Abstract Algebra Math 444

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, Second Edition, by John Beachy and William Blair
Related resources from the authors on John Beachy's website:

•  On-line Study Guide written by the authors provides an excellent supplement to the text.
• The guide includes sample problems with solutions! Use it!
• A version of this guide has been formatted for printing, either as one pdf or ps file, or in segments.
• Also by the authors: Abstract Algebra On-Line has a summary of parts of the text, including the following linked indexes.
• Index of Definitions.
• Index of Theorems (in alphabetical order).
• List of Theorems (ordered as in the text).

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.)

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:

 

Thursday, September 27	Midterm 1: Parts of Chapters 1
Thursday, Novermber 1	Midterm 2: Chapter 3 and parts of Chapter 4
Thursday, December 13 12:30-2:30	Final Exam in two sections:  Section 1:  Parts of Chapters 4, 5 and 6 Section 2:  Cumulative

Grades:

 

Grade Distributions. Homework and Quizzes 40% Midterm 1 15% Midterm 2 15% Final Exam Section 1 Section 2 15% 15%

Cut-offs for letter grades.   Homework and Quizzes Midterm 1 Midterm 2 Final (out of 200) A 90  90  87 155 B 80  80  75 130 C 70  68  62 110 D 60  55 50  80

[(Homework+Quiz Scores)/Total Possible]*4 + [Midterm 1]*0.15+ [Midterm 2]*0.15+[Final]*0.30.

Cut-offs for the weighted grades up to the second midterm are (if you do the above calculation, here is where you stand):