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Undergraduate Research

Undergraduate Research

Our Department has experience offering Research Experiences for Undergraduates (REU).  We also encourage our undergraduate students to seek research experiences, summer programs and internships in mathematics and statistics. The National Science Foundation (NSF) maintains a comprehensive list of REU sites, the American Mathematical Society (AMS) maintains a list of summer programs suitable for undergraduate students.

The annual Southwestern Undergraduate Mathematics Research Conference (SUnMaRC) provides opportunities for undergraduate students to present mathematics research in a supportive and fun atmosphere. In addition, at the conference invited speakers from a variety of areas including academia, industry and government give lectures accessible to undegraduate students.

Current and Previous REU and Honors Projects  

The following is a list of current and previous undergraduate Research and Honors projects. Links to the research proposals, the Honors theses, and to any related published papers, are included.

2019-2020: David Vargas, mentored by Prof. Jacob Schroder and Prof. Yi He
             Exploring the Folding of DNA Origami with Time Parallel Integration
             In progress.

2019-2020: Frank Kouzelmartinez, mentored by Prof. Alexander Korotkevich
             Traffic Flow Modeling
             In progress.

2019-2020: Kyle Ritchie, mentored by Prof. Dimiter Vassilev.
             Positive Energy Theorems in Asymptotically Anti-deSitter Spacetimes
             In progress.

2019-2020: Kaitlin O'Dell, mentored by Prof. Deborah Sulsky.
             Double-Cantilever Beam Model for Compact Tension
             In progress.

2019-2020: Kobe Bellas, mentored by Prof. Deborah Sulsky.
             Estimating Fractures in Sea Ice from Satellite Observations
             In progress.

2018-2019: Patrick DeBonis, mentored by Prof. Terry Loring.
             Emergent Topology of Multivariable Spectrum
             Defense 4/3/2019. Thesis completed.
             Supported by Department. Presented at SUnMaRC 2019.

2018-2019: Bibiana Seng, mentored by Prof. James Degnan.
             A Comparison of Clustering Algorithms and Identication Methods
             on Genomic Variants to Compare Modern Dogs and Wolves

             Defense 4/3/2019. Thesis.
             Supported by Department.

2017-2018: Gabriella Dalton, mentored by Prof. Deborah Sulsky.
             Estimating methane emissions from Albuquerque's
             Los Angeles closed landfill.

             Defense 5/2/2018. Proposal. Thesis.
             Supported by Department. Presented at SUnMaRC 2018.

2017-2018: Andrew Hollis, mentored by Prof. James Degnan.
             Text clustering and summarization for intelligence analysis.
             Defense 5/2/2018. Proposal. Thesis.
             Supported by Department. Presented at SUnMaRC 2018.

2017-2018: Ari Rappaport, mentored by Prof. Jehanzeb Chaudry.
             Exploration of black box multigrid for preconditioning
             linear system modeling resistive MHD.

             Defense 5/2/2018. Proposal. Thesis.
             Supported by Department. Presented at SUnMaRC 2018.

2016-2017: Sarka Blahnik, mentored by Prof. Ana Skripka.
             Perturbations with zero spectral shift functions.
             Defense: 4/20/2017. Proposal. Thesis.
             Supported by MCTP NSF DMS-1148801.

2016-2017: Montie Avery, mentored by Prof. Matt Pennybacker.
             Multiple scales asymptotic analysis in pattern forming systems.
             Defense: 4/20/2017. Thesis.
             Supported by MCTP NSF DMS-1148801. Presented at SUnMaRC 2017.

2016-2017: Dustin Enyeart, mentored by Prof. Janet Vassilev.
             Proposal. Thesis incomplete.
             Graduated May 2017.

2016: Hannah Butler, mentored by Prof. Janet Vassilev.
             Standard closure operations on ideals of hypersurface rings.
             Defense: 12/04/2016. Thesis.

2015-2016: Lionel Fiske, mentored by Dr. Lane McConnell.
             Population Dynamics.
             Defense: 4/20/2016. Proposal. Thesis.
             Supported by MCTP NSF DMS-1148801. Presented at SUnMaRC 2015.

2015: Melody Walker, mentored by Prof. Helen Wearing.
             With-in Host Models of Dengue.
             Defense: 4/20/2016. Proposal. Thesis completed.
             Supported by MCTP NSF DMS-1148801. Presented at SUnMaRC 2015.

2014-2015: Juan Pablo Madrigal Cianci, mentored by Prof. Jens Lorenz.
             Study of Modifications of The Option Pricing Theory: A Practical Approach.
             Defense: 4/28/2015. Proposal. Thesis.
             Presented at SUnMaRC 2015.

