In the autumn of 2024, I held several lectures on Advanced Algebra for all freshmen of Xingjian College, Tsinghua University.

Lecture for the Midterm Exam

This lecture mainly reviews the basic knowledge such as matrices, the linear relationships of vector groups, the theory of solutions to systems of linear equations, determinants, canonical forms, etc., and provides basic and advanced example problems for students to practice. The video recording and the manuscript of this lecture are available at the following link Tsinghua Cloud.

Lecture for the Final Exam

This lecture mainly reviewed the knowledge of linear spaces, linear mappings, polynomials, etc., and combined geometric intuition with algebraic reasoning. It is hoped that it can help students flexibly apply geometric and algebraic methods when solving problems. The video recording and the manuscript of this lecture are available at the following link Tsinghua Cloud.