从一道普特南竞赛题看高等代数课程中的图论方法  

Graph Theory Problems and Methods in Advanced Algebra Through a Putnam Competition Problem

作　　者：刘乐乐 汪毅[1] LIU Lele;WANG Yi(School of Mathematical Sciences,Anhui University,Hefei 230601,China)

机构地区：[1]安徽大学数学科学学院,安徽合肥230601

出　　处：《黄山学院学报》2024年第5期102-106,共5页Journal of Huangshan University

摘　　要：以一道普特南数学竞赛试题作为切入点,探讨图论思想如何融入高等代数课程中,展示图论课程与高等代数课程之间的联系。进一步分析图论在解决高等代数问题中的多元应用,如矩阵横贯、逆序数、矩阵幂计算及向量组线性相关性等。通过图论视角,深化对高等代数知识的理解与运用。Using a problem from the Putnam Mathematical Competition as a starting point,this article explores how graph theory concepts can be integrated into advanced algebra courses,highlighting the connections between graph theory and advanced algebra.It further analyzes the diverse applications of graph theory in solving advanced algebra problems,such as matrix traversal,inversion number,matrix power computation,and the linear dependence of vector sets.Through the lens of graph theory,it deepens the understanding and application of advanced algebraic knowledge.

关 键 词：图论 高等代数 横贯 Hall定理 

分 类 号：O157[理学—数学]