Mathematics is a constituent of the education of Engineering students. This paper reports on a study investigating the attitudes and perceptions towards mathematics of first year Engineering students. The sample consisted of 145 freshmen (80 men and 65 women) from one Greek university, derived from three Engineering departments (Mechanical, Electrical and Civil). A two-part questionnaire with satisfactory reliability in each part was completed by the participants. Data was analyzed using descriptive statistics, correlations and exploratory factor analysis. The data analysis led to nine factors which shape and mediate students' mathematical attitudes and perceptions. These factors are: Anxiety, Confidence, Learning goals, Theory of intelligence, Persistence, Approach, Learning strategies, Prior experience and General issues. Demographic variables (sex, age, learning disability and choice of study) are found to have an effect on students' attitudes and perceptions. The findings of this study need to be viewed in relation to the redesign of the Engineering Mathematics curriculum to teach effectively all students and raise their mathematical confidence and motivation.