Abstract algebra is the study of the common principles that govern computations with seemingly disparate objects. One way to begin is by studying groups, which are sets with a single operation under which each non-identity element is invertible. Examples include the integers with addition, invertible matrices of size n, permutations of a fixed set, and the symmetries of an object. Our goal is to study a definition of groups that unifies all of the important examples above and more.

Graph theory gives us both an easy way to pictorially represent many major mathematical results and insights into the deep theories behind them. Graphs seem simple -- they're just collections of dots connected by curves -- but are very rich structures that arise naturally in applications ranging from social networks to electric power grids. We will examine properties such as isomorphism, connectivity, planarity, and coloring using classic examples such as paths, cycles, trees, complete graphs, and polyhedral graphs.

Chamber Music for wind instruments

Chamber Music for piano instruments

This ensemble, composed of all instruments--including piano, strings, brass, and woodwinds--performs dance music of Eastern Europe. Students at all levels of experience will use their classical training to go beyond the printed page into the folk tradition, learning to play different modes of the tunes and employing 'untraditional' techniques that are traditional in this unique folk music.

Study and perform music for flute ensembles.

This course offers opportunities to play and sing chamber music from the Medieval, Renaissance, and Baroque eras, collaborating with musicians from the Five Colleges and with the support of a specialist coach. Ensemble members will draw on historical context and performance practice as they refine performance technique and ensemble skills. Singers and instrumentalists will be sorted into ensembles based on level- from beginner to advanced- and areas of interest.

Chamber Music for percussion instruments.

The Five College Collegium is the flagship ensemble of the Five College Early Music Program. The ensemble is made up of experienced singers and instrumentalists from the Five College Consortium, and prepares two large-scale projects in the course of the academic year for public performance. The Collegium rotates its rehearsal residency among the schools in the Five College system, and focuses on repertoire from the Medieval, Renaissance, and Baroque periods.

Continuation of Renaissance and Baroque Dance I. Sixteenth- through eighteenth-century European social dance, contemporary with the eras of Elizabeth I and Shakespeare in England, the Medicis in Italy, Louis XIV in France, and colonial America. The focus will be on learning the dances, supplemented by historical and social background, discussion of the original dance sources, and reconstruction techniques.