Comparing expert and learner mathematical language: A corpus linguistics approach

Corpus linguists attempt to understand language by statistically analyzing large collections of text, known as corpora. We describe the creation of three corpora designed to enable the study of expert and learner mathematical language. Our corpora were formed by collecting and processing three different genres of mathematical texts: mathematical research papers, undergraduate-level textbooks, and undergraduate dissertations. We pay particular attention to the method by which our corpora were created, and present a mechanism by which LaTeX source files can be easily converted to a form suitable for use with corpus analysis software packages. We then compare these three different types of mathematical texts by analyzing their word frequency distributions. We find that undergraduate students write in remarkably similar ways to textbook authors, but that research papers are substantially different. These differences are discussed.