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Andrew Alaniz

Publications and source records attributed to Andrew Alaniz.

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The Social and Work Structure of an Afterschool Math Club

The objective of this exploratory study was to examine the interpersonal dynamics of an afterschool math club for middle schoolers. Using social network analysis, two networks were identified and analyzed: (a) a network of friendship relationships and (b) a network of working relationships. The interconnections and correlations between friendship relationships, working relationships, and a student opinion survey were studied. We identified a core working group of students from within the network of working relations. This group acted as a central go-between for other members in the club. This core working group also expanded into the largest friendship group in the friendship network. A second group was formed from popular but aloof students who reported less impact from the club. Although there were working isolates, they were not found to be socially isolated. Students who were less popular tended to report a greater favorable impact from club participation than those who were more popular.

math.HO

On cubic multisections of Eisenstein series

A systematic procedure for generating cubic multisections of Eisenstein series is given. The relevant series are determined from Fourier expansions for Eisenstein series by restricting the congruence class of the summation index modulo three. We prove that the resulting series are rational functions of η(τ) and η(3τ), where ηis the Dedekind eta function. A more general treatment of cubic dissection formulas is given by describing the dissection operators in terms of linear transformations. These operators exhibit properties that mirror those of similarly defined quintic operators.

math.NT