Abstract: College mathematics education plays an irreplaceable role in the training of engineering professionals. This paper focuses on the concept of“student-centered”and from the perspective of talent training in application-oriented undergraduate universities, explores how to realize the rebalancing and re-integration among mathematics knowledge teaching, thinking training and application ability improvement in limited class hours. At the same time, with the goal of cultivating students'ability of mathematics application innovation, the educational barriers between different courses are broken down, the commonness and characteristics of different mathematics public basic courses are highlighted, the bridge between professional courses and mathematics courses is established, and the linkage training of practical courses is established, so as to promote the cultivation and improvement of students'ability of application innovation.

Key words: Applied undergraduate, College mathematics, Mathematical thinking, Mathematics application innovation ability, Course group linkage, Blended teaching practice