#### Participant Quotes

- I was able to learn about open and accessible problems for undergraduates in graph theory, and I have begun my own research in the area to enhance my knowledge and skills when working with undergraduates. I know of no other opportunity like REUF where one can learn the basics of a new research area and even be given open questions accessible to undergraduates.
- Meeting faculty in similar situations as me has been the most beneficial. I like knowing a network of people to keep in touch with.
- I feel re-energized as a mathematician. The possibilities for my own as well as student research have far exceeded my expectations. The multitude and variety of collaborations has been wonderful.
*I have greatly benefited from the variety of problems described, the discussion on the logistics of running an undergraduate research program, and the camaraderie, with other liberal arts faculty. This has been easily been the most worthwhile workshop or conference I’ve ever attended.*

## Undergraduate and Faculty Research Outcomes

A high proportion of faculty from each REUF workshop go on to mentor undergraduate researchers, and many faculty also continue collaborating with fellow faculty workshop participants and mathematical leaders. Outcomes are tracked for two years after each workshop, starting a year after the workshop.

**Faculty participants:** 144 faculty from 117 primarily undergraduate institutions have participated in a REUF workshop since 2008.

**Student research:** 250 undergraduate students were mentored by 73 faculty. Collectively, the students made 159 presentations, completed 21 honors theses, and co-authored 3 publications. Twenty-eight student-faculty collaborations received other grant funding. Several students were accepted to off-site NSF REU programs, and one won first prize for a presentation at a national meeting.

**Faculty research:** 59 undergraduate faculty were involved in new collaborations with other faculty. Twelve small research groups met for an additional week, eleven of these with support from the REUF program. All together, their research has resulted in 35 presentations and 26 research articles in various stages of publication, some with student co-authors.

**Other notable outcomes:**

- Special sessions at the Joint Mathematics Meetings organized by REUF alumni
- Development of new undergraduate courses on REUF research topics
- Departmental changes such as the creation of a for-credit undergraduate research seminar for math majors

## Research Publications

*Peer-reviewed journal articles resulting from research begun at REUF workshops.*

#### REUF 2016

Asplund, J., Edoh, K., Haas, R., Hristova, Y., Novick, B., Werner, B., (2018). Reconfiguration graphs of shortest paths. *Discrete Mathematics, 341*, 2938-2948.

Benesh, B., Carter, J., Coleman, D. A., Crabill, D. G., Good, J. H., Smith, M. A., Travis, J., & Ward, M. D. (2018). Periods in Subtraction Games, in *29th International Conference on Probabilistic, Combinatorial and Asymptotic Methods for the Analysis of Algorithms (AofA 2018)*, 8:1–8:3.

#### REUF 2015

Benson, K. F., Ferrero, D., Flagg, M., Furst, V., Hogben, L., Vasilevska, V., & Wissman, B. (2018). Power domination and zero forcing. *Australasian Journal of Combinatorics, 70*, 221-235. Available at http://arxiv.org/abs/1510.02421.

Benson, K. F., Ferrero, D., Flagg, M., Furst, V., Hogben, L., & Vasilevska, V. (in press). Note on Nordhaus-Gaddum problems for power domination. *Discrete Applied Mathematics*, https://doi.org/10.1016/j.dam.2018.06.004.

Köse, E., Moore, S., Ofodile, C., Radunskaya, A., Swanson, E. R., & Zollinger, E. (2017). Immuno-kinetics of immunotherapy: Dosing with DCs. *Letters in Biomathematics, 4*, 39-58.

Ledder, G., Sylvester, D., Bouchat, R., & Thiel, J. (2018). *Mathematical Biosciences and Engineering, 15*, 841-862.

#### REUF 2014

Baker Swart, B, Beck, K., Crook, S., Eubanks-Turner, C., Grundman, H., Mei, M., & Zack, L. (2017). Augmented generalized happy functions. *Rocky Mountain Journal of Mathematics, 47*, 403-417.

Baker Swart, B., Beck, K., Crook, S., Eubanks-Turner, C., Grundman, H., Mei, M., & Zack, L. (2018). Augmented generalized happy functions. *Rocky Mountain Journal of Mathematics, 48*, 47-58.

