教科書： Minking Eie and Shou-Te Chang, A Course on Abstract Algebra， 2nd ed.



課程內容：

1. Definition and examples of rings. Basic properties

2. Units. Zerodivisors and nonzerodivisors. Nilpotent elements. Integral domains. Reduced rings. Fields and skew fields

3. Ideals. Quotient rings

4. Ring homomorphisms. Fundamental theorem of ring homomorphisms. Three isomorphisms

5. Polynomial rings

6. Factorization. Irreducible elements and prime elements.

7. Euclidean domains. Unique factorization domains. Principal ideal domains

8. Polynomial extensions of UFD’s

9. Field extensions. Algebraic and transcendental extensions. Finite extensions

10. Geometric constructions

11. Introduction to Galois Theory （Optional)

每次交作業（至少有做出部分的題目，並沒有抄襲或借人抄襲者）可得1至2分，上限20分
另有Bonus Probloems每次1分，上限4分
總和為原始成績
原始成績*5為研習課成績

Bonus Problems交給張老師
平常作業交給趙文脩助教

這個課是代數（2）的輔助課程，強力建議有修代數（2）的同學亦修習這個課。