Fall 2016, MTH 310: Abstract Algebra I & Number Theory

  • Course syllabus (Section 2, Section 3): read this! The material on this page is merely a condensed version of the syllabus.
  • Meeting information:
    • Section 2: MWF, 12:40 PM -- 1:30 PM, Wells Hall A208
    • Section 3: MWF, 1:50 PM -- 2:40 PM, Wells Hall A216
  • Exam information:
    • Midterm: Friday, October 7, 2016, in-class
    • Final:
      • Section 2: Thursday, December 15, 2016, 12:45 PM -- 2:45 PM, Wells Hall A208
      • Section 3: Monday, December 12, 2016, 12:45 PM -- 2:45 PM, Wells Hall A216
  • 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.
  • 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. 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.
  • Tentative schedule of topics:
    • Week 1
      • 8/31: Introductions; sets and binary relations
      • 9/2: Review of logic and proof techniques
    • Week 2
      • 9/5: Labor Day -- no class
      • 9/7: The division algorithm in Z
      • 9/9: Divisibility and the Euclidean Algorithm
    • Week 3
      • 9/12: Primes and unique factorization
      • 9/14: (cont'd)
      • 9/16: Congruence and congruence classes
    • Week 4
      • 9/19: (cont'd)
      • 9/21: Modular arithmetic
      • 9/23: The structure of Zp (p prime) and Zn
    • Week 5
      • 9/26: Rings: definitions and examples
      • 9/28: (cont'd)
      • 9/30: Basic properties of rings
    • Week 6
      • 10/3: (cont'd)
      • 10/5: Review
      • 10/7: Midterm Exam
    • Week 7
      • 10/10: Isomorphisms and homomorphisms
      • 10/12: (cont'd)
      • 10/14: Polynomial arithmetic and the division algorithm
    • Week 8
      • 10/17: Divisibility in F[x]
      • 10/19: (cont'd)
      • 10/21: Irreducibles and unique factorization
    • Week 9
      • 10/24: Polynomial functions, roots, reducibility
      • 10/26: (cont'd)
      • 10/28: Irreducibility in Q[x]
    • Week 10
      • 10/31: (cont'd)
      • 11/2: (cont'd)
      • 11/4: Irreducibility in R[x] and C[x]
    • Week 11
      • 11/7: (cont'd)
      • 11/9: TBD
      • 11/11: Congruence in F[x] and congruence classes
    • Week 12
      • 11/14: (cont'd)
      • 11/16: Congruence class arithmetic
      • 11/18: The structure of F[x]/(p(x)) when p is irreducible
    • Week 13
      • 11/21: (cont'd)
      • 11/23: Ideals and congruence
      • 11/25: Thanksgiving Break -- no class
    • Week 14
      • 11/28: (cont'd)
      • 11/30: Quotient Rings and homomorphisms
      • 12/2: The structure of R/I when I is prime or maximal
    • Week 15
      • 12/5: (cont'd)
      • 12/7: Review
      • 12/9: Review