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

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

Quadratic reciprocity via resultants

We give a simple inductive proof of quadratic reciprocity using resultants

Note on the number of divisors of reducible quadratic polynomials

DOI: 10.1017/S000497271800073

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

The classification and nomenclature of endogenous viruses of the family Caulimoviridae

Endogenous members of the family Caulimoviridae have now been found in the genomes of many plant species. Although these sequences are usually fragmented and rearranged and show varying degrees of decay, the genomes of the ancestral viruses can often be reassembled in silico, allowing classification within the existing viral taxonomic framework. In this paper, we describe analyses of endogenous members of the family Caulimoviridae in the genomes of Oryza sativa, Nicotiana tabacum and Solanum spp. and on the basis of phylogeny, genome organization and genetic distance within the pol gene, propose two new virus genera called Orendovirus and Solendovirus. A system of nomenclature for endogenous virus sequences in plants is also proposed