Math 461 Syllabus
Fall 2009
Course number and title: Math 461 Abstract Algebra
II
Credit Hours: Three (3)
Semester: Fall 2009
Prerequisites: Grade of “C” or better in Math 460
Instructor: Dr. Craig M. Steenberg: Office: MLH 302. Phone: 792 2343. e-mail:
csteenbe@lcsc.edu
Office hours: OPEN: TTh 10:00-12:00. By appointment: All other times. Note: Open office hours are on a first-come first-serve basis. I will make every effort to be in my office at these times, or advise students of a conflict. By appointment office hours are reserved for those students making prior arrangements with me. If no appointments are made, I may or may not be available in my office at these times without notice to students.
Text: “Contempory Abstract Algebra, 6th ed.”, by Joseph A