Algebra I, Math 5420, Fall 2006

New assignments for sections 3.3 and 3.4 have been posted, as well as solutions for 3.1.

Solutions to the homework assignments are on the assignments page.

The university has made some changes in grading policy.

Class data
Professor
Overview
Prerequisites
Writing Intensive Requirement
Advice
Schedule
Grades
Assignments

Class:

Math 5420, Section 001
20 Manoogian
MTWF 11:45 - 12:40
Text: Abstract Algebra, 3rd ed. John A. Beachy and William D. Blair

Professor:

Robert Bruner
Office: 1201 FAB, (313)-577-3179
Math Department: (313)-577-2479
Fax: (313)-577-7596 (shared)
e-mail: rrb at mathZwayneZedu (Z is .)
Office hours: Mon, Wed, Fri: 9:35 - 10:30.
Short questions can often be answered after class. In addition, you are welcome to make appointments to see me at other times. Finally, if you are willing to take a chance that I am busy or not in, you can simply drop by my office.

This is a first course in abstract algebra. It serves as an introduction to a very powerful way of thinking, which allows us to derive quite complex concepts from first principles. If things go well, you will remember this semester as an exhilarating intellectual experience. At the same time, you may find that this course can be quite demanding of your time and energy. It will certainly be harder to "catch up" in this course than it would be in a lower-level mathematics course.

Class participation will be essential to mastering this material, and attendance is mandatory. You should notify me if you are unable to attend even a single meeting of the class. Tests will presume familiarity with material presented in class as well as the material in the text.

Prerequisites:

MAT 2030 and MAT 2250 are the formal prerequisites for this course, but you will find that this course operates at a much higher level of mathematical sophistication. MAT 5400 (Number theory) and/or MAT 5000 (Proof Writing) are not prerequisites, but may serve as a gentler introduction to this level of mathematical thought. Similar courses, such as MAT 5410, 5520 or 5600, may also be helpful. None of the material in these 5000 level courses will be required to understand MAT 5420.

Writing Intensive Course:

Undergraduate mathematics majors taking this course will normally be co-enrolled in MAT 5993, Writing Intensive Course in Mathematics, which satisfies a WSU General Education Requirement. The distinctive feature of mathematical writing is the use of formal proofs. The two main obstacles to good proof writing are fear and sloppiness. I expect to discuss these further during the semester, both individually and with the whole class. As with many other skills, the key to mastery is regular and consistent practice to build confidence and good technique. The section To the Student (pp. xii - xx of the text) contains extremely good advice on these matters.

Advice:

READ THE BOOK . You should read each section before we talk about it in class, then again after class, before doing the homework for the section. In fact, you should read it several times. First, quickly, for an overall idea what the section is about, then in detail, working through the proofs and examples, line by line, to make sure you know why each statement is true. Only after this should you start the homework. You will be pleasantly surprised how much easier the homework is with this sort of preparation. You will certainly understand the material and retain more of it, if you study in this way. Further, you will know the sections well enough to refer to them precisely in your writing. Accurate and precise citations play an important role in mathematical writing.

Schedule:

The first class is Tuesday, September 5, 2006, and the last class is Wednesday, December 13, 2006. The final exam is Monday, December 18, from 10:40 to 1:10 in 20 Manoogian.

We will cover most of the first five chapters of the book. Here is a schedule of the topics and chapters we will cover, as well as the timing of the tests.

Introduction (Integers
and Functions) Chap. 1 and 2, and
Appendix A.1 - A.4    Sept. 5 - 29

Test 1    Friday, Sept 29

Group Theory, Part I Chap. 3    Oct. 2 - 25

Test 2    Wednesday, Oct. 25

Group Theory, Part II Chap. 3 (cont.)    Oct. 27 - Nov. 17

Test 3    Friday, Nov. 17

Ring theory (Polynomials
and commutative rings) Chap. 4 and 5    Nov. 20 - Dec. 11

No class WSU Thursday    Nov. 21

No class Thanksgiving break    Nov. 24

Test 4    Monday, Dec. 11

Review    Dec. 12 - 13

Classes end    Dec. 13

Final Exam    Monday, Dec. 18
10:40 - 1:10, in 20 Manoogian

Requirements and grades:

Grades will be computed as follows:

4 In-class exams	400
Homework	200
Final	200
Total	800

New Grading Policy

There has been a change in University policy on grades. This affects withdrawals, unofficial withdrawals (i.e., stopping attending without filling out any paperwork) and the name of the lowest grade (changed from E to F). See the official notice for full details.