Department of Mathematics

Advanced Mathematics Program Instructors

 AMP 2019


Real Analysis



Jonathan Dugan is entering his fourth year as a graduate student at UCR. His area of research is lie theory and representation theory. When not working on math, Jonathan enjoys trips to Disneyland and playing board games. He enjoys teaching and looks forward to working with students this summer in the AMP program.


Savanna Gee will start her fourth year of graduate school in the fall of 2019. She studies Riemannian geometry and wants to be a professor at a liberal arts or community college upon earning her PhD.  


Abstract Algebra



 Jonathan Alcaraz is starting his fourth year as a graduate student. The type of math he studies is low-dimensional topology and geometric group theory. He is also very passionate about teaching mathematics, especially when it comes to equity in math education and how marginalized groups are affected by traditional education systems.



Mike Pierce studies representation theory and category theory, among other less trendy mathematics. More importantly, away from work, Mike can be found making pickles, tending to his succulent garden, studying the finer points of typographic design, or unsuccessfully trying to cajole other graduate students to play tennis with him.


AMP 2018


Real Analysis



Bryan Carrillo  is a fifth-year mathematics graduate student at University of California, Riverside. He obtained his Bachelors of Arts in Mathematics at Bates College. His dissertation research is on the axi-symmetric Navier Stokes equations under the guidance of Doctor Qi Zhang. He enjoys real and complex analysis, and partial differential equations.


Christina Knox is a graduate student entering into her 5th year. Her research is in the areas of inverse problems and partial differential equations. Real analysis was her favorite class as an undergrad.


Abstract Algebra


Dane Lawhorne is a 5th year PhD student who specializes in representation theory, which uses linear transformations of vector spaces to study algebraic structures. He enjoys teaching and discussing all aspects of topology and abstract algebra.


Brandon Coya earned his PhD at UC Riverside after 6 years. He worked on applications of category theory to networks. Brandon enjoys all of the experiences that come from being a graduate student; this includes being a teaching assistant, instructor, and mentor. In the fall, Brandon will continue his academic career as a visiting assistant professor at Whittier College. He hopes to continue supporting students and encouraging them to pursue further education. 


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Department of Mathematics
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Fax: (951) 827-7314

Office Hours: 8:30 a.m. - 11:45 a.m. & 1:00 p.m. - 4:45 p.m.

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