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
-
- (Basic Text) It is assumed you all have a copy of this
|
Title: |
Algebra |
|
Author: |
Michael Artin |
|
Publisher: |
Prentice-Hall |
|
Year: |
1991 |
- (Optional Text)
|
Title: |
Undergraduate Algebra |
|
Author: |
Serge Lang |
|
Publisher: |
Springer |
|
Edition: |
Third |
-
Syllabus
-
- Groups
- The Operation of a Group on Itself
- Operations on Subsets
- The Sylow Theorems
- The Structure Theorem for Abelian Groups
- 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
- 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
- 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
- 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
-
- Homework will be posted at the course
website on Tuesdays. Homework will be due at the beginning of lab
one week after they are assigned. Late homeworks will not be accepted.
- After all homeworks have been turned in, a solution set will
be posted on the Blackboard
website as well as the course website
- Collaberation on homeworks is strongly encouraged.
However, each person must write up their solutions themselves and put
on the homework the names of everyone they worked with.
- In determining the grades for the homework two problems will
be chosen at random. The break up of the homework will then be
|
Finishing All Problems: |
20% |
|
Problem 1: |
40% |
|
Problem 2: |
40% |
- The lowest homework grade will be dropped.
This page was created by Nate
Ackerman, and last revised on September 2, 2007.