The hypersensitization of sixteen millimeter black and white motion picture film by pre-exposure to light.

Thesis (M.S.)--Boston Universit

The 3x+1 Semigroup

The 3x+1 semigroup is the multiplicative semigroup generated by the rational numbers of form (2k+1)/(3k+2) for non-negative k, together with 2. This semigroup encodes backward iteration under the 3x+1 map, and the 3x+1 conjecture implies that it contains every positive integer. We prove this is the case, and show that this semigroup consists of all positive rational numbers a/b such that 3 does not divide b.Comment: 16 pages, latex; minor change

An Analysis of Differences in Approaches to Systems of Linear Equations Problems Given Multiple Choice Answers

This descriptive study focuses on the approaches college students (ages 20 -24) use when solving systems of linear equations problems that have multiple choice answers. Participants were from a midsize public university in the northeast. Four approaches were considered – three forwards approaches: 1) substitution, 2) elimination, and 3) graphing, and one backwards approach: plugging in the x and y values from each multiple choice option. Participants solved systems of linear equations problems and answered questions based on their methods in a structured clinical interview. Each participant also filled out a questionnaire. It was shown from the results of this study that the major of a student does not change the approach used to solve a problem by very much. Most students in the study chose to use substitution to solve the problems, usually because this was the method students remembered most and was deemed the “easiest” method by the students