Tangible topology through the lens of limits

article Tangible topology through the lens of limits published yes Barbara A. Shipman author Elizabeth R Stephenson author 2D04F932-F248-11E8-B48F-1D18A9856A870000-0002-6862-208X HeEd department GradSch department Point-set topology is among the most abstract branches of mathematics in that it lacks tangible notions of distance, length, magnitude, order, and size. There is no shape, no geometry, no algebra, and no direction. Everything we are used to visualizing is gone. In the teaching and learning of mathematics, this can present a conundrum. Yet, this very property makes point set topology perfect for teaching and learning abstract mathematical concepts. It clears our minds of preconceived intuitions and expectations and forces us to think in new and creative ways. In this paper, we present guided investigations into topology through questions and thinking strategies that open up fascinating problems. They are intended for faculty who already teach or are thinking about teaching a class in topology or abstract mathematical reasoning for undergraduates. They can be used to build simple to challenging projects in topology, proofs, honors programs, and research experiences. Taylor & Francis2022 eng EducationGeneral Mathematics PRIMUS 1051-1970 1935-405310.1080/10511970.2021.1872750 325593-609 Shipman BA, Stephenson ER. Tangible topology through the lens of limits. PRIMUS. 2022;32(5):593-609. doi:<a href="https://doi.org/10.1080/10511970.2021.1872750">10.1080/10511970.2021.1872750</a> B. A. Shipman and E. R. Stephenson, “Tangible topology through the lens of limits,” PRIMUS, vol. 32, no. 5. Taylor & Francis, pp. 593–609, 2022. Shipman, Barbara A., and Elizabeth R. Stephenson. “Tangible Topology through the Lens of Limits.” PRIMUS, vol. 32, no. 5, Taylor & Francis, 2022, pp. 593–609, doi:<a href="https://doi.org/10.1080/10511970.2021.1872750">10.1080/10511970.2021.1872750</a>. Shipman BA, Stephenson ER. 2022. Tangible topology through the lens of limits. PRIMUS. 32(5), 593–609. B.A. Shipman, E.R. Stephenson, PRIMUS 32 (2022) 593–609. Shipman, B. A., & Stephenson, E. R. (2022). Tangible topology through the lens of limits. PRIMUS. Taylor & Francis. <a href="https://doi.org/10.1080/10511970.2021.1872750">https://doi.org/10.1080/10511970.2021.1872750</a> Shipman, Barbara A., and Elizabeth R Stephenson. “Tangible Topology through the Lens of Limits.” PRIMUS. Taylor & Francis, 2022. <a href="https://doi.org/10.1080/10511970.2021.1872750">https://doi.org/10.1080/10511970.2021.1872750</a>. 123072023-01-16T10:07:21Z2024-10-09T21:03:58Z