For publications listed below, an asterisk * indicates an undergraduate author.

There is one paper already published from this research, and a second paper is foreseen once some additional results are proven.

1. P. Baginski, Scott T. Chapman, Christopher Crutchfield*, K. Grace Kennedy*, and Matthew Wright*. *Elastic Properties and Prime Elements* Results Math. 49 (2006), 187-200.

- Delta sets of arithmetical congruence monoids.
- Characterizations of half-factorial block monoids over infinite abelian groups.
- Factorization properties of numerical monoids.

1. Paul Baginski, Scott T. Chapman, Natalie Hine,* and João Paixão.* *On the Asymptotic Behavior of Unions of Sets of Lengths in Atomic Monoids* Involve 1 (2008), No. 1, 101-110.

2. Paul Baginski, S. T. Chapman and George J. Schaeffer.* *On the Delta Set of a Singular Arithmetical Congruence Monoid* J. Théor. Nombres Bordeaux, 20 (2008), 45-59.

3. Paul Baginski and Ross Kravitz.* *A New Characterization of Half-Factorial Krull Monoids* J. Algebra Appl. 9 (2010), No. 5, 825-837.

The group's research resulted in one publication and a second one is in preparation.

1. Paul Baginski, S. T. Chapman, Ryan Rodriguez,* George J. Schaeffer, and Yiwei She.* *On the Delta Set and Catenary Degree of Krull Monoids with Infinite Cyclic Divisor Class Group* J. Pure Appl. Alg., 214 (2010) 1334-1339.

During the summer of 2001, I spent two months under an NSF Research Experience for Undergraduates (REU) grant working at Trinity University in San Antonio, Texas. My project advisor was Dr. Scott T. Chapman and my research partners were Kathryn McDonald and Lara Pudwell. Our research focused on minimal zero sequences of additive finite Abelian groups. Our results have been published and can be viewed under the first publication listed on my publications page. A more in-depth explanation of our work and related results can be found here. Posters based on this research won prizes at the undergraduate poster competition of the Joint Meetings of the AMS and MAA in January 2003, and at the Meeting of the Minds undergraduate poster competition at Carnegie Mellon University.

**University of Idaho REU, Summer 2002**

During the summer of 2002, I spent two months at the University of Idaho in Moscow, Idaho under an NSF REU grant. My project advisor was Dr. Arie Bialostocki, who has provided a description of the program and potential areas of research on the following link. My research focused on a combination between zero-sum Ramsey theory and the Ramsey theory of sparse graphs. The final version of the paper may be found under the second link on my publications page. A poster based on this research won first place at the Meeting of the Minds undergraduate poster competition at Carnegie Mellon University.

**Pennsylvania State University REU, Summer 2003**

During the summer of 2003, I spent two months at Penn State doing research on elliptic curves with a fellow student, Elena Fuchs. Dr. Yuri Zarhin directed us to a problem on calculating the coefficients of the modular equation. As a result of our work, Elena and I obtained an algorithm for calculating the coefficients of the modular equation of degree n for n=pq the product of two distinct primes. This algorithm operates in linear time as a function of the number of coefficients. Our research is the first collection of notes listed on my publications page. Elena and I presented our research at the Undergraduate Mathematics Day at the University of Dayton in Dayton, Ohio in November 2003.

*
(c) All material accessible through this page is copyright by Paul Baginski and his coauthors. Permission is granted for fair use in personal, noncommercial, and academic projects.*

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