Antonella Perucca

Tactile Tools for Teaching: Implementing Knuth's Algorithm for Mastering Mastermind

Thomas M. Fiore (tmfiore@umich.edu, MR ID 740565) received a B.S. in Mathematics and a B.Phil. in German at the University of Pittsburgh. He completed his Ph.D. in Mathematics at the University of Michigan in 2005. After postdoctoral positions in Chicago and Barcelona, he joined the University of Michigan–Dearborn. A Humboldt research fellowship supported Fiore’s sabbatical at the University of Regensburg in 2015–2016. His research interests include algebraic topology, higher category theory, and mathematical music theory. Alexander Lang (alexander-lang1@gmx.de, MR ID 1262561) studied Mathematics at the University of Regensburg in Germany and is currently training to become a mathematics teacher. He is very passionate about didactics, especially in creating exercises for his students or finding solutions for pedagogical challenges such as the Mastermind Wheel, the subject of his diploma thesis. Antonella Perucca (antonella.perucca@uni.lu, MR ID 857706) studied Mathematics at the Scuola Normale in Pisa, Italy. After working in various countries, she is now Professor for Mathematics and its Didactics at the University of Luxembourg. Perucca is a researcher in number theory and develops mathematical applications such as the Chinese remainder clock featured in this JOURNAL in 2017. To find out more, explore her webpage www.antonellaperucca.net.

Reductions of one-dimensional tori

Consider a non-split one-dimensional torus defined over a number field K. For a finitely generated group G of rational points and for a prime number l, we investigate for how many primes 𝔭 of K the size of the reduction of G modulo 𝔭 is coprime to l. We provide closed formulas for the corresponding Dirichlet density in terms of finitely many computable parameters. To achieve this, we determine in general which torsion fields and Kummer extensions contain the splitting field.

The Chinese Remainder Clock

Summary We present an analog clock with five hands that illustrates the Chinese remainder theorem and that can be understood also by nonmathematicians. Moreover, we interpret the Chinese remainder theorem in terms of rotations and prove it without equations.

Characterizing abelian varieties by the reduction of the Mordell–Weil group

Let

THE MULTILINEAR SUPPORT PROBLEM FOR PRODUCTS OF ABELIAN VARIETIES AND TORI

A

The order of the reductions of an algebraic integer

be an abelian variety defined over a number field

Radical characterizations of elliptic curves

K

Reductions of algebraic integers

. If

The constant of the support problem for abelian varieties

\mathfrak{p}

Reductions of points on algebraic groups

is a prime of