Browsing by Author "Williams, G. Brock (TTU)"
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Item Dynamics of Iterations of the Newton Map of sin(z)(2024) Cloutier, Aimée; Dwyer, Jerry; Barnard, Roger W. (TTU); Stone, William D.; Williams, G. Brock (TTU)The dynamical systems of trigonometric functions are explored, with a focus on (Formula presented.) and the fractal image created by iterating the Newton map, (Formula presented.), of (Formula presented.). The basins of attraction created from iterating (Formula presented.) are analyzed, and some bounds are determined for the primary basins of attraction. We further prove (Formula presented.) and (Formula presented.) -axis symmetry of the Newton map as well as some interesting results on periodic points on the real axis.Item Fixed Points, Symmetries, and Bounds for Basins of Attraction of Complex Trigonometric Functions(2020) Bray, Kasey; Dwyer, Jerry (TTU); Barnard, Roger W. (TTU); Williams, G. Brock (TTU)The dynamical systems of trigonometric functions are explored, with a focus on tz=tanz and the fractal image created by iterating the Newton map, Ftz, of tz. The basins of attraction created from iterating Ftz are analyzed, and some bounds are determined for the primary basins of attraction. We further prove x- A nd y-axis symmetry of the Newton map and explore the nature of the fractal images.Item Layered circle packings(2005) Dennis, David (TTU); Williams, G. Brock (TTU)Given a bounded sequence of integers {d0, d1, d2,...}, 6 ≤ dn ≤ M, there is an associated abstract triangulation created by building up layers of vertices so that vertices on the nth layer have degree dn. This triangulation can be realized via a circle packing which fills either the Euclidean or the hyperbolic plane. We give necessary and sufficient conditions to determine the type of the packing given the defining sequence {dn}. Copyright © 2005 Hindawi Publishing Corporation.Item Supporting undergraduate stemm education: Perspectives from faculty mentors and learning assistants in calculus ii(2021) Hite, Rebecca (TTU); Johnson, Levi (TTU); Velasco, Richard Carlos L.; Williams, G. Brock (TTU); Griffith, Ken (TTU)In higher education, Learning Assistants (LAs)—a relatively recent evolution grounded in peer mentorship models—are gaining popularity in classrooms as universities strive to meet the needs of undergraduate learners. Unlike Teaching Assistants, LAs are undergraduate students who receive continuous training from faculty mentors in content-area coaching and pedagogical skills. As near-peers, they assist assigned groups of undergraduates (students) during class. Research on LAs suggests that they are significant in mitigating high Drop-Fail-Withdrawal rates of large enrollment undergraduate science, technology, engineering, mathematics, and medical (STEMM) courses. However, there is a dearth of description regarding the learning between LAs and STEMM faculty mentors. This paper reports on perspectives of faculty mentors and their cooperating LAs in regard to their learning relationships during a Calculus II at a research-oriented university during Spring of 2020. Using an exploratory-descriptive qualitative design, faculty (oral responses) and LAs (written responses) reflected on their relationship. Content analysis (coding) resulted in four salient categories (by faculty and LA percentages, respectively) in: Showing Care and Fostering Relationships (47%, 23%); Honing Pedagogical Skills (27%, 36%); Being Prepared for Class and Students (23%, 28%); and Developing Content Knowledge in Calculus (3%, 13%). Benefits of LAs to faculty and ways to commence LA programs at institutions are also discussed.