This dissertation presents four studies on the mathematical education of engineering students. The first study is a qualitative analysis of the beliefs of engineering faculty at a single institution regarding what constitutes “mathematical maturity” for engineering students. Faculty emphasized the need for mathematical modeling skills, fluent symbolic representation skills, and a combination of effortless algebraic fluency and ability to use computational tools. The second study is an analysis of the beliefs of engineering faculty at a variety of institutions. These faculty also emphasized modeling, representation, and computation, corroborating the results of the first study. The third study is an analysis of the mathematical content of engineering circuits and statics homework problems. Just 8% of statics problems and 20% of circuits problems use calculus, and in a much more limited way than what is taught in calculus. The fourth study presents a quantitative survey of engineering sophomores’ perceptions of the relevance of mathematics to their engineering studies. The students have somewhat favorable views of the relevance of mathematics, but some high-performing students view mathematics as irrelevant.
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