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.     

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.     

Novel [2 + 2] photocycloaddition-induced rearrangement of bichromophoric naphthalene-tethered resorcinol ethers

The first examples of sequential photocycloaddition-rearrangement reactions of naphthalene-tethered resorcinol ethers are described. Bichromophoric aromatic compounds with naphthalene and resorcinol ether moieties were irradiated in the presence/absence of a small amount of acid to give the corresponding cycloaddition-rearrangement products. From the determination of quantum yields, steady-state fluorescence spectral studies, and fluorescence lifetime measurements, the mechanism of this novel photoinduced multistep reaction was elucidated to involve the initial intramolecular exciplex formation, followed by the intramolecular [2 + 2] photocycloaddition between the two aromatic rings and the subsequent acid-catalyzed skeletal rearrangement of the resulting cyclobutane derivative leading to the final products.     

Photoréduction d'esters d'acides perfluorés dans l'hexaméthylphosphortriamide (HMPT). Elimination sélective du fluor en α du groupe carboxyle

The first example of fluorine elimination α to a carboxyl group is reported. The defluorination occurs when solution of perfluorocarboxylic esters in hexamethyl-phosphortriamide are irradiated with UV light (254 nm). Mechanistic and synthetic aspects of this new reaction are described.