2014-2015: Sam Mundy, mentored by Prof. Alexander Buium.
             Adeles and the Riemann-Roch theorem for number fields.
             Defense: 4/28/2015. Proposal. Thesis.
             Supported by MCTP NSF DMS-1148801. Presented at SUnMaRC 2015.

2014-2015: Mo Li, mentored by Dr. Huining Kang (Internal Medicine, Cancer Research Facility).
             Statistical Modeling of Genomics Data to Improve Cancer
             Risk Classication and Outcome Prediction.

             Defense: 4/28/2015. Thesis.

2014-2015: Nikhil Addleman, mentored by Prof. Helen Wearing.
             A Stochastic Model of Childhood Disease on Metapopulations.
             Proposal. Graduated May 2015.
             Supported by MCTP NSF DMS-1148801. Presented at SUnMaRC 2015.

2014-2015: Charlie Clauss, mentored by Prof. Monika Nitsche.
             Introductory Fluid Dynamics.
             Graduated May 2015.
             Partially supported by MCTP NSF DMS-1148801.

2014: Miranda Mundt, mentored by Prof. Monika Nitsche.
             Mixing induced by an oscillating plate.
             Defense: 12/13/2014. Proposal. Thesis.
             Supported by MCTP NSF DMS-1148801. Presented at SUnMaRC 2014.

2013-2014: Kirstin Harriger, mentored by Prof. Anna Skripka.
             Spectral shift functions for pairs of matrices.
             Defense: 05/01/2014. Proposal. Thesis (draft).
             Supported by MCTP NSF DMS-1148801. Presented at SUnMaRC 2014.

2013-2014: Andrew Baxter, mentored by Prof. Janet Vassilev.
             Numerical semigroups: basically full ideals and their closures.
             Defense: 05/01/2014. Proposal. Thesis (draft).
             Supported by MCTP NSF DMS-1148801. Presented at SUnMaRC 2012, 2013, 2014.

2013-2014: Cullen Roth, mentored by Prof. Cristina Pereyra.
             The fast wavelet transform and its application to electroencephalography:
             A study of schizoprenia.

             Defense: 05/01/2014. Proposal. Thesis (draft).
             Supported by MCTP NSF DMS-1148801. Presented at Biology 2014 Annual Research Day.

2013-2014: Scott Guernsey, mentored by Prof. Jens Lorenz.
             Analyzing a non-linear Black-Scholes option pricing model: The
             cost of constant volatility.

             Defense: 05/01/2014. Proposal. Thesis.
             Supported by MCTP NSF DMS-1148801. Presented at SUnMaRC 2014.

2013: Cameron LaVigne, mentored by Prof. Cristina Pereyra.
             Fourier analysis on finite Abelian groups.
             Defense: 12/02/2013. Proposal. Thesis.
             Supported by MCTP NSF DMS-1148801.

2013: Yuridia Leyva, mentored by Prof. Cristina Pereyra.
             Is there a representation of the finite Hilbert Transform in terms of
             Haar shift transforms?

             Partially supported by MCTP NSF DMS-1148801. Presented at SUnMaRC 2013.

2013: Reed Young, mentored by Prof. Monika Nitsche.
             Computational modeling of fluid mixing.
             Proposal.
             Partially supported by MCTP NSF DMS-1148801.

2012-2013: Stephen Pietromonaco, mentored by Prof. Matt Blair.
             L^p asymptotics on the zonal and sectoral harmonics.
             Defense: 12/02/2013. Proposal. Thesis.
             Supported by MCTP NSF DMS-0739417, DMS-1148801. Presented at SUnMaRC 2012,2013.

2012-2013: Jeff Gordon, mentored by Profs. Jens Lorenz and Deborah Sulsky.
             Chaos and Legendre Polynomials: Visualization in MATLAB and Paraview.
             Defense: 12/02/2013. Proposal. Thesis.
             Supported by MCTP NSF DMS-0739417. Presented at SUnMaRC 2012,2013.

2012-2013: Anastassiya Semenova, mentored by Prof. Alexander Korotkevich.
             Visualization and Algorithm for Simulations of Electro-Magnetic Field in an
             Elementary Cell of a Layer of Metamaterials.

             Defense: 5/02/2013. Proposal. Thesis.
             Supported by NSF OCE 1131791. Presented at SUnMaRC 2013.

2012-2013: Katherine Freeland, mentored by Prof. Michael Sonksen.
             An Exploration of Mortality Trends Using the SEER Data Set.
             Defense: 5/02/2013. Proposal. Thesis.
             Supported by MCTP NSF DMS-1148801. Presented at SUnMaRC 2013.

