Reconstruction of Teaching Content for Linear Algebra in the Context of Artificial Intelligence: From Pure Computation to Matrix Thinking

Abstract

With the breakthrough of artificial intelligence technology, linear algebra's mathematical foundation, running through each aspect of model construction and semantic representation, has been greatly transformed. Most curricula are still based on the old tradition by emphasizing proficiency in symbolic computation without satisfying the requirement of data science for high dimensional geometric intuition and structural insight. Based upon that, we proposed a teaching reconstruction path from pure computation to matrix thinking; defined matrix thinking as a three level connotation (a data structure language, a spatial mapping tool, and an information processing paradigm); reshaped the three major modules of systems of linear equations, matrix factorization, and the eigenvalue problem respectively; promoted the return of linear algebra from being an algorithmic tool into a thinking framework; laid a mathematical cognition foundation for cultivating artificial intelligence talents.