Jennifer Hyndman

An algebra that is dualizable but not fully dualizable

Abstract We give an example of a finite algebra which is dualizable but not fully dualizable in the sense of natural duality theory.

Assessment on Previous Course Work in Calculus and Subsequent Achievement in Calculus at the Post-Secondary Level

There is limited research examining the effect of antecedent work in calculus and subsequent achievement in post-secondary calculus. This study examines the effects of prior coursework in calculus, often a locally developed secondary school calculus class, and ensuing achievement in a first-year university calculus class. Analysis of covariance confirms that studentswho had successfully completed antecedent course work in calculus are achieving higher final grades than their equally capable peers, even after gender differences and prior achievement are accounted for in the ANCOVA model. Sequential linear regression results substantiate the significance of antecedent coursework as a predictor of final grades.RésuméIl y a encore peu d’études de recherche analysant les effets du travail scolaire en calcul sur les résultats obtenus dans cette matière dans les cours de niveau postsecondaire subséquents. La présente étude se penche sur les effets du travail effectué précédemment dans un cours de calcul, en général un cours de calcul mis sur pied dans une école secondaire, et les résultats qui ont suivi dans un cours de calcul de première année universitaire. Une analyse des covariances confirme que les étudiants de niveau postsecondaire ayant suivi avec succès des cours précédents en calcul obtiennent de meilleurs résultats de fin d’année dans cette matière que leurs pairs de même niveau, même si on tient compte des différences de sexe et de résultats antécédents grâce au modèle ANCOVA. Les résultats de la régression linéaire séquentielle fournissent des preuves de l’importance du travail scolaire antécédent comme indice des résultats universitaires de fin d’année.

PRIMITIVE POSITIVE FORMULAS PREVENTING A FINITE BASIS OF QUASI-EQUATIONS

A finite unary algebra with a primitive positive formula that defines the graph of a finite group operation does not have a finite basis for its quasi-equations.

How finite is a three-element unary algebra?

We show that, within the class of three-element unary algebras, there is a tight connection between a finitely based quasi-equational theory, finite rank, enough algebraic operations (from natural duality theory) and a special injectivity condition.

Interval Dismantlable Lattices

A finite lattice is interval dismantlable if it can be partitioned into an ideal and a filter, each of which can be partitioned into an ideal and a filter, etc., until you reach 1-element lattices. In this note, we find a quasi-equational basis for the pseudoquasivariety of interval dismantlable lattices, and show that there are infinitely many minimal interval non-dismantlable lattices.

Congruence Lattices of Semilattices with Operators

The duality between congruence lattices of semilattices, and algebraic subsets of an algebraic lattice, is extended to include semilattices with operators. For a set G of operators on a semilattice S, we have

1-Unary Algebras

{{\rm Con}(S,+,0,G) \cong^{d} {{\rm S}_{p}}(L,H)}

Pure Unary Relational Structures

Con(S,+,0,G)≅dSp(L,H), where L is the ideal lattice of S, and H is a corresponding set of adjoint maps on L. This duality is used to find some representations of lattices as congruence lattices of semilattices with operators. It is also shown that these congruence lattices satisfy the Jónsson–Kiefer property.