Catral, M., Ford, P., Harris, P., Miller, S. J., & Nelson, D. (2014). Generalizing Zeckendorf’s Theorem: The Kentucky Sequence. *Fibonacci Quarterly, 52*(5), 68-90.

Dorward, R., Ford, P., Fourakis, E., Harris, P. E., Miller, S. J., Palsson, Eyvi, & Paugh, H. (2017). A generalization of Zeckendorf’s Theorem via circumscribed *m*-gons. *Involve, 19*, 125-150.

Dorward, R., Ford, P., Fourakis, E., Harris, P. E., Miller, S. J., Palsson, Eyvi, & Paugh, H. (2017). Individual gap measures from generalized Zeckendorf decompositions. *Uniform Distribution Theory, 12*, 27-36.

#### REUF 2013

Beier, J., Fierson, J., Haas, R., Russell, H., & Shavo, K. (2016). Classifying coloring graphs. *Discrete Math, 339*(8), 2100-2112.

C. Buell, A. Helminck, V. Klima, J. Schaefer, C. Wright, & E. Ziliak. (2017). On the structure of generalized symmetric spaces of SL_n(F_q). *Communications in Algebra, 45*, 5123-5136.

C. Buell, A. Helminck, V. Klima, J. Schaefer, C. Wright, & E. Ziliak. (2017). On the structure of generalized symmetric spaces of SL_2(F_q) and GL_2(F_q). *Note di Matematica, 37*, 1-10.

Callahan, J., Rebarber, R., Strawbridge, E., & Yuan, S. (2015). Analysis of a coupled, *n*-patch population model with density dependence. *International Journal of Difference Equations, 10*, 137-159.

Schaefer, J., & Schlechtweg, K. (2017). On the structure of symmetric spaces of the semihedral groups. *Involve, 10*, 665-676.

#### REUF 2012

Ansil, T., Jacob, B., Penzellna, J., & Saavedra, D. (2016). Failed skew zero forcing on a graph. *Linear Algebra and Its Applications, 509*, 40-63.

Ansill, T., Jacob, B., Podlisny, B., Saavedra, D., & Yeung, P. (2015). Three-state zero forcing on graphs. *Congressus Numerantium, 225,* 73-81.

Berliner, A., Dean, N., Hook, J., Marr, A., Mbirika, A., & McBee, C. D. (2016). Coprime and prime labelings of graphs. *Journal of Integer Sequences, 19*(16.5.8).

Fetcie, K., Jacob, B, & Saavedra, D. (2015). The failed zero forcing number of a graph. *Involve, 8*(1), 99-117.

Grood, C., Harmse, J.A., Hogben, L., Hunter, T., Jacob, B., Klimas, A., McCathern, S. (2014). Minimum rank of zero-diagonal matrices described by a graph. *Electronic Journal of Linear Algebra, 27*, 458-477.

#### REUF 2011

Camenga, K. A., Rault, P. X., Sendova, T., & Spitkovsky, I. M. (2014). On the Gau-Wu number for some classes of matrices. *Linear Algebra and Its Applications, 444*, 254-262

Cunningham, K. K. A., Edgar, T., Helminck, A. G., Jones, B. F., Oh, H., Schwell, R., & Vasquez, J. F. (2014). On the structure of involutions and symmetric spaces of dihedral groups. *Note di Matematica, 34*(2), 23-40.

Deaett, L., Lafuente-Rodrigues, R. H., Marin Jr., J., Martin, E. H., Patton, L., Rasmussen, K., & Johnson Yates, R. B. (2013). Trace conditions for symmetry of the numerical range. *Electronic Journal of Linear Algebra, 26*, 591-603.

Militzer, E., Patton, L., Spitkovsky, I. M., & Tsai, M.-C. (2017). Numerical ranges of 4-by-4 nilpotent matrices: Flat portions on the boundary. *Operator Theory Advances and Applications, 259*, 561-591.

#### REUF 2009

Fleming, P. S., Garcia, S. R., & Karaali, G. (2011). Classical Kloosterman sums: representation theory, magic squares, and Ramanujan multigraphs. *Journal of Number Theory, 131*, 661-680.