Ztttachr. 1. mdh. und (;kundJaq~n d. M d n . Bd. 21, S. 417-426 ( 1 9 7 5 ) SMALL GRZEGORCZYK CLASSES AND LIMITED MINIMUM by KEITH HARROW in Brooklyn, New York (U.S.A.),) 1. Introduction I n his paper [ 5 ] , classifying the primitive recursive functions, A. GRZEGIORCZYR defined two operations for building primitive recursive functions : limited recursion and limited minimum. GRZEQORCZYK thoroughly studied limited recursion. We have extended his work to limited minimum, leading to some new results. I n particular, wv amwcr two questions of GRZEQORCZYR concerning the relationship between the small (n < 3) GRZEGORCZYK (i.e. limited recursion) classes and limited minimum.We show that limited minimum cannot be used instead of limited recursion to define thc two smallest classes. The classes definable from limited minimum are strictly contained within the corresponding limited recursion classes. Also, we show that a characterization of the classes of relations (a"),, which holds for n >= 3, does not hold for these small classes. We give necessary and sufficient conditions for the characterization to hold for n = 2.
The Computer and Information Science (CIS) Department at Brooklyn College is unable to use full-time CIS faculty for most sections of the introductory programming course. Instead of using adjuncts, the administration of the College would like to use full-time faculty from overstaffed departments to teach these courses. In an attempt to certify these people, the CIS Department launched a two part Faculty Development Program in the Summer of 1981. Program I was an intensive introduction to computing for those with no previous experience. Program II was designed to enable those with some previous computing experience to teach computer programming. Both programs were successful. The participants in Program I gained quite a bit of programming experience. Almost half of those in Program II have taught in the CIS Department in the Fall of 1981, with others planning to do so next year. Based in part on the information gathered from this model, the entire City University is offering a Faculty Development Program in computer science as well.
scite is a Brooklyn-based organization that helps researchers better discover and understand research articles through Smart Citations–citations that display the context of the citation and describe whether the article provides supporting or contrasting evidence. scite is used by students and researchers from around the world and is funded in part by the National Science Foundation and the National Institute on Drug Abuse of the National Institutes of Health.