Browsing by Author "Prince, R N"

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    A framework for understanding the quantitative demands of higher education
    (Unisa Press, 2009) Frith, Vera; Prince, R N
    For many students entering higher education in South Africa there is an articulation gap between the demands of the curriculum and their competencies. This mismatch is particularly critical in the area of quantitative literacy (mathematical literacy, numeracy) and if not addressed, has negative consequences for equity of outcomes for higher education. There is a need to make explicit the quantitative literacy demands of the curriculum so that they can be examined critically and addressed by educational interventions and other curriculum changes. We describe our approach to characterizing the quantitative literacy demands in curricula in disciplines, by presenting a framework for analysing aspects of quantitative literacy events in the curriculum. This is useful for helping educators to recognize the demands on students' quantitative literacy (and assumptions about students' competencies) that are often implicit in their curricula, for the purpose of informing the design of education interventions and for developing test constructs.
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    On the theory of Krull rings and injective modules
    (1988) Prince, R N; Hughes, Kenneth R
    In the first chapter we give an outline of classical KRULL rings as in SAMUEL (1964), BOURBAKI (1965) and FOSSUM (1973). In the second chapter we introduce two notions important to our treatment of KRULL theory. The first is injective modules and.the second torsion theories. We then look at injective modules over Noetherian rings as in MATLIS [1958] and then over KRULL rings as in BECK [1971]. We show that for a KRULL ring there is a torsion theory (N,M) where N is the pseudo-zero modules and M the set of N-torsion-free (BECK calls these co-divisorial) modules. From LAMBEK [1971] there is a full abelian sub category C, namely the category of N-torsion-free, N-divisible modules, with exact reflector. We show in C (I) every direct sum of injective modules is injective and (II) C has global dimension at most one. It is these two properties that we exploit in the third chapter to give another characterization of KRULL rings. Then we generalize this to rings with zero-divisors and find that (i) R has to be reduced (ii) the ring is KRULL if and only if it is a finite product of fields and KRULL domains (iii) the injective envelope of the ring is semi-simple artinian. We then generalize the ideas to rings of higher dimension.