M380D Algebra: Spring 2018

Day/Time: MWF 1-2pm; Location: RLM 12.166; Unique: 54270

Instructor
Mirela Ciperiani (mirela at math dot utexas dot edu); Office: RLM 12.164

Office Hours
Wednesday 2-3pm in RLM 12.164.

Text
Abstract Algebra, 3rd edition by Dummit and Foote, published by Wiley. We will cover material from chapters 13, 14, 18, 19.
The book should be available at the University Co-op.

Prerequisites
M380C. Contact me for more details if you are not sure whether this course is for you.

Teaching Assistant
Tom Gannon (gannon at math dot utexas dot edu)
Please contact Tom if you have any questions about the grading of the homework.

Midterm exam
Thursday, March 7 in class.

Final exam
Saturday, May 12, 9:00 am -12:00 pm in RLM 12.166.
All students must take the final at the time scheduled by the university.

Homework
The weekly homework assignments and the grades will be posted on Canvas. The homework will be due on Mondays at the beginning of class and the solutions will be posted on Canvas on that day. The lowest homework grade will be dropped.

Grading
Plus/minus grades will be assigned for the final grade in this course.

Homework 30%
Midterm 30%
Final exam 40%

Conflicts
If you have a conflict with any of the exams (for example, due to a religious holiday), you must notify the instructor by the 12-th class day.

Disabilities
Students with disabilities may request appropriate academic accommodations from the Division of Diversity and Community Engagement, Services for Students with Disabilities, 512-471-6259. If you plan on using accommodations, you need to notify the instructor by the 12-th class day.



Recommended reading

This schedule is tentative and will be modified as necessary.

Date
Reading
  Jan. 17, 19   13.1, 13.2: Basic theory of field extensions, Algebraic extensions
  Jan. 22, 24, 26   13.4, 13.5: Splitting fields and algebraic closures, Separable and inseparable extensions
  Jan. 29, 31, Feb. 2   More on inseparability. Finite fields.
  Feb. 5, 7, 9   13.6, 14.1: Cyclotomic fields, Galois Theory
  Feb. 12, 14, 16   14.2: The Fundamental Theorem of Galois Theory
  Feb. 19, 21, 23   14.2, 14.3 : Examples, Galois theory for finite fields
  Feb. 26, 28, Mar. 2   14.4, 14.5: Composite extensions and Simple extensions, Cyclotomic extensions
  Mar. 5
Review
  Mar. 7
Midterm
  Mar. 9   14.7 : Abelian extensions, Solvable extensions
  Mar. 19, 21, 23   14.6, 14.8: Galois groups of polynomials, Computation of Galois groups over Q
  Mar. 26, 28, 30   14.9: Examples,Transcendental extensions, Inseparable extensions
  Apr. 2, 4, 6   14.9, 18.1: Infinite Galois group, Introduction to the representation theory of finite groups,
                    Maschke's Theorem
  Apr. 9, 11, 13   18:1, 18:3: Schur's Lemma, Character theory and Orthogonality relations
  Apr. 16, 18, 20   19.1: Number of irreducible characters, Character tables, Lifted characters
  Apr. 23, 25, 27   19.3: Restriction of characters, Induced characters, Frobenius reciprocity.
  Apr. 30, May 2, 4   Additional topics depending on interest, and Review