Math 113 (Fall 2017)

General information

  • Where and when: Monday, Wednesday and Friday 12:00-1:00pm in 241 Cory.
  • Textbook: D. Dummit and R. Foote, Abstract Algebra, third edition.
  • Office hours: in Evans 1091:
    • Wednesday 9:00-10:30am.
    • Friday 2:00-3:30pm.
  • GSI: Justin Chen will be holding office hours in 959 Evans at the following times:
    • Tuesday: 11 am - 3 pm
    • Wednesday: 2 pm - 7 pm
    • Friday: 11 am - 12 pm
  • Piazza: I encourage you to ask your questions there.
  • Grade:
    • 10% homeworks, 20% each midterm, 50% final.
    • The final grade can replace one of the midterms.
    • You can drop one homework.

Broad syllabus

  • Groups: We will be covering Ch. 1, 2 and 3.
  • Rings: We will be covering Ch. 7, 8 and 9.
  • Fields: We will be covering parts of of Ch. 13 and 14.

Homework

Exams

Syllabus

  • August 23rd: Preliminaries (DF 0.1).
  • August 25th: Arithmetic and equivalence relations (DF 0.1 and 0.2).
  • August 28th: Equivalence relations and modular arithmetic (DF 0.1 and 0.3)
  • August 30th: Groups (DF 1.1).
  • September 1st: Order of an element (DF 1.1).
  • September 6th: Symmetric groups (DF 1.3).
  • September 8th: Dihedral groups (DF 1.2).
  • September 11th: Homomorphisms (DF 1.6).
  • September 13th: Subgroups (DF 2.1).
  • September 15th: Examples of subgroups (DF 2.2).
  • September 18th: Cyclic groups (DF 2.3).
  • September 20th: Generated subgroups and cosets (DF 2.4 and 3.2).
  • September 22nd: First midterm.
  • September 25th: Lagrange's theorem, normal subgroups and quotient groups (DF 3.2 and 3.1).
  • September 27th: First and second isomorphism theorems (DF 3.1 and 3.3).
  • September 29th: Third isomorphism theorem and groups actions (DF 3.3 and 1.7).
  • October 2nd: Stablizers, orbits and the class equation (DF 2.2, 4.1 and 4.3).
  • October 4th: Cauchy's theorem (DF 3.4 and 4.3).
  • October 6th: Signature of a permutation (DF 3.5).
  • October 9th: Rings, Definitions and examples (DF 7.1).
  • October 11th: Ring homomorphisms, ideals and quotients (DF 7.3).
  • October 13th: Ring quotients and polynomial rings (DF 7.3 and 7.2).
  • October 16th: Polynomial rings and generated ideals (DF 7.3 and 7.4).
  • October 18th: Maximal ideals (DF 7.4).
  • October 20th: Prime ideals and Chines remainder theorem (DF 7.4 and 7.6).
  • October 23rd: Chinese remainder theorem and Euclidian domains (DF 7.6 and 8.1).
  • October 25th: Euclidian domains and principal ideal domains (DF 8.1 and 8.2).
  • October 27th: Greatest common divisors and unique factorization domain (DF 8.1 and 8.2).
  • October 30th: Second midterm
  • November 1st: Unique factorization domains and fraction fields (DF 8.3 and 7.5).
  • November 3rd: Polynomial factorization (DF 9.3).
  • November 6th: Roots of polynomials (DF 9.5)
  • November 8th: Field extensions (DF 13.1).
  • November 13th: Algebraic extensions (DF 13.1 and 13.2).
  • November 15th: Algebraic extensions (DF 13.2).
  • November 17th: Algebraic extensions (DF 13.2).
  • November 20th: Spliting fields (DF 13.4).
  • November 27th: Algebraic closure dand finite fields (DF 13.4 and 13.5).

Approximate syllabus of future classes

  • November 29th: Finite fields and introduction to Galois theory (DF 13.5, 14.1 and 14.2).
  • December 1st: The fundamental theorem of algebra (DF 14.6).