Thoughts on Mathematical Ideology of lLinear Spacer

This paper is about the author's thoughts on mathematical thinking method while teaching "linear space" of Advanced Algebra. The ideas of finite and infinite, transformation, unity and isomorphism of algebra and geometry are expounded. If we bring mathematical thinking method to teaching process to share our cognition, feelings and ideas with students, they can profoundly understand the logic of math and appreciate the beauty of math, so as to better learn math, use math, and love math.