This book presents the basic concepts of classical psychophysics, derived from Gustav Fechner, as seen from the perspective of modern measurement theory. The theoretical discussion is elucidated with examples and numerous problems, and solutions to one-quarter of the problems are provided in the text.
This book presents the basic concepts of classical psychophysics, derived from Gustav Fechner, as seen from the perspective of modern measurement theo...
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,...
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 ch...
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 orde...
Sometime in the late sixties, one of the editors of this volume realized that the mathematica psychologists in Europe-an odd lot mostly concentrated in Germany, the Netherlands, France, England and Belgium-were suffering from an acute sense of isolation. The papers that they presented at meetings of their national or regional societies had to be 'sanitized' to the point of misrepresentation. They were misunderstood. The mood was grim, depression was lurking. He decided that urgent action was required: a European gathering of mathematical psychologists was called in April 1971. Not being...
Sometime in the late sixties, one of the editors of this volume realized that the mathematica psychologists in Europe-an odd lot mostly concentrated i...
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...
The authors describe systematic methods for uncovering scientific laws a priori, on the basis of intuition, or Gedanken Experiments . Mathematical ...
This book describes current applications and theory in knowledge spaces, including the bilingual ALEKS system, and its applications in mathematics and chemistry across the educational arc. Discusses knowledge spaces in teaching of college chemistry much more.
This book describes current applications and theory in knowledge spaces, including the bilingual ALEKS system, and its applications in mathematics and...
