Honors Program

The Mathematics and Statistics Undergraduate Honors Program is designed to provide intensive and personal instruction for selected students. For those who intend to pursue graduate or professional study, it provides extra guidance and leads to graduating with departmental honors at commencement. Please see the Department of Mathematics and Statistics Undergraduate Honors Thesis fact sheet for more details. Email your completed Application for Dept. Honors form to mathstatugprogram@unm.edu

Purposes:

• Intensify and deepen the student's knowledge within the fields of Mathematics and Statistics

• Put this specialized knowledge into better relationship with the larger area of the student's specialization and related fields

• Bring the student under closer guidance of, and acquaintance with, faculty in the Department of Mathematics and Statistics

Outcomes:

• Graduation with Departmental Honors with cum laude, magna cum laude, or summa cum laude mention from the Department. The departmental honors designation will be reflected on the student's diploma

• Opportunity for mentored research at the undergraduate level and completion of an Undergraduate Honors thesis

Requirements:

    The following requirements for departmental honors are in addition to the requirements for the undergraduate major in the Department of Mathematics and Statistics:

• Grade point average of 3.5 in the Mathematics or Statistics major and overall GPA of 3.2 at UNM

• Finding a Mathematics or Statistics faculty to mentor the student in the Undergraduate Honors thesis project

• Completion of the Department of Mathematics and Statistics Honors form and submission to the Department Advisor no later than two full semesters before graduation

• Approval of the Undergraduate Honors thesis research project by the Undergraduate Committee

• Successful completion of six credit hours of independent study under either Math 499 or Stat 495

• Submission of the Undergraduate Honors thesis to the faculty mentor and the Undergraduate Committee no later than ten days before the thesis defense

• Oral presentation and defense of the Undergraduate Honors thesis. In cases where the Undergraduate Committee requests additional changes to the thesis, the student will be allowed one week to submit a final corrected version of the Undergraduate Honors thesis.

Funding Information

The department may have limited funds for the purchase of materials and supplies, conference travel to disseminate the results of the undergraduate research, or purchase of Honors cords for commencement. These funds are awarded by the Undergraduate Committee on a competitive basis. For more information please contact the Department Advisor.

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.

Undergraduate students in our department have gone to graduate schools and on to successful careers in the mathematical sciences: in academia, industry, national laboratories, government, as teaching professionals: in K12 education, colleges, and universities across the US and the world; as data analysts: working in hospitals, insurance companies and start-ups.

See also the student lead Directed Reading Program (DRP).

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.

2024-2025: Cordelia Russell, mentored by Prof. Janet Vassilev
             Free Resolutions of Monomial Ideals
             Defense 4/21/25. Thesis

2024-2025: Judah Towery, mentored by Prof. Terry Loring
            Proof Assistants and Type Theory
             Defense 4/21/2025. Thesis

2023-2024: Franklin Pezzuti Dyer, mentored by Prof. Maria Cristina Pereyra
             Algebraic Structure of Growth Orders
             Defense 5/1/2024. Thesis

2022-2023: Kioshi Morosin, mentored by Prof. Maria Cristina Pereyra
             An Algebraist’s Introduction to Multiresolution Analysis
             Defense 5/3/2023. Thesis

2022-2023: Meilin Zheng, mentored by Prof. Yiliang Zhu
             Covid-19 Related Treatments and Outcomes
             Defense 5/3/2023. Thesis completed.

2019-2020: David Vargas, mentored by Prof. Jacob Schroder and Prof. Yi He
             Exploring the Folding of DNA Origami with Time Parallel Integration
             Defense 4/22/2020. Thesis completed.

2019-2020: Frank Kouzelmartinez, mentored by Prof. Alexander Korotkevich
             Traffic Flow Modeling
             Defense 4/22/2020. Thesis completed.

2019-2020: Kyle Ritchie, mentored by Prof. Dimiter Vassilev.
             Positive Energy Theorems in Asymptotically Anti-deSitter Spacetimes
             Defense 4/22/2020. Thesis completed.

2019-2020: Kaitlin O'Dell, mentored by Prof. Deborah Sulsky.
             Double-Cantilever Beam Model for Compact Tension
             Defense 4/22/2020. Thesis completed.

2019-2020: Kobe Bellas, mentored by Prof. Deborah Sulsky.
             Estimating Fractures in Sea Ice from Satellite Observations
             Defense 4/22/2020. Thesis completed.

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).