My research is in the area of time scales. The calculus of time scales was developed to unify and extend results obtained for differential equations and difference equations. Currently, my focus is on oscillation criteria for certain linear and nonlinear second order dynamic equations. I am also interested in applications of time scales to mathematical biology and issues that affect pre-service teachers ability to teach mathematics.

External Funding

• Pre-Alliance Planning: The Bridges Across Texas Louis Stokes Alliance for Minority Participation: NSF Award No. 1701664
• South Plains Mathematics Fellows: NSF Award No. 1356604
• West Texas Middle School Math Partnership: NSF Award No. 0831420
• Leveraging Learning Assistantships, Mentoring, and Scholarships to Develop Self-Determined Mathematics Teachers for West Texas: NSF Award No. 1852944
• Louis Stokes New STEM Pathways Implementation-Only Alliance: The Bridges Across Texas Louis Stokes Alliances for Minority Participation: NSF Award No. 2110048
• Investigating Pre-College Predictors and Post-Secondary Effects of Course-Based Undergraduate Research Experiences in Texas: NSF Award No. 2201863

Publications

• Higgins, R. (2022). The Road Less Traveled: My Journey to Mathematics.  In: Beery, J.L., Greenwald, S.J., Kessel, C. (eds) Fifty Years of Women in Mathematics. Association for Women in Mathematics Series, vol 28. Springer, Cham.
• Higgins, R., & Berger, H. (2022). The N_0 Story: Discrete Fractional Calculus. Notices Amer. Math. Soc., 69 (2), 180-189.
• Smith, D. J., Spott, J. L., Higgins, R., & McNaughtan, J. (2021). Beyond articulation agreements: Fostering success for community college transfer students in stem. Community College Journal of Research and Practice.
• Öztürk, O., Higgins, R., & Kittou, G. (2021). Oscillation of Three-Dimensional Time Scale Systems with Fixed Point Theorems. Filomat , 35 (6).
• Higgins, R., Mills, Casey J, & Peace, A. (2020). A time scales approach for modeling intermittent hormone therapy for prostate cancer. Bulletin of Mathematical Biology , 82 (11), 1–16.
• Öztürk, O., & Higgins, R. (2018). Limit behaviors of nonoscillatory solutions of three-dimensional time scale systems. Turkish J. Math., 42 (5), 2576–2587.
• Aguirre-Muñoz, Z., Stevens, T., Harris, G., & Higgins, R. (2018). Mathematics Teacher Learning Preferences: Self-Determination Theory Implications for Addressing Their Learning Needs. Journal of Education and Practice, 9 (32), 127–140.
• Higgins, R. (2016). Asymptotic and oscillatory behavior of dynamic equations on time scales. In Advances in the Mathematical Sciences (Vol. 6, pp. 341–355). Springer, [Cham]. 
• Higgins, R. J., Kent, C. M., Kocic, V. L., & Kostrov, Y. (2015). Dynamics of a nonlinear discrete population model with jumps. Appl. Anal. Discrete Math., 9 (2), 245–270.
• Higgins, R. (2015). Oscillation of certain dynamic equations on time scales. Commun. Appl. Anal., 19 (1), 113–128.
• Adivar, M., Akin, E., & Higgins, R. (2014). Oscillatory behavior of solutions of third-order delay and advanced dynamic equations. J. Inequal. Appl., 2014:95, 16.

• Stevens, T., Aguirre-Munoz, Z., Harris, G., Higgins, R., & Liu, X. (2013). Middle level mathematics teachers' self-efficacy growth through professional development: Differences based on mathematical background. Australian Journal of Teacher Education, 38 (4), 9.

• Higgins, R. (2012). Oscillation of a second-order linear delay dynamic equation. Commun. Appl. Anal., 16 (3), 403–414.
• Higgins, R. (2011). Oscillation of second-order dynamic equations. Int. J. Dyn. Syst. Differ. Equ., 3 (1-2), 189–205.
• Harris, G., Stevens, T., & Higgins, R. (2011). A professional development model for middle school teachers of mathematics. International Journal of Mathematical Education in Science and Technol- ogy , 42 (7), 951-961.
• Higgins, R. (2010d). Some oscillation results for second-order functional dynamic equations. Adv. Dyn. Syst. Appl., 5 (1), 87–105.
• Higgins, R. (2010c). Some oscillation criteria for second-order delay dynamic equations. Appl. Anal. Discrete Math., 4 (2), 322–337. 
• Higgins, R. (2010b). Oscillation results for second-order delay dynamic equations. Int. J. Difference Equ., 5 (1), 41–54.
• Higgins, R. (2010a). Asymptotic behavior of second-order nonlinear dynamic equations on time scales. Discrete Contin. Dyn. Syst. Ser. B , 13 (3), 609–622. 
• Erbe, L., & Higgins, R. (2008). Some oscillation results for second order functional dynamic equations. Adv. Dyn. Syst. Appl., 3 (1), 73–88. 

Refereed Proceedings

• Stevens, T., Harris, G., Higgins, R., Aguirre-Munoz, Z., & Liu, X. (2014). Rigorous math courses for middle-school math teachers. In Proceedings of the 41st Annual Meeting of the Research Council on Mathematics Learning (pp. 10–17).
• Higgins, R., & Peterson, A. (2004). Cauchy functions and Taylor's formula for time scales T. In Proceedings of the Sixth International Conference on Difference Equations (pp. 299–308). Chapman Hall/CRC.

Home Page

Teaching

Outreach & Engagement