This book presents the four-and-a-half year research journey investigating the way mathematics is taught to prospective engineers and the way mathematics is used by practising engineers. The study was inspired by the lacuna in the scholarly literature concerning the nature of mathematics role, if any, as a significant cause of the declining number of students entering professional engineering courses and also by the absence of any broad picture of the mathematical expertise required or used by practising engineers. The study illustrates that feelings about mathematics are an important factor in mathematics learning and usage and that mathematics learning generally focuses on objective analysis while thinking usage, subjective analysis and communicating mathematics are also required in engineering practice. We hope this book will provide rich insights into both mathematics learning and engineering practice for second and third level students, parents, mathematics teachers and engineering educators as well as for engineers who wish to better understand their own career.