M380C Algebra: Fall 2025

Day/Time: TTh 12:30pm-2pm; Location: RLM 10.176; Unique: 59160

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

Office Hours
Thursday 10-11am in RLM 12.164 or by appointment.

Text
Abstract Algebra, 3rd edition by Dummit and Foote, published by Wiley. We will cover material from parts I-III.
The book should be available at the University Co-op.

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

Teaching Assistant
Wang Yao (WangYao at utexas dot edu)
Office Hours: Monday 4-5pm & Tuesday 4:30-5:30pm in PMA 12.128
Please contact Wang if you have any questions about the grading of the homework.

Midterm exam
Thursday, October 16 in class.

Final exam
Saturday, December 13, 3:30-5:30pm in RLM 10.176.
All students must take the final at the time scheduled by the university.

Homework
The weekly homework assignments will be posted on Gradescope by Thursday evening each week. The homework will be due on Wednesdays at 11pm (upload on Gradescope) and will be returned to you within a week.
Sample solutions will be posted on Canvas on Thursdays.
Late homework is not accepted but the lowest homework grade will be dropped.

Grading
Homework 30%
Midterm 30%
Final exam 40%

On all work, your grade will be computed as a percentage: the number of points you earned divided by the number of points possible. The percentages of each type of work that will be used to compute your final grade are given above. Your letter grade will be given based on your numerical average earned in the class, on a scale not stricter than the following: you are guaranteed a D for 40 or above, C- for 50 or above, C for 55 or above, C+ for 65 or above, B- for 70 or above, B for 75 or above, B+ for 85 or above, A- for 90 or above, and an A for 93 or above.

Conflicts
Students with special concerns, be they athletes who might miss class meetings, students with religious observances that interfere with class meetings, or students with disabilities who need special accommodation, are all supposed to notify the instructor about these special needs.
Both exams must be taken at the date/time announced above barring serious personal/health issues.

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.

Topics
  1. Groups
    • Definitions and Examples
    • Homomorphisms
    • Subgroups and Quotient Groups
    • Group Actions
    • The Sylow Theorems
  2. Ring Theory
    • Ideals and Homomorphisms
    • Factorization in rings
    • Polynomial rings
  3. Module Theory
    • Basic definitions and Examples
    • Module homomorphisms
    • Tensor products
    • Modules over PIDs
    • Canonical Forms
  4. Possible Supplemental Topics
    • Homological Algebra
    • Basic Commutative Algebra


Recommended reading

The reading topics may shift as the course progresses.

Date
Reading
  Aug. 26, 28   1.1 - 1.5, 2.1, 2.3, 3.1 - 3.2: Groups and subgroups, definition and examples; Cosets and quotient groups
  Sept. 2, 4   1.6 - 1.7, 3.3, 2.2, 4.1: Homomorphisms and isomorphisms; Isomorphisms theorems; Group actions
  Sept. 9, 11   4.2, 4.3, 4.5: Applications of groups actions; Sylow theory
  Sept. 16, 18   4.4, 4.5: Applications of Sylow theory; Representations induced by group actions; Automorphism group
  Sept. 23, 25   4.6, 5.1, 5.5: Automorphisms of Sn; The simplicity of An; Direct and indirect products
  Sept. 30, Oct. 2   5.4, 6.1, 5.2: Solvable and Nilpotent groups; Classification of finite abelian groups
  Oct. 7, 9   7.1 - 7.3: Rings, definition and examples; Ring homomorphisms and quotient rings; Ideals and their properties
  Oct. 14
Review
based on your questions/requests.
  Oct. 16
Midterm
On the material covered Aug. 26 - Oct. 2
  Oct. 21, 23   7.4 - 7.5: Properties of ideals, Rings of fractions
  Oct. 28, 30   7.6, 8.1 - 8.2: The Chinese Remainder theorem, Euclidean Domains, Principal ideal domains
  Nov. 4, 6   9.6, 8.3: Noetherian rings, Hilbert basis theorem, Unique factorization domains
  Nov. 11, 13   9.1 - 9.5: Polynomial rings
  Nov. 18, 20   10.1-10.3: Introduction to modules
  Nov. 25, 27  
Fall Break
  Dec. 2, 4   10.3,12.1: Modules over Principal Ideal Domains