Abstract Algebra

Course Description
The second term of Math 120 will be devoted primarily to Field and Galois Theory. Time permitting, topics should include: 

Field extensions: Algebraic closure. Splitting fields and normal extensions. Separable and Inseparable extensions and degree. Primitive element theorem. Linear independence of characters. Traces and norms. Normal basis theorem. Transcendental extensions. Transcendence bases theorem. 

Galois theory: Galois extensions. Absolute Galois group. Galois theory for infinite extensions.

Examples: Finite fields. Cyclotomic fields. Local fields. Function fields.

Galois Cohomology: Galois Cohomology. Hilbert's 90 theorem. Cyclic extensions. Abelian extensions. Solvable extensions. Kummer Theory.

Ring extensions: Integral extensions. Noether Normalization Theorem. Integral closure. Integral Galois extensions. Going-up theorem. Decomposition groups. Extension of homomorphisms. Valuation rings. Dedekind domains. DVR's.


Course Meeting Time and Location
Monday, Wednesday and Friday
9:00 - 9:55 am
255 Linde

Course Instructor Contact Information and Office Hours
275 Linde Hall
Monday 10:00 - 11:00 am or by appointment

TA Contact Information and Office Hours
306 Linde Hall
Tuesday 18:00 - 19:00 am or by appointment

Textbook
Algebra, Serge Lang, Springer, ISBN: 978-0-387-95385-4

We will also discuss some topics not covered by the book.

Course Policies and Grading Breakdown
There will be no midterms nor final exam. The grade will be based on: 
Homework   75% 
Attendance  25%

Registered students are required to attend lectures, unless get the permission from the instructor.
Homework will be posted here every Wednesday and will be due the following Wednesday at 4pm. As usual, collaborations are encouraged by solutions must be written independently. Homework must be typed in Tex and can be handed in either in hard copy or in electronic version. Late homework will not be accepted EXCEPT ONE time (per term). You may email me PRIOR to the due time requesting an extension of up to one week (for the last HW up to two days) and it will granted. 

Assignments
 Date PostedAssignment Due Date 
 1/09/2019PS1.pdf 1/16/2019 4pm 
 1/16/2019 PS2.pdf 1/23/2019 4pm
 1/23/2019
 1/30/2019 4pm 
 1/30/2019
2/06/2019 4pm
 2/06/2019
 2/13/2019 4pm 
 2/13/2019
 2/20/2019 4pm 
 2/20/2019
 2/27/2019 4pm 
 2/27/2019
3/06/2019 4pm
 3/06/2019
3/13/2019 4pm
 3/13/2019
3/20/2019 4pm

Ċ
PS1.pdf
(61k)
Xinwen Zhu,
Jan 8, 2019, 9:01 PM
Ċ
PS2.pdf
(34k)
Xinwen Zhu,
Jan 15, 2019, 9:07 PM