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Learning spaces offer a rigorous mathematical foundation for practical systems of educational technology. Learning spaces generalize partially ordered sets and are special cases of knowledge spaces. The various structures are investigated from the standpoints of combinatorial properties and stochastic processes.

Leaning spaces have become the essential structures to be used in assessing students' competence of various topics. A practical example is offered by ALEKS, a Web-based, artificially intelligent assessment and learning system in mathematics and other scholarly fields. At...

Learning spaces offer a rigorous mathematical foundation for practical systems of educational technology. Learning spaces generalize partially ordered sets and are special cases of knowledge spaces. The various structures are investigated from the standpoints of combinatorial properties and stochastic processes.

Leaning spaces have become the essential structures to be used in assessing students' competence of various topics. A practical example is offered by ALEKS, a Web-based, artificially intelligent assessment and learning system in mathematics and other scholarly fields. At...

Originally published in 1975, this volume contains original reports of new models and data in the areas of propositional reasoning, syllogistic reasoning, and transitive inference in children and adults of the time. A wide range of theoretical viewpoints is represented, and an effort is made to integrate the models and empirical findings, as well as place them in a common perspective and elucidate the general issues and questions relevant to these various approaches. The study of logical reasoning was undergoing rapid expansion at the time and this volume brings together the latest...

The authors describe systematic methods for uncovering scientific laws a priori, on the basis of intuition, or Gedanken Experiments . Mathematical expressions of scientific laws are, by convention, constrained by the rule that their form must be invariant with changes of the units of their variables. This constraint makes it possible to narrow down the possible forms of the laws. It is closely related to, but different from, dimensional analysis. It is a mathematical book, largely based on solving functional equations. In fact, one chapter is an introduction to the theory of functional...