the DelPhi for solving the nonlinear Poisson-Boltzmann equation",  which appeared in Mathematical Biosciences and Engineering 2020, Volume 17, Issue 6.
• Cameron Campbell (former MS student in the Applied and Computational program) and Stacy Ashlyn (former undergraduate student in the  Applied and Computational program) , working with Professor Chuan Li, were co-authors of the paper "Alternating direction ghost-fluid methods for solving the heat equation with interfaces",  which appeared in Computers & Mathematics with Applications Volume 80, Issue 5, 1 September 2020, Pages 714-732.

Updated bibliographic information for papers previously submitted:

• J. Brazas, P. Gillespie, Topological monoids are transfinitely pi_1-commutative. Topology Proceedings 57 (2021) 1-14.
• J. Brazas, P. Gillespie, Infinitary commutativity and abelianization in fundamental groups. Journal of the Australian Math. Soc. 112 (2022), no. 3, 289-311.
• J. Brazas, P. Gillespie, Fundamental groups of James reduced products. Topology Appl. 317 (2022) 108193.

A big "thank you" to Professor Chuan Li for the extra effort he made in the Spring 2022 semester to collect and organize the names of the students and their presentation titles,  all files for the posters, the pictures of the students and the various videos from the two Spring 2022 student research events, all of which were used to create the record of these events found immediately below. Here is a video Professor Li put together from these materials.

CSM Research Poster Session 5/2/2022

The Mathematics Department was also well represented at the  CSM Student Recognition Ceremony held on Monday, May 2nd, 2022 (the CSM record of the event may be accessed here ).

Katie DeRosa (undergraduate), a student of Professor Barbara Swartz, was the 2nd place winner of undergraduate student poster presentations.

Katie DeRosa (undergraduate), with her poster presentation "Investigating the Impact of “Take Home Manipulative Kits” on Teacher Candidates Self-Reported Growth in Their Mathematical Content Knowledge Dispositions".

Several students of Professor Laura Pyott also presented posters (see below for links to individual posters).

Some students of Professor Laura Pyott, who presented posters at the CSM Poster Session

Emma DeLuca (undergraduate) presented the poster entitled "The Jewish Relief Agency Services Received 2022 vs 2020 ".

Gianna LaFrance (undergraduate) presented the poster entitled "JRA Client food Insecurity: Post Pandemic ".

Boning Liu  presented the poster entitled "Comparison of Food Insecurity Among Holocaust Survivors from 2020 to 2022 ".

Jack Ross (undergraduate), with his poster "Assistance for Elderly Households in Philadelphia ".

Julia Zelinsky (undergraduate) with her poster entitled "Rising Food Insecurity in Philadelphia Families due to COVID-19".

Here is a video of Julia discussing her poster.

Three students of Professor Chuan Li, Brendan Coffey (undergraduate, speaker), Julia Zelinsky (undergraduate) and Eric Boerman (graduate) presented a poster "Development of a Numerical Solver for Modeling Magnetic Hyperthermia". Here is a short video of Brendan discussing the poster.

Research and Creative Activity Day 4/29/2022

Several students from the Mathematics Department participated in the Spring 2022 Research and Creative Activity Day.

Two groups of students working under the supervision of Professor Chuan Li gave oral presentations.

Students Eric Boerman (graduate, speaker), Brendan Coffey (undergraduate) and Julia Zelinsky (undergraduate)   worked on the project "Developing an FFT-Accelerated High-Order Solver for Heat Equations Over Irregular Domains ".  Eric was a 2nd place winner of graduate student oral presentations.  Here is a video of Eric delivering the presentation.

Students Scott Moon (graduate, speaker), Corey Zhang (graduate) and Chhatra Sule (undergraduate) worked on the project "Cardiac Action Potential – The Luo-Rudy Model ". Scott was a 2nd  place winner of graduate student oral presentations. Here is a video of Scott making the presentation.

Scott and Eric with their awards, with Professor Chuan Li.

Three students of Professor Laura Pyott, Austin Eveland (undergraduate), Sehrish Khan (undergraduate) and Evan Parker (undergraduate), gave poster presentations (see below for links to individual posters, if they are available).

Austin Eveland (undergraduate) with his poster "Uncovering Utility: Analysis of Monthly Food Box Subscriptions"

Evan Parker (undergraduate) with his poster "Food Box Preferences: Ukrainians vs. Non-Ukrainians".

Sehrish Khan (undergraduate) with her poster "Analyzing Response Disparities Between Food Needs and Overall Satisfaction of JRA in Holocaust Survivors".

