Experiences and Thoughts on STEMTEC-Inspired Changes in Teaching Physics for Life Science Majors

I have taught an introductory course for life science majors three times, each time introducing one or more teaching techniques discussed during the Science, Technology, Engineering, and Mathematics Teaching Education Collaborative (STEMTEC) meetings. Typical class size was 275 students. I cannot make quantitative statements about comparisons between the results of STEMTEC-type teaching methods and traditional teaching methods because I have never taught this course in a completely traditional lecture style. During the first year, I introduced conceptual questions into my lectures. The lecture would be interrupted several times with questions posed to the class. The students then had several minutes to discuss each question among their neighbors, then present their answers. During the second year, I switched from traditional homework to a computerized system which allowed instant feedback to the students, and the ability to resubmit solutions to problems they had not successfully solved. I also introduced an exam format that enabled the students to work individually, then redo the exam in groups and hand in a second set of solutions. The goal of each of these techniques was to increase the engagement of the students with the material of the course. Each of the techniques had both successes and limitations. The most serious problems I confronted were technical difficulties which diverted attention from the tasks at hand to the necessity of keeping the system functioning

Serre Duality, Abel's Theorem, and Jacobi Inversion for Supercurves Over a Thick Superpoint

The principal aim of this paper is to extend Abel's theorem to the setting of complex supermanifolds of dimension 1|q over a finite-dimensional local supercommutative C-algebra. The theorem is proved by establishing a compatibility of Serre duality for the supercurve with Poincare duality on the reduced curve. We include an elementary algebraic proof of the requisite form of Serre duality, closely based on the account of the reduced case given by Serre in Algebraic Groups and Class Fields, combined with an invariance result for the topology on the dual of the space of repartitions. Our Abel map, taking Cartier divisors of degree zero to the dual of the space of sections of the Berezinian sheaf, modulo periods, is defined via Penkov's characterization of the Berezinian sheaf as the cohomology of the de Rham complex of the sheaf D of differential operators, as a right module over itself. We discuss the Jacobi inversion problem for the Abel map and give an example demonstrating that if n is an integer sufficiently large that the generic divisor of degree n is linearly equivalent to an effective divisor, this need not be the case for all divisors of degree n.Comment: 14 page

Periodicity and Growth in a Lattice Gas with Dynamical Geometry

We study a one-dimensional lattice gas "dynamical geometry model" in which local reversible interactions of counter-rotating groups of particles on a ring can create or destroy lattice sites. We exhibit many periodic orbits and and show that all other solutions have asymptotically growing lattice length in both directions of time. We explain why the length grows as $\sqrt{t}$ in all cases examined. We completely solve the dynamics for small numbers of particles with arbitrary initial conditions.Comment: 18 pages, LaTe