Office: Stevenson 313C (Enter through STV 313)
Office Hours: W 2:00-2:50, R 11:00-11:50, F 12:00-12:50
TEXT: Abstract Algebra, An Introduction, by Thomas W. Hungerford, 2nd Edition, Brooks/Cole, 1997.
COURSE WEB PAGE: http://www.math.ilstu.edu/gfseeli/m236121/
Here you will find links to the current assignments, possible posting of hints, and other resources available on the WEB.
Some Definitions and Theorems (To be updated throughout the semester.)
ABOUT THE COURSE: In this course we will cover most of Chapters 1-6 and Chapter 12 of the text with occassional excursions in the appendices. We will start by examining the familiar set of integers. Our emphasis in looking at the integers is twofold. First, we want to emphasize the algebraic properties of the integers. Second, we want to try to develop the students' ability to understand theoretical mathematical arguments and to be able to write coherent mathematical arguments. Almost all of the mathematical arguments you will be expected to understand and to write take the form of mathematical proofs. Once we gain some experience in the relatively concrete setting of the integers, we will develop some understanding of abstract rings and the functions between them. In this less familiar context, the skills of mathematical argumentation that we developed earlier will become more important to the understanding of these topics. To further our understanding of rings, we then look at the arithmetic of polynomials as an example of a ring that is not the integers. We will then begin the study of quotient fields and the construction of field extensions, the depth of this coverage will depend on the time available at the end of the course.
GRADING: In this course you will be graded on your performance on three one hour in class exams, a comprehensive final exam, and weekly homework assignments. The relative weights of these components will be
Test 1 100 pts (Friday, Feb. 17) Test 2 100 pts (Friday, Mar. 23) Test 3 100 pts (Friday, Apr. 27) Homework 150 pts Classwork 50 pts Final Exam 200 pts (Tuesday, May 8, 3:10 - 5:50 pm, STV 229)
Exam I Solutions
Exam II Solutions
Exam III Solutions
Final Exam Review Problems
HOMEWORK: Homework assignments will consist of four or five proofs a
week. Assignments will be given in class and will be due each Thursday by the
beginning of class. As developing your skills at writing mathematical arguments
is one of the central goals in this course, doing as much as you can on each
homework assignment is essential for a good grade. NOTE: In general you should
not expect to be able to do a good job on a homework assignment if you start the
day before it is due. Some problems may require numerous attempts before you
will be able to solve them. As well as the formal written assignments given in
class, it will be necessary for most students to read and re-read the relevant
sections of the text. For your FIRST READING ASSIGNMENT please read ``Appendix
A, Logic and Proof'' (pp. 493-503) in the text.