課程內容:

 

1.        Definition and basic concepts of modules

2.        Free modules. Bases of free modules and vector spaces.

3.        R-linear maps

4.        Properties of matrices

5.        Direct sum of modules

6.        Finitely generated modules

7.        Fundamental Theorem of finitely generated modules over a PID.

8.        Canonical forms

9.        Fundamental Theorem of finitely generated abelian groups

10.   Algebraic closure (optional)

11.   Galois Theory. Insolvability of the quintic (optional)

12.   Group actions (optional)

13.   Sylow theorems (optional)

 

評分方式:

作業100%