Math 371 Course Information - Fall 2006

Tuesdays and Thursdays, 3 pm - 4:30 pm in DLR 4C2

Faculty: Nate Ackerman TA: Chenxu He
Office: DRL 4N53 Section Location: DRL 2C6
Office Hours: Thursdays 4:30 pm - 5:30 pm or by appointment Section Time: Tuesdays 6:30 pm - 8:30 pm
E-mail: nate AT math.upenn.edu E-mail: hech 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

In Class Test: 20 Points

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.
In Class Exam
The in class midterm will be held on Thursday October 5th.
Take Home Exam
The take home exam will be handed out in class in class on November 30 and will be due in class one week later on December 4th. Unlike homeworks, there will be NO collaboration
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 12, 2006.