Victor Scharaschkin

A mathematics support programme for first-year engineering students

This article describes a mathematics support programme at the University of Queensland, targeted at first-year engineering students identified as having a high risk of failing a first-year mathematics course in calculus and linear algebra. It describes how students were identified for the programme and the main features of the programme. The success of the programme was evaluated using student feedback as well as a comparison of the performance of students who participated in the support programme with those of a similar background who briefly attended or did not attend the programme. The pass rate in the supported group of regular attendees was 79% compared with 43% and 46% in the briefly supported and unsupported groups, respectively. Both student feedback and statistical data indicate that the programme was highly successful in improving the performance of those who regularly engaged with it.

Assessment of an Innovative System of Lecture Notes in First-Year Mathematics

Lectures are a familiar component in the delivery of mathematical content. Lecturers are often challenged with presenting material in a manner that aligns with the various learning styles and abilities within a large class. Students complain that the old-fashioned lecture style of copying notes from a board hinders the learning process, as they simply concentrate on writing. In recent times, distributing elaborate lecture notes has become a widespread alternative, but has its own problems, alienating the audience with lack of participation. The authors have developed a system of lecture notes, we call partially populated lecture notes, that have enjoyed success with students and addressed these difficulties.

On the non-existence of pair covering designs with at least as many points as blocks

We establish new lower bounds on the pair covering number Cλ(υ,k) for infinitely many values of υ, k and λ, including infinitely many values of υ and k for λ=1. Here, Cλ(υ,k) denotes the minimum number of k-subsets of a υ-set of points such that each pair of points occurs in at least λ of the k-subsets. We use these results to prove simple numerical conditions which are both necessary and sufficient for the existence of (Kk − e)-designs with more points than blocks.

Descent on Simply Connected Surfaces Over Algebraic Number Fields

We study descent and obstructions to the Hasse principle on simply connected surfaces over number fields.

Pell conics and quadratic reciprocity

We give a proof of quadratic reciprocity, based on the arithmetic of conics. The proof works in all cases, and the calculations are remarkably simple.