MATH 511B: Algebra (Spring 2018)

Essential course information is contained in the syllabus.

Instructor

Jack Hall
lectures: Tuesday and Thursday, 12:30-1:45pm in MATH 501
office hours: Tuesdays 4:30-5:30pm and Wednesdays 3-4pm in ENR2 S349
email: firstnamelastname at math dot arizona dot edu

Teaching Assistant

Anthony Kling
problem sessions: Mondays 5-6pm in ENR2 S375
email: amlastname at math dot arizona dot edu

Texts

We will be using Lang's Algebra for the section on Galois Theory.
On campus, this is available through SpringerLink.

Examinations

Midterm 1: 2/22/2018, in class. Topics: everything covered in class and on homework up to and including 2/20/2018.
Midterm 2: 4/3/2018, in class. Topics: everything covered in class and homework up to and including 3/29/2018.
Final: 5/9/2018, in our usual room from 1-3pm. Topics: everything covered in class and homework up to and including 4/12/2018.

Homework

Homework 1: due 1/18/2018 handed out in class
Homework 2: due 1/25/2018 handed out in class
Homework 3: due 2/1/2018 handed out in class
Homework 4: due 2/13/2018 handed out in class
Homework 5: due 2/20/2018 handed out in class
Homework 6: due 3/13/2018 handed out in class
Homework 7: due 3/22/2018 handed out in class
Homework 8: due 3/29/2018 handed out in class
Homework 9: due 4/12/2018 emailed to the class
Homework 10: due 4/19/2018 handed out in class

Topics covered

1/11/2018: Polynomials over a field [Lang IV.1]
1/16/2018: Polynomials over a UFD and irreducibility criteria [Lang IV.2-3]
1/18/2018: Algebraic extensions [Lang V.1]
1/23/2018: Algebraic closure [Lang V.2]
1/25/2018: Algebraic closure (continued) and normal extensions [Lang V.3]
1/30/2018: Normal extensions (continued) and separable extensions [Lang V.4]
2/1/2018: Separable extensions (continued)
2/6/2018: The primitive element theorem and finite fields [Lang V.5]
2/8/2018: Finite fields (continued) and purely inseparable extensions [Lang V.6]
2/13/2018: Purely inseparable extensions (continued)
2/15/2018: Galois extensions [Lang VI.1]
2/20/2018: Galois extensions (continued) and examples [Lang VI.2]
2/22/2018: Midterm 1
2/27/2018: Discriminants
3/1/2018: More examples of Galois extensions
3/13/2018: Fundamental theorem of algebra and cyclotomic extensions [Lang VI.3]
3/15/2018: Cyclotomic extensions (continued)
3/20/2018: Linear independence of characters [Lang VI.4] and norms and traces [Lang VI.5]
3/22/2018: Norms and traces (continued)
3/27/2018: Cyclic extensions [Lang VI.6]
3/29/2018: Solvable and radical extensions [Lang VI.7]
4/3/2018: Midterm 2
4/10/2018: Integral Galois extensions [Lang VII.2]
4/12/2018: Integral Galois extensions (continued)
4/17/2018: Projective space
4/19/2018: Projective space (continued)
4/24/2018: Review of algebraic extensions
4/26/2018: Review of Galois theory
5/1/2018: Review
5/9/2018: Final