Background: The main objective of the study was to examine the relevance of engineering mathematics to the emerging industries. The level of abstraction, the standard of rigor, and the depth of theoretical treatment are necessary skills expected of a graduate engineering technician to be derived from mathematical knowledge. The question of whether these skills are imparted to benefit emerging economies still remains a big area of investigation. This study investigated the relevancy of engineering mathematics to the benefit of local industry in a developing economy, Uganda. Results: There was a significant difference between the mathematics being taught to the engineering technical students and the mathematics relevant to the engineering technical work in the industries (p value < 0.05). Implying that the mathematics taught to engineering technical students, though relevant, is not in the form of what the industries require. The use, practicability, depth, rigor, modernity, relevancy, and usefulness of the taught mathematics were all statistically different from the desired mathematical skills for the industry. Moreover, the extent of use of the engineering mathematics did not differ between the required and taught and among the civil, electrical, and mechanical branches of engineering. Conclusions: The mathematics syllabi for polytechnic institutes should be developed to directly support innovations and efficiency in the local industries. Therefore, a close collaboration between the polytechnic colleges and the local industries should be facilitated to achieve a sustainable industrial.