Abstract: Advanced Mathematics, a fundamental course that underpins scientific knowledge, cultivates logical thinking, and fosters scientific literacy, encounters several challenges in its instructional approach. These include a lack of innovation in concepts, slow updates in content, traditional and monolithic teaching methods, insufficient integration of ideological and political education, and a deficiency in reformative evaluation methods. Such issues have led to difficulties in curriculum reform, rendering the quality of teaching unable to meet the demands for new engineering talent cultivation. To align with the needs of new engineering education, the teaching of Advanced Mathematics should adhere to the top-level design, foundational logic, practical logic, and disciplinary logic of curriculum reform. This involves a gradual progression in addressing these challenges and predicaments: first, by refining the overarching design, updating concepts, and reshaping course objectives; second, by deepening the integration of ideological and political education to enhance educational effectiveness; third, by breaking away from traditional norms to meet demands and re-construct the content system; fourth, by emphasizing distinctive teaching features and developing a diversified model; and fifth, by moving beyond conventional thinking to reform evaluation and guide comprehensive development.