An Empirical Measure on the Set of Symbols Occurring in Engineering Mathematics Texts

Certain forms of mathematical expression are used more often than others in practice. A quantitative understanding of actual usage can provide additional information to improve the accuracy of software for the input of mathematical expressions from scanned documents or handwriting and more natural forms of presentation of mathematical expressions by computer algebra systems. Earlier work has examined this question for the diverse set of articles from the mathematics preprint archive arXiv.org. That analysis showed showed the variance between mathematical areas. The present work analyzes a particular mathematical domain more deeply. We have chosen to examine second year university engineering mathematics as taught in North America as the domain. We have analyzed the set of expressions occurring in the most popular textbooks, weighted by popularity. Assuming that early training influences later mathematical usage, we take this as a model of the set of mathematical expressions used by the population of North American engineers.  We present an empirical analysis of the symbols and $n$-grams occurring in these expressions.