The impact of faculty-in-residence programs: A difference-in-differences and cross-sectional approach

Purpose: Faculty-in-Residence (FIR) programs are implemented based on research that shows positive effects on student success when students interact with faculty outside of the classroom. However, most research is limited by cross-sectional studies of only students and does not look at the Faculty-in-Residence programs from a holistic perspective that investigates the impact on faculty. This study focuses on the impact, not only on students over time but additionally on the perceived impact on faculty who participate in Faculty-in-Residence programs. Methods: We examined the effect of FIR programs at a large, public California university on both student success (i.e., cumulative grade point average, retention, and credits earned per unit attempted) as well as student experience (i.e., based on data from the National Survey of Student Engagement). Results: The quantitative results confirm the literature that faculty-student interactions outside of the classroom are statistically significant but point to differences between the demographics of students and that the mere presence of faculty is not as important as the quantity and quality of interactions. Conclusion: FIR programs can contribute to student success, but the magnitude and direction of this link depend on the level of the interaction between students and faculty as well as the specific outcome of interest

The impact of faculty-in-residence programs: A difference-in-differences and cross-sectional approach

Purpose: Faculty-in-Residence (FIR) programs are implemented based on research that shows positive effects on student success when students interact with faculty outside of the classroom. However, most research is limited by cross-sectional studies of only students and does not look at the Faculty-in-Residence programs from a holistic perspective that investigates the impact on faculty. This study focuses on the impact, not only on students over time but additionally on the perceived impact on faculty who participate in Faculty-in-Residence programs. Methods: We examined the effect of FIR programs at a large, public California university on both student success (i.e., cumulative grade point average, retention, and credits earned per unit attempted) as well as student experience (i.e., based on data from the National Survey of Student Engagement). Results: The quantitative results confirm the literature that faculty-student interactions outside of the classroom are statistically significant but point to differences between the demographics of students and that the mere presence of faculty is not as important as the quantity and quality of interactions. Conclusion: FIR programs can contribute to student success, but the magnitude and direction of this link depend on the level of the interaction between students and faculty as well as the specific outcome of interest

Implementation of a Thue-Mahler equation solver

A practical algorithm for solving an arbitrary Thue-Mahler equation is presented, and its correctness is proved. Methods of algebraic number theory are used to reduce the problem of solving the Thue-Mahler equation to the problem of solving a finite collection of related Diophatine equations having parameters in an algebraic number field. Bounds on the solutions of these equations are computed by employing the theory of linear forms in logarithms of algebraic numbers. Computational Diophantine approximation techniques based on lattice basis reduction are used to reduce the upper bounds to the point where a direct enumerative search of the solution space becomes possible. Such an enumerative search is carried out with the aid of a sieving procedure to finally determine the complete set of solutions of the Thue-Mahler equation. The algorithm is implemented in full generality as a function in the Magma computer algebra system. This is the first time a completely general algorithm for solving Thue-Mahler equations has been implemented as a computer program.Science, Faculty ofMathematics, Department ofGraduat

Restriction theorems and Salem sets

In the first part of this thesis, I prove the sharpness of the exponent range in the L² Fourier restriction theorem due to Mockenhaupt and Mitsis (with endpoint estimate due to Bak and Seeger) for measures on ℝ. The proof is based on a random Cantor-type construction of Salem sets due to Laba and Pramanik. The key new idea is to embed in the Salem set a small deterministic Cantor set that disrupts the restriction estimate for the natural measure on the Salem set but does not disrupt the measure's Fourier decay. In the second part of this thesis, I prove a lower bound on the Fourier dimension of Ε(ℚ,ψ,θ) = {x ∊ ℝ : ‖qx - θ‖ ≤ ψ(q) for infinitely many q ∊ ℚ}, where ℚ is an infinite subset of ℤ, Ψ : ℤ → (0,∞), and θ ∊ ℝ. This generalizes theorems of Kaufman and Bluhm and yields new explicit examples of Salem sets. I also prove a multi-dimensional analog of this result. I give applications of these results to metrical Diophantine approximation and determine the Hausdorff dimension of Ε(ℚ,ψ,θ) in new cases.Science, Faculty ofMathematics, Department ofGraduat