Fall 2017, MTH 310-001: Abstract Algebra I and Number Theory

  • Course syllabus: click here. Make sure to read this! The content of this page is merely a condensed version of the syllabus.
  • Meeting information: MWF, 11:30 AM -- 12:20 PM, Wells Hall A324
  • Exam information:
    • Midterm: Friday, October 13, 2017, in-class
    • Final: Wednesday, December 13, 2017, 7:45 AM -- 9:45 AM, Wells Hall A324
  • Textbook: "Abstract Algebra: An Introduction," third edition, by Thomas W. Hungerford. You may also find supplementary notes by Prof. Ulrich Meierfrankenfeld useful, which are available here.
  • See (here) as well for some additional discussion of polynomials and extension fields.
  • Online Discussion: Piazza is a very nice communication platform for classes (especially math classes). Instead of sending me questions by email, I encourage you to post questions and/or answers using Piazza, so that everyone in the class can see both the questions and answers. Piazza also allows you to post anonymously, in case you are reluctant to have your name attached to a post. You will receive an invitation in the beginning of the semester inviting you to join. Our Q&A page is
  • Homework: Homework sets will be posted in this section regularly, so make sure to check back for any new assignments. All homework must be typed using LaTeX; I recommend all students use www.sharelatex.com for their homework, as it is easy to get started with and many of you have used it in a previous class. Each assignment will be collected at the beginning of class, and late work will not be accepted under any circumstances. To offset this strict policy, your three lowest homework scores will be dropped automatically.
  • LaTeX: some information about getting started with LaTeX can be found here ( .pdf | .tex ). You can learn not only from the content of the .pdf file, but from looking at how some of the formatting was done by looking at the .tex file itself. If you want to brush up on using it, or learn how to use it at all, there will be a help session on Thursday, 8/31 at 6:00 pm -- 7:00 pm in Wells Hall, room A320.
  • Tentative schedule of topics:
    • Week 1
      • 8/30: Introductions; what is "abstract algebra"?
      • 9/1: Review of notation, logic, and proof techniques
    • Week 2
      • 9/4: Labor Day -- no class
      • 9/6: The division algorithm in Z
      • 9/8: Divisibility and the Euclidean Algorithm
    • Week 3
      • 9/11: Primes and unique factorization
      • 9/13: (cont'd)
      • 9/15: Equivalence and equivalence classes
    • Week 4
      • 9/18: (cont'd)
      • 9/20: Modular arithmetic
      • 9/22: The structure of Zp (p prime) and Zn
    • Week 5
      • 9/25: Rings: definitions and examples
      • 9/27: (cont'd)
      • 9/29: Basic properties of rings
    • Week 6
      • 10/2: (cont'd)
      • 10/4: Isomorphisms and homomorphisms
      • 10/6: (cont'd)
    • Week 7
      • 10/9: Finding isomorphisms
      • 10/11: Review
      • 10/13: Midterm Exam
    • Week 8
      • 10/16: Polynomial arithmetic and the division algorithm
      • 10/18: (cont'd)
      • 10/20: Divisibility in F[x]
    • Week 9
      • 10/23: (cont'd)
      • 10/25: Irreducibles and unique factorization
      • 10/27: Polynomial functions, roots, reducibility
    • Week 10
      • 10/30: (cont'd)
      • 11/1: Irreducibility in Q[x]
      • 11/3: (cont'd)
    • Week 11
      • 11/6: Irreducibility in R[x] and C[x]
      • 11/8: (cont'd)
      • 11/10: Equivalence in F[x] and equivalence classes
    • Week 12
      • 11/13: (cont'd)
      • 11/15: Equivalence class arithmetic
      • 11/17: The structure of F[x]/(p(x)) when p is irreducible
    • Week 13
      • 11/20: (cont'd)
      • 11/22: Ideals and equivalence
      • 11/24: Thanksgiving Break -- no class
    • Week 14
      • 11/27: (cont'd)
      • 11/29: Quotient Rings and homomorphisms
      • 12/1: class canceled
    • Week 15
      • 12/4: The structure of R/I when I is prime or maximal
      • 12/6: Review
      • 12/8: Review