Meaningful learning, physical

Mathematical operations occur regularly both in the theory and problems of physical chemistry, contributing greatly to the complexity of the subject. Mathematics is essential for the meaningful learning of physical chemistry, but for this to happen it must be coupled with understanding of the underlying physical concepts. 

Williams, K. A. and A. M. L. Cavallo (1995) Reasoning ability, meaningful learning and students understanding of physics concepts. Journal of College... 

Halloun, 1. (1996). Schematic modelling for meaningful learning of physics. Journal of Research in Science Teaching, 33(9), 1019-1041. 

If the class membership of the patterns are known one speaks about supervised learning (learning with a teacheh) More difficult is the problem if no natural classes of patterns are known a priori. In this case an unsupervised learning (learning without a teacher) requires a cluster analysis and a physically meaningful interpretation of the clus- ters. 

The digital learning network classifier may offer advantages when few carefully selected training patterns are available. Most work has been carried out with random connections of features. Significant improvements may be expected if physically meaningful connections of features are found and realized in a classification network. 

An obstacle faced by many chemistry students in learning quantum mechanics is their unfamiliarity with much of the required mathematics. In this text I have included detailed treatments of the needed mathematics. Rather than putting all the mathematics in an introductory chapter or a series of appendices, I have integrated the mathematics with the physics and chemistry. Immediate application of the mathematics to solving a quantum-mechanical problem will make the mathematics more meaningful to students than would separate study of the mathematics. I have also kept in mind the limited physics background of many chemistry students by reviewing topics in physics. 

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