I love talking about my research, and am also passionate about teaching. You can find more information on both below!
I love teaching! You can find my teaching statement here.
MA145 Multivariable Calculus
DS251 STEM Education, Democracy, and Poverty in South Africa, Spring 2020
MA400/413 Advanced Linear Algebra, Fall 2016, Spring 2019, Fall 2020
MA471 Topics in Algebra, Spring 2021
MA332/410 Abstract Algebra, Fall 2017, Fall 2019, Fall 2021
MA300 Introduction to Proofs, Spring 2020
MA231/213 Linear Algebra and Differential Equations, Fall 2015, Spring 2016, Spring 2017, Spring 2018, Fall 2020, Spring 2021, Spring 2022
MA124/145, Multivariable Calculus, Spring 2016, Fall 2016, Fall 2017, Spring 2018, Fall 2019, Spring 2022
MA123/135, Calculus, Fall 2015
MA130 Essentials of Calculus, Spring 2019, Fall 2021
Math 71, Honors Algebra, Fall 2013. (Dartmouth)
Math 3, Calculus, Fall 2012. (Dartmouth)
U.S. Fulbright Scholar, South Africa, 2022-2023
Pedagogical Practice Project, 2019
Pedagogical Practice Project (with L. Ludwig), 2016
Dartmouth Center for the Advancement of Learning (DCAL) Outstanding Graduate Student Teacher, April 2014.
In Summer 2014, I had the opportunity to spend several months at the University of Pretoria in South Africa, under an NSF GROW with USAID Research and Innovation Fellowship. I worked with Professors Johann Engelbrecht and Caroline Long on developing, implementing, and testing mathematics education materials in South African public schools.
I returned to South Africa in 2023 as a U.S. Fulbright Scholar, working with Sol Plaatje University and the Maths and Science Leadership Academy in Kimberley. I taught classes and holiday academies, mentored students, and assisted with curriculum development and teacher training.
Assignments to Help Students Reflect on their Learning, MAA Mathfest, Chicago, IL, July 2017
Student Writing as a Tool for Synthesizing Ideas in Calculus, MAA Mathfest, Chicago, IL, July 2017
Fundamental Misunderstandings, Teaching Matters GIFTS, Denison University, February 2017
A Question-Based Approach to Linear Algebra, MAA MathFest, Columbus, OH, August 2016
Introducing Inquiry-Based Mathematics Learning Materials into South African Public Schools, Joint Mathematics Meetings, Seattle, WA, January 2016
Sonia Kovalevsky Women in Math Day, Dartmouth College, May 2015, organizer.
Sonia Kovalevsky Women in Math Day, Dartmouth College, May 2014, session leader.
Graduate Women in Science and Engineering Science Day, Dartmouth College, April 2014, session leader.
Johns Hopkins University Center for Talented Youth (CTY), Dartmouth College, October 2013, session leader.
Graduate Women in Science and Engineering Science Day, Dartmouth College, April 2013, session leader.
Johns Hopkins University CTY, Dartmouth College, May 2013, session leader.
Dartmouth Summer Math Camp, Dartmouth College, July-August 2012 co-organizer (with I.Adelstein, J.Bloom, M.Martinez, N.McNew, and L.Zhao).
Sonia Kovalevsky Women in Math Day, Dartmouth College, October 2012, panelist.
Sonia Kovalevsky Women in Math Day, Darmouth College, October 2011, panelist.
Soccer Without Borders, Grandada, Nicaragua, Spring 2010, volunteer.
I am particularly excited about exploring the link between algebra and graph theory by translating algebraic problems into combinatorial questions about graphs, and vice versa. My graduate research unites discrete mathematics with representation theory and algebraic combinatorics through a generalization of the classical discrete Fourier transform to finite groups and semisimple algebras. I have developed efficient algorithms to compute generalized Fourier transforms and have also analyzed their applications to random walks. For more details, you can view my research statement here. You can also hear me talk about classical Fourier transforms here (starting around 1:36).
Asymptotic Growth of Associated Primes of Certain Graph Ideals, Communications in Algebra 42 (2014)
Generalized Fourier Transforms and their Applications, dissertation (2015).
Random walks on the BMW monoid: an algebraic approach, Journal of Algebraic Combinatorics (2019)
Inferring Rankings from First Order Marginals, Recent Developments in Mathematical, Statistical and Computational Sciences (2021)
Computational Bounds for Doing Harmonic Analysis on Permutation Modules of Finite Groups (with M. Hansen, M. Koyama, M.B.A McDermott, and M.E. Orrison), Journal of Fourier Analysis and Applications (2021)
National Science Foundation Graduate Fellowship, 2011-2015.
National Science Foundation GROW with USAID Research and Innovation Fellow, South Africa, Summer 2014.
Fourier Analysis on Groups and Algebras: an Algorithm and a Walk (invited), CU Boulder Algebraic Lie Theory Seminar, Boulder, CO, March 2017
Separation of Variables and the Computation of Fourier Transforms on Finite Groups, II (poster), FPSAC, Vancouver, BC, July 2016
Generalized Fourier Transforms (invited), Sam Houston St. Univ. Colloquium, Huntsville, TX, March 2016
A Random Walk Through Algebra, Denison Scientific Association, Denison University, February 2016
Random Walks on the BMW Monoid: an Algebraic Approach, MSRI/PIMS Summer School in Probability, June 2015
When not math-ing, I am running as much as possible. I played soccer in college (go tigers!) and have since taken up distance running. I've run many half-marathons, five marathons, three 50ks, a two-day stage race, four 50-milers, eight Alonzo-Stagg 50/20s, and a backyard ultra. In January 2020, I completed the HURT100 100-mile race in the mountains above Honolulu. Here’s me kissing the finish line sign that says ‘Aole makou e ho’ohikiwale kela (We Wouldn’t Want It To Be Easy).
Photo Credit: Augusto Decastro
Trail running and mathematics are more related than you might think! In 2018, I gave an Ignite! talk at PCMI on this subject. You can watch it here.
Email: wolffs@denison.edu
Office: 211 Olin