2012-2013: Andrew Herring, mentored by Prof. Alex Buium.
             The Quaternion Algebra Unit Circle.
             Defense: 5/02/2013. Proposal. Thesis.
             Supported by MCTP NSF DMS-0739417, DMS-1148801. Presented at SUnMaRC 2012,2013.

2012-2013: Joseph DeAguero, mentored by Prof. Helen Wearing.
             Dengue strain competition within a mosquito.
             Supported by the IMSD program. Presented at SACNAS 2012, SUnMaRC 2013, Biology Research Day 2013.

2012-: Gabe Arrillaga, mentored by Prof. Helen Wearing.
             Modeling the Effects of Immunological Memory in Dengue Virus.
            
Proposal.
             Partially supported by MCTP NSF DMS-1148801. Presented at SUnMaRC 2013.

2011-2012: Rodrigo Orozco, mentored by Prof. Deborah Sulsky.
             Studying HIV-protease dynamics using scattered data approximations.
             Defense: 04/26/2012. Proposal. Thesis. Codes.

2011-2012: Sam Bonin, mentored by Prof. Helen Wearing.
             Applying continuous wavelet transforms to the study of variable astrophysical masers.
             Defense: 04/26/2012. Proposal. Thesis. Paper.
             Supported by MCTP NSF DMS-0739417. Presented at SUnMaRC 2012.

2011-2012: Alex Benedict, mentored by Prof. Stephen Lau.
             Radiation boundary conditions and waveform extraction for blackhole perturbations.
             Defense: 04/26/2012. Proposal. Paper.
             Supported by MCTP NSF DMS-0739417. Presented at SUnMaRC 2012.

2011-2012: Fred Kaul, mentored by Prof. Dimiter Vassilev.
             Classification and Contractions of Three-Dimensional Lie Algebras.
             Defense: 04/26/2012. Proposal. Thesis.
             Supported by MCTP NSF DMS-0739417. Presented at SUnMaRC 2011.

2010-2011: Dusty Brooks, mentored by Prof. Michael Nakamaye.
             N-Impact Trajectories in Rectangular Billiards.
             Defense: 05/02/2011. Thesis.
             Supported by MCTP NSF DMS-0739417. Presented at SUnMaRC 2011.

2009-2010: Bobby Sena, mentored by Profs. Helen Wearing and Eric Toolson.
             Probabilistic Modeling of Action Potential Generation by Neurons.
             Defense: 05/6/2010. Thesis.
             Supported by MCTP NSF DMS-0739417. Presented at SUnMaRC 2011.

2009-2010: Jason Archer, mentored by Prof. Monika Nitsche.
             Deflection of an elliptically loaded vortex sheet by a flat plate.
             Defense: 05/6/2010. Thesis. Paper.
             Supported by MCTP NSF DMS-0739417. Presented at SUnMaRC.

2009-2010: Alex Washburn, mentored by Professor Helen Wearing
             Comparative modeling of lytic and lysogenic virus life cycles.
             Defense: 05/6/2010. Thesis.
             Supported by MCTP NSF DMS-0739417. Presented at SUnMaRC 2009.

2009-2010 Bob Cordwell, mentored by Prof. Terry Loring.
             Supported by MCTP NSF DMS-0739417.

2008-2009: Joshua Beach, mentored by Prof. Jens Lorenz.
             Financial Mathematics.
             Defense: 04/28/2009.
             Supported by MCTP NSF DMS-0739417. Presented at SUnMaRC 2009.

2008-2009: Walker Williamson, mentored by Prof. Michael Nakamaye.
             Representing Music Geometrically.
             Defense: 04/28/2009.
             Supported by MCTP NSF DMS-0739417. Presented at SUnMaRC 2009.

2008-2009 Jeremy Johnson, mentored by Prof. Monika Nitsche.
             Evolution of Two Cylindrical Vortex Sheets.
             Defense: 04/28/2009. Thesis.
             Supported by MCTP NSF DMS-0739417. Presented at SUnMaRC 2008.

2008-2009 Roman Wowk, mentored by Prof. Monika Nitsche.
             Setup of evolution equations for two cylindrical vortex sheets.
             Defense: 04/28/2009. Thesis.
             Supported by MCTP NSF DMS-0739417. Presented at SUnMaRC 2008.

2008-2009: Matt Gooden, mentored by Prof. James Ellison
             Paper (published in PRSTAB).
             Supported by MCTP NSF DMS-0739417 and Argonne National Lab (summer).