Math 371 Course Information  Fall 2007
Tuesdays and Thursdays 1:30 pm  3 pm DRL 4C6
Faculty: 
Nate Ackerman 
TA: 
JoeKai
Tsay 
Office: 
DRL 4N53 
Section Location: 
DRL 4C19 
Office Hours: 

Section Time: 

Email: 
nate AT math.upenn.edu 
Email: 
jetsay AT math.upenn.edu 
 Texts

 (Basic Text) It is assumed you all have a copy of this

Title: 
Algebra 

Author: 
Michael Artin 

Publisher: 
PrenticeHall 

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: 
3050 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.