The focus of this book is a mathematical structure modeling a physical or biological system that can be in any of a number of states. Each state is characterized by a set of binary features, and di?ers from some other nei- bor state or states by just one of those features. In some situations, what distinguishes a state S from a neighbor state T is that S has a particular f- ture that T does not have. A familiar example is a partial solution of a jigsaw puzzle, with adjoining pieces. Such a state can be transformed into another state, that is, another partial solution or the ?nal solution,...

This title describes current applications and theory in knowledge spaces, including the bilingual ALEKS system, and its applications in mathematics and chemistry across the educational arc.