Core Curriculum for Graduate Study Advanced Algebra I (221U3830)
Instructor: Jungkai A. Chen Office: Old Math. Bldg 108 Office Hour: by appointment.
TEL: 33662848
Email: [email protected]
Fri. 3.4 (10:20-12:10), Fri. 7 (15:30-16:20) TA: Chen, Jeng-Jie
TA session: Fri. 8 (16:20-17:10) http://www.math.ntu.edu.tw/~jkchen
Course outline:
1. Set Theory 2. Group theory
Basics definitions and properties.
Group actions and symmetry.
Sylow’s theorem.
Finitely generated abelian groups.
Solvable and nilpotent groups.
3. Field Theory
Algebraic extensions.
Galois groups
Cyclotomic extension and cyclic extensions.
Radical extensions.
Transcendental extensions.
4. Ring and modules
factorization in polynomial rings localization
exact sequences Hom
Tensor products.
Reference:
1. Hungerford, Algebra, GTM 73
2. Lang, Algebra, GTM 211
3. Herstein, Noncommutative rings
4. Atiyah, MacDonald, Introduction to commutative algebra 5. Artin, Algebra, Prentice Hall
Grading:
1. Homework 30%
2. Midterm 30%
3. Final Examination 40%
