Math 371 Course Information - Fall 2007

Tuesdays and Thursdays 1:30 pm - 3 pm DRL 4C6

Faculty: Nate Ackerman TA: Joe-Kai Tsay
Office: DRL 4N53 Section Location: DRL 4C19
Office Hours:
Section Time:
E-mail: nate AT math.upenn.edu E-mail: jetsay AT math.upenn.edu

Texts


Syllabus
  1. Groups
    • The Operation of a Group on Itself
    • Operations on Subsets
    • The Sylow Theorems
    • The Structure Theorem for Abelian Groups
  2. Bilinear Forms
    • Definition of Bilinear Form
    • Symmetric Forms: Orthogonality
    • The Geometry Associated to a Positive Form
    • Hermitian Forms
    • The Spectral Theorem
    • The Spectral Theorem for Normal Operators
  3. Rings
    • Formal Construction of Integers and Polynomials
    • Homomorphisms and Ideals
    • Quotient Rings and Relations in a Ring
    • Adjunction of Elements
    • Integral Domains and Fraction Fields
    • Maximal Ideals
    • Factorization of Integers and Polynomials
    • Unique Factorization Domains, Principal Ideal Domains, and Euclidean Domains
    • Guass' Lemma
  4. Fields
    • Algebraic and Transcendental Elements
    • The Degree of a Field Extension
    • Symbolic Adjunction of Roots
    • Transcendental Extensions
    • Finite Fields
    • Algebraically Closed Fields
    • Constructions with a Ruler and Compass
  5. Galois Theory
    • The Main Theorem of Galois Theory
    • Primitive Elements
    • Proof of the Main Theorem
    • Unsolvability of the General Quintic


Grades
Grades will be broken up as follows

1st Take Home Test: 20 Points

2nd Take Home Test: 30 Points

Homework: 50 Points

(Possible) Final: 30-50 Points


Tests
If anyone has a religious holiday during any of the tests please let me know as soon as possible. Unlike homeworks, there will be NO collaboration on the take home exams.
1st Take Home Exam
This 1st take home exam will be handed out on October 18th and due at the beginning of class on October 23th.
2nd Take Home Exam
The take home exam will be handed out in class in class on November 29th and will be due in class one week later on December 6th. 
Final Exam
The final exam (if it is given) will be during the normal time for final exams. Depending on the progress of the course we may not have a final. The decision on whether or not to have a final and how much it will be worth (if it is given) will be made later in the semester.
Test scores will be posted on the Blackboard website for this class


Homeworks

This page was created by Nate Ackerman, and last revised on September 2, 2007.