PURE Math Residents



Resident Advisors: Dr. Roberto Pelayo - University of Hawai`i at Hilo

                            Dr. Brian Wissman - University of Hawai`i at Hilo

Graduate Assistants: Felix Gotti - University of California, Berkeley

    The Residents topic introduces twelve undergraduates to factorization theory of monoids. The Residents Program was directed by Dr. Roberto Pelayo and Dr. Brian Wissman, with assistance from Felix Gotti.


Rebecca Conaway - Monmouth University

Rachel Domagalski - Central Michigan University

Daniel Gonzalez - Florida International University

Jesse Horton - University of Arkansas

Dana Lacey - North Central College

Miguel Landeros - California State Polytechnic University, Pomona

James Pangelinan - University of Guam

Karina Pena - California State Polytechnic University, Pomona

Mesa Pracht - Lee University

Jimmy Ren - University of Guam

Cameron Wright - Carleton College

Jenna Zomback - SUNY-Geneseo


Shifting Numerical Semigroups and the Catenary Degree

Rebecca Conaway, Jesse Horton, Mesa Pracht

Technical Paper               Presentation

Monotone Catenary Degree in Numerical Monoids

Daniel Gonzalex, Cameron Wright, Jenna Zomback

Technical Paper               Presentation

On the Catenary Degree of Numerical Monoids Generated by Generalized Arithmetic Sequences          

Rachel Domagalski, Dana Lacey, James Pangelinan, Marley Cormar

Technical Paper               Presentation

Leamer Monoids and the Huneke-Wiegand Conjecture

Miguel Landeros, Karina Pena, Jimmy Ren

Technical Paper               Presentation

Course Descriptions

Factorization Theory of Monoids - The Residents will spend eight weeks investigating numerical monoids and their factorization properties.  We all have come to know and love the unique factorization of the natural numbers under multiplication.  Numerical monoids, however, are a subset of the natural numbers that, when we use addition instead of multiplication, have very interesting and complicated factorizations.  Our goal will be to study these factorizations using several algebraic methods.