What are We Developing? A Case Study of a College Mathematics Program

Over one‐third of all college mathematics enrollments are in courses considered to be developmental. While such courses have been the subject of a large body of research, one question that seems not to have been studied empirically is the alignment of the content of developmental and college level mathematics courses. This paper gives the results of such a study, conducted at a medium sized public liberal arts university. While the content of the developmental mathematics courses was used subsequently in the Precalculus course, most of the content of the Intermediate Algebra course was not used in other college level mathematics courses. It is hoped that the results of this paper will serve as a catalyst for other institutions to examine carefully and define the mission of both their developmental and college level mathematics courses.     

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Experimental Techniques -     

A facile synthesis of 4- and 6-chloromethyl-1H-indole-2-carboxylates: replacement of a sulfonic acid functionality by chlorine

Valuable new synthetic intermediates, 4- or 6-chloromethyl-1H-indole-2-carboxylates, were prepared by the elimination of SO₂ from 2-ethoxycarbonyl-1H-indole-4- or 6-methanesulfonic acids, respectively, which are easily accessible by Fischer-type indolization.     

A graph-theoretic approach to quantitative structure—activity/reactivity studies

Characterization of molecular species based on the use of suitable graph invariants (graph paths, in particular) can provide a quantitative means of encoding structure; the technique is complementary to commoner approaches to studies of quantitative structure— activity relationships. Graph path encoding is here applied to quantitative studies of relationships between molecular structures and biological activity; the examples are the rates of various substrate reactions with hexoldnase, and the potential opiate-like activity of enkephalin analogs.     

Nitrogen bridgehead compounds part 21. Preparation of new quaternary 2,3a,6a-triazaphenalenium salts

The first representatives of a new ring system, the 2,3a,6a-triazaphenalenium quaternary salts are prepared by the cycloaddition of tetrahydro-4H-pyrido[1,2-a] pyrimidin-4-ones containing an α-chloroenamine moiety with azomethines.     

Reactivite photochimique des α-aminoenones: reactions de cyclisation et nouveau type de reaction dans les α-sulfonamido-cyclohexenones

The photochemical behaviour of 2-alkylamino 2-cyclohexenones is very sensitive to the nitrogen substituents. α-Ketoazetidines are produced by irradiation of 2-methanesulfonamido-2-cyclohexenones; however a desulfonation and aryl migration process can compete in the case of 2-arenesulfonamido-2-cyclohexenones. Furthermore divinylamine and photo-Fries rearrangements are the main reactions with 2-anilino 2-cyclohexnone and 2-benzoylamido 2-cyclohexenone respectively.     

Reactivity of singlet oxygen toward strained substrates and a novel non-photochemical method for determination of quenching constants of singlet oxygen.

Rate constants for quenching of ¹O₂ by a number of strained molecules have been determined by the competitive rubrene photooxidation method; the rate constant for quenching by Q may be evaluated by adaption of a kinetic analysis already in the literature for the rubrene photooxidation method.