Abstract Algebra Math 444, Fall 2006

Office hours (held in my office:  FO3-218): 
 
 

Mathematics is the study of  numbers and space, communicated through the precise use of language. This course focuses on abstract algebra, which is not only a subject of current research, but describes fundamental structures that, in some way, exist in all areas of mathematics.

Topics:  groups, subgroups, cyclic groups, symmetric groups, Lagrange's Theorem, quotient groups. Homomorphisms and isomorphisms of groups. Rings, integral domains, ideals, quotient rings, homomorphisms of rings. Further topics in groups, rings and fields as time permits.

The goals of this course are to introduce the students to algebraic structures, such as groups, rings and fields, and to provide the students with a foundation in mathematical reasoning and writing (a.k.a. proofs!) that will aid the students in their future mathematics courses, as well as give them tools with which to communicate, in a logical and organized way, throughout the curriculum.

Text:

Abstract Algebra: An Introduction
Thomas W Hungerford
0030105595
Pub: Brooks Cole; 2, Edition: 2
Year: 1996, Next Ed:
Status: Required

Homework.  Expect daily homework assignments, due the following class period.  The assignments will be graded subject to the following rules:

• A problem completed correctly and on time will receive 10 points.
• A problem completed correctly and up to one week late will receive 8 points. (I really want you to do the homework!!)
• An incorrect problem (one which is either mathematically wrong or written poorly) will receive partial credit and may be corrected and resubmitted within a week from when it is returned for up to 8 points.  (In fact, I really want you to do the homework correctly!! Even if you need help or more time.)

To accommodate a wide range of student abilities, I will often assign two sets of homework, allowing the student to choose which problems to complete. For example, I might say, "Do 2 of the following 4 problems."  The problems will be labeled "Fundamental" and "Challenging."  All students will be held responsible for the Fundamental problems on the exams, independent of which problems they choose to complete as homework. The challenging problems will reinforce the ideas of the fundamental problems, but will often require students to use skills and ideas that extend beyond the focus of the current sections.   All students are encouraged to attempt all problems!

Quizzes.  From time to time you will be asked to start class with a short activity, for example recalling definitions and theorems from the previous lecture, or writing down a proof from the solved problems on the author's website.  By and large, these are not to be graded, but when they are, you will be warned in advance.  The scores from any graded quizzes will be added into the homework scores for the purposes of creating a course grade.

Exams:

 

October 5th	Midterm 1
November 21st	Midterm 2
	Final Exam in two sections:  Section 1: Material since Midterm 2 Section 2:  Cumulative

Grades:

 

Grade Distributions. Homework and Quizzes 40% Midterm 1 20% Midterm 2 20% Final Exam      Section 1      Section 2 10% 10%

Cut-offs for letter grades.   Homework (and Quizzes) Midterm 1 Midterm 2 Final  A 90       B 80       C 70       D 60

[Homework and Quizzes %]*0.4 + [Midterm 1]*0.2+ [Midterm 2]*0.2+[Final]*0.20.