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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 equations.
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 equations.
The book describes up-to-date applications and relevant theoretical
results. These applications come from various places, but the most
important one, numerically speaking, is the internet based
educational system ALEKS. The ALEKS system is bilingual
English-Spanish and covers all of mathematics, from third grade to
the end of high school, and chemistry. It is also widely used in
higher education because US students are often poorly prepared when
they reach the university level. The chapter by Taagepera and
Arasasingham deals with the application of knowledge spaces,
independent of ALEKS, to the teaching of college chemistry. The
four chapters by Albert and his collaborators strive to give
cognitive interpretations to the combinatoric structures obtained
and used by the ALEKS system. The contribution by Eppstein is
technical and develops means of searching the knowledge structure
efficiently.
The book describes up-to-date applications and relevant theoretical
results. These applications come from various places, but the most
important one, numerically speaking, is the internet based
educational system ALEKS. The ALEKS system is bilingual
English-Spanish and covers all of mathematics, from third grade to
the end of high school, and chemistry. It is also widely used in
higher education because US students are often poorly prepared when
they reach the university level. The chapter by Taagepera and
Arasasingham deals with the application of knowledge spaces,
independent of ALEKS, to the teaching of college chemistry. The
four chapters by Albert and his collaborators strive to give
cognitive interpretations to the combinatoric structures obtained
and used by the ALEKS system. The contribution by Eppstein is
technical and develops means of searching the knowledge structure
efficiently.
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