Due to COVID-19, universities across Canada were forced to undergo a transition from classroom-based face-to-face learning and invigilated assessments to online-based learning and non-invigilated assessments. This study attempts to empirically measure the impact of COVID-19 on students’ marks from eleven science, technology, engineering, and mathematics (STEM) courses using a Bayesian linear mixed effects model fitted to longitudinal data. The Bayesian linear mixed effects model is designed for this application which allows student-specific error variances to vary. The novel Bayesian missing value imputation method is flexible which seamlessly generates missing values given complete data. We observed an increase in overall average marks for the courses requiring lower-level cognitive skills according to Bloom’s Taxonomy and a decrease in marks for the courses requiring higher-level cognitive skills, where larger changes in marks were observed for the underachieving students. About half of the disengaged students who did not participate in any course assessments after the transition to online delivery were in special support.

Let C F (X) be the socle of C(X). It is shown that each prime ideal in C(X)/C F (X) is essential. For each h ∈ C(X), we prove that every prime ideal (resp. zideal) of C(X)/(h) is essential if and only if the set Z(h) of zeros of h contains no isolated points (resp. int Z(h) = ∅). It is proved that dim(C(X)/C F (X)) ≥ dim C(X), where dim C(X) denotes the Goldie dimension of C(X), and the inequality may be strict. We also give an algebraic characterization of compact spaces with at most a countable number of nonisolated points. For each essential ideal E in C(X), we observe that E/C F (X) is essential in C(X)/C F (X) if and only if the set of isolated points of X is finite. Finally, we characterize topological spaces X for which the Jacobson radical of C(X)/C F (X) is zero, and as a consequence we observe that the cardinality of a discrete space X is nonmeasurable if and only if υX, the realcompactification of X, is first countable. Introduction. Let C(X) be the ring of real-valued continuous functions on an infinite completely regular Hausdorff space X, and C ⋆ (X) be its subring of bounded functions. The socle of C(X), denoted by C F (X), is the sum of all minimal ideals of C(X), which is the intersection of all essential ideals in C(X) (recall that, an ideal is essential if it intersects every nonzero ideal nontrivially); see [15]. It can be easily seen that C F (X) = 0 if and only if X has isolated points, and when the set of isolated points in X is finite, then C(X)/C F (X) ∼ = C(Y), where Y is the set of nonisolated points of X. This implies that in this case C(X)/C F (X) ∼ = eC(X), where e 2 = e ∈ C(X), as a ring will enjoy all the general algebraic properties of C(X). Although in general C(X)/C F (X) may not be isomorphic to C(Y) for any topological space Y , in any case, one encounters a curious similarity between the two rings C(X) and C(X)/C F (X), and their common properties usually give rise to useful information about X. For example, X is a P-space (resp. an extremally disconnected P-space with only a finite number of isolated points) if and only if C(X) or equivalently C(X)/C F (X) is an ℵ 0-self-injective (resp. self-injective) ring (see [11, Theorems 1, 2 and Lemma 3.1]). Neither of the two partially ordered rings C(X) and C(X)/C F (X) (note that C F (X) is

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Due to COVID-19, universities across Canada were forced to undergo a transition from classroom-based face-to-face learning and invigilated assessments to online-based learning and non-invigilated assessments. This study attempts to empirically measure the impact of COVID-19 on students’ marks from eleven science, technology, engineering, and mathematics (STEM) courses using a Bayesian linear mixed effects model fitted to longitudinal data. The Bayesian linear mixed effects model is designed for this application which allows student-specific error variances to vary. The novel Bayesian missing value imputation method is flexible which seamlessly generates missing values given complete data. We observed an increase in overall average marks for the courses requiring lower-level cognitive skills according to Bloom’s Taxonomy and a decrease in marks for the courses requiring higher-level cognitive skills, where larger changes in marks were observed for the underachieving students. About half of the disengaged students who did not participate in any course assessments after the transition to online delivery were in special support.