In an elementary undergraduate abstract algebra or group theory course, a student is introduced to a variety of methods for constructing and deconstructing groups. What seems to be missing from contemporary texts and syllabi is a theorem, first proved by Edouard Jean-Baptiste Goursat (1858-1936) in 1889, which completely describes the subgroups of…

Presents an example from the combinatorial theory of partially ordered sets. Discusses algorithms of on-line antichain partitioning problems, a topic in discrete optimization. (YP)

Explored are various aspects of drawing graphs on surfaces. The Euler's formula, Kuratowski's theorem and the drawing of graphs in the plane with as few crossings as possible are discussed. Some applications including embedding of graphs and coloring of maps are included. (YP)

Determines which chessboards contain a chromatic rectangle having all four corners the same color for any black-white coloring. Expands the problem to a three color problem. (YP)