This thesis reports on a study investigating the mathematical skills and attitudes of incoming engineering students in Dublin City University. The following questions are posed in this thesis: What are the students' strengths and weaknesses in basic areas of mathematics? What beliefs do the students express in relation to mathematics? The research attempted to answer these questions using two approaches: Firstly, an attitudinal survey was undertaken to identify students' attitudes towards mathematics, under a selection of different headings. Secondly, mathematics tests were run, focusing on the core mathematical skills necessary for engineering students. Both the test and survey were run at the beginning and/or end of the academic years 2012/2013 and 2013/2014 to give comparative data. The results of the survey reflected high levels of confidence in relation to mathematics and high goals in relation to mathematical achievement. The test results showed a number of strengths and weaknesses in understanding or dealing with basic mathematical problems and concepts. The test was graded using certainty-based marking, which allowed the identification of misconceptions as well as knowledge gaps in students‟ mathematical skills. Based on these findings, recommendations are made in relation to the mathematical education of engineers in DCU.