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 combinatoric and stochastic search engine described in the book monitors a unique knowledge assessment mechanism that produces the exact list of concepts that the student is ready to learnThis technology is meant to replace psychometric techniques and models that are the basis for current standardized testingThe technology is the basis of the ALEKS system, which has been used successfully by millions of students in the US and abroad in both K12 and higher education