In Spring 2022, John Aceti won a Scholarly Research & Creative Activity (SRCA) Award, and he gave an oral presentation at the Research and Creative Activity Day in Fall 2022 as part of his acceptance. John also won an award for his presentation at this years Research and Creative Activity Day.

John also received the first Viorel Nitica Mathematics Scholarship at the Department Of Mathematics 35th Annual Awards in November 2021 and Dr. Jeremy Brazas received an RAWA to collaborate on  research with John.

Research and Creative Activity Day 4/29/2021

Eric Boerman (graduate student,  Applied and Computational Mathematics (A&C) Program, working with Professor Chuan Li) won 1st place for his oral  presentation in the Research and Creative Activity Day held on Thursday 4/29/2021 (see the Promotional Flyer ).

Eric's presentation was entitled

Parallel Computing of Action Potentials in the Hodgkin-Huxley Model via the Parareal Algorithm

and was joint work with Khanh Pham and Katie Peltier

Mathematics graduate students Mick Bauer and Henry Brown, also working with Professor Li, presented in this Research and Creative Activity Day also. Mick Bauer's presentation was entitled

Solving the Heat Equation with Interfaces

and was joint work with Rex Llewellyn and Shauna Frank. Henry Brown's presentation was entitled

Solving Parabolic Interface Problems with a Finite Element Method

Congratulations to everyone for their excellent work.

 CSM Research Poster Session 4/27/2021

Some students of Professor Chuan Li presented posters at the CSM Research Poster Session, on Tuesday 4/27/2021.

Rex Llewellyn (graduate student,  Applied and Computational Mathematics (A&C) Program) presented a  poster entitled

Matched Interface and Boundary Method for Solving the Heat Equation with Interfaces

and which was joint work with Shauna Frank (above) and Michael Bauer.

    

Khanh Pham (graduate, A&C program) and Katherine Peltier (undergraduate, A&C BS), presented another poster entitled

Parallel Computing of Action Potentials in the Hodgkin-Huxley Model via the Parareal Algorithm

and which was joint work with Eric Boerman.

Congratulations to all of them for their excellent work.

Student Publications

Patrick Gillespie, who is now a PhD student at The University of Tennessee, Knoxville, wrote three papers with Dr. Jeremy Brazas. One is published, one is accepted, and the other is still under review.

• J. Brazas, P. Gillespie, Topological monoids are transfinitely pi_1-commutative. Topology Proceedings 57 (2021) 1-14.
• J. Brazas, P. Gillespie, Infinitary commutativity and abelianization in fundamental groups. To appear in the Journal of the Australian Mathematical Society. 2020. https://doi.org/10.1017/S1446788720000427
• J. Brazas, P. Gillespie, Fundamental groups of James reduced products. Submitted for publication. 2020.

Evolution in Philadelphia Conference (EPiC), September 8, 2018, at the Academy of Natural Sciences in Philadelphia.

Two students of Dr. Allison Kolpas, graduate student Lane D’Alessandro and undergraduate student Jeremy Budgeon , presented posters at the Evolution in Philadelphia Conference (EPiC) on Saturday, September 8th at the Academy of Natural Sciences in Philadelphia.

 Paper Published in the Bulletin of Mathematical Biology

The paper “Optimal Mating Strategies for Preferentially Outcrossing Simultaneous Hermaphrodites in the Presence of Predators” has been published in the Bulletin of Mathematical Biology.

This paper was coauthored by Dr. Allison Kolpas and student Corin Stratton from the mathematics department,  and Dr. Josh Auld, biology - see https://rdcu.be/4ikr.

Corin Stratton was an undergraduate researcher in mathematics at the time the paper was written and is currently in the MA in Mathematics program at WCU.

Corin was supported by an NSF RUI Grant that Dr. Auld and Dr. Kolpas share.

Applied Mathematics Seminar  
January 31st, West Chester University

Research in Mathematics and Sciences (RIMS) Award

23rd Industrial Mathematical and Statistical Modeling Workshop for Graduate Students

July 16-26, 2017, SAS Hall on the campus of North Carolina State University

Evolution in Philadelphia Conference (EPiC)

April 15 2017, University of Pennsylvania, Philadelphia

Applied Mathematics Seminar

April 12 2017, West Chester University

EPaDel Spring 2017 Section Meeting

April 1 2017, Kutztown University

Applied Mathematics Seminar

March 22, 2017, West Chester University

Lane D’Alessandro and Maggie Celentano, students working with Dr. Allison Kolpas, and Ben Plumridge and Cathy Yu, students also working with Dr. Allison Kolpas, gave presentations in the Applied Mathematics Seminar.

Lane and Maggie's talk was entitled Using Rarefaction to Assess Optimal Sampling Effort in Stream Invertebrates. Here is the abstract and the presentation .

Ben and Cathy's talk was entitled Developing a Habitat Suitability Index for Brown Trout in White Clay Creek Using Fuzzy Logic. Here is the abstract and the presentation .

Paper Publication

A paper on which Dr. Allison Kolpas and her student Adam Helker are two of the co-authors was published in the Journal of Evolutionary Biology in December 2016.

Auld, J. R., Helker, A. D. and Kolpas, A. (2016), Consequences of mating and predation risk for longevity in a freshwater snail: abstinence makes the heart beat longer. Journal of Evolutionary Biology, 29: 2539–2544. doi: 10.1111/jeb.12976

Research Day October 2016

All Science Poster Day Fall 2016

Paper Publication

Dr. Viorel Nitica and his student Kenneth Gill published a paper in the Open Journal of Discrete Mathematics in July 2016.

Gill, K. and Nitica, V. (2016)Signed Tilings by Ribbon L n-Ominoes, n Even, via Grobner Bases.Open Journal of Discrete Mathematics,6, 185-206. doi:10.4236/ojdm.2016.63017. To view the journal's abstract page for the paper please use the links above.

SIAM Conference on the Life Sciences

July 11 - 14 2016, Boston, MA.

Corin Stratton, a student working with Dr. Allison Kolpas, gave a poster presentation at the SIAM Conference on the Life Sciences. Click here to download the pdf file for Corin's poster .

Research Day April 2016

All Science Poster Day Spring 2016

Adam Helker and Corin Stratton, students working with Dr. Allison Kolpas,gave poster presentations at the All Science Poster Day Spring 2016. Here are links to Adam's poster and Corin's poster .

SRCA Award, Spring 2016

Corin Stratton, a student working with Dr. Allison Kolpas, received an Award for Excellence in Student Research, Scholarly, and Creative Activities, in Spring 2016, for his project entitled Optimal Mating Strategies of Hermaphroditic Snails.

West Chester University Research, Scholarly and Creative Activities Report, 2014-15

A research project of Dr. Kolpas from the WCU mathematics department is described on page 5 , and the research carried out by her students is described on page 16 .

All Science Poster Day Fall 2015

MAA MathFest:Using Social Networking Analysis in Higher Education

Washington, August 6, 2015 - Prabhat Kumar, Natalie Hurd, and Paul Johnson

The speakers will discuss several Social Network Analysis (SNA) research projects of which they were a part at their university. The aim of these SNAs was determine ways to maximize interactions between faculty and the flow of information across the campus. Areas of particular interest included the use of High Impact Educational Practices and support systems for Underrepresented Minorities. This talk will highlight the research methods used to conduct the SNA and the major results of several SNAs.

MAA EPaDel Meeting

Dickinson College, April 6, 2013 - A Generalization of the Game of Shove, Brian Stoyell-Mullholland

A brief exposition of the algebra of combinatorial game theory. The solution of the game of Shove is demonstrated and how, by a simple alteration to the rules, the game can be generalized. This generalization, Stumble, creates infinitesimals that are not present in Shove. Although not completely solved yet, interesting propositions have been discovered.

SIAM Conference on Computational Science & Engineering

February 25th - March 1st 2013, Boston, MA.

Alex Meade, a student working with Dr. Allison Kolpas, gave a presentation at the SIAM Conference on Computational Science & Engineering.

Student Research Opportunities

• EDGE Summer Program for Women
• IPAM Research in Industrial Projects for Students (RIPS)
• Research Experience for Undergraduates (REU) Summer Programs (AMS page)
• REU SITES: MATHEMATICAL SCIENCES (NSF page)
• Summer Program for Women in Mathematics
• Summer Undergraduate Applied Mathematics Institute
• University of Nebraska Summer IMMERSE Program

Student Research Publications

• The Harvard College Mathematics Review (HCMR)
• Journal of Young Investigators
• Rose Hulman Undergraduate Math Journal
• SIAM Undergraduate Research Online (SIURO)

Meetings/Conferences where student research may be presented

• Joint Mathematics Meetings (JMM) (see the "students" tab at towards the bottom left)
• MAA MathFest
• MAA Section Meetings
• Nebraska Conference for Undergraduate Women in Mathematics
• Young Mathematicians Conference (YMC)