An Online Tutor for Astronomy: The GEAS Self-Review Library

We introduce an interactive online resource for use by students and college instructors in introductory astronomy courses. The General Education Astronomy Source (GEAS) online tutor guides students developing mastery of core astronomical concepts and mathematical applications of general astronomy material. It contains over 12,000 questions, with linked hints and solutions. Students who master the material quickly can advance through the topics, while under-prepared or hesitant students can focus on questions on a certain topic for as long as needed, with minimal repetition. Students receive individual accounts for study and course instructors are provided with overview tracking information, by time and by topic, for entire cohorts of students. Diagnostic tools support self-evaluation and close collaboration between instructor and student, even for distance learners. An initial usage study shows clear trends in performance which increase with study time, and indicates that distance learners using these materials perform as well as or better than a comparison cohort of on-campus astronomy students. We are actively seeking new collaborators to use this resource in astronomy courses and other educational venues.Comment: 15 pages, 9 figures; Vogt, N. P., and A. S. Muise. 2015. An online tutor for general astronomy: The GEAS self-review library. Cogent Education, 2 (1

A fractional B-spline collocation method for the numerical solution of fractional predator-prey models

We present a collocation method based on fractional B-splines for the solution of fractional differential problems. The key-idea is to use the space generated by the fractional B-splines, i.e., piecewise polynomials of noninteger degree, as approximating space. Then, in the collocation step the fractional derivative of the approximating function is approximated accurately and efficiently by an exact differentiation rule that involves the generalized finite difference operator. To show the effectiveness of the method for the solution of nonlinear dynamical systems of fractional order, we solved the fractional Lotka-Volterra model and a fractional predator-pray model with variable coefficients. The numerical tests show that the method we proposed is accurate while keeping a low computational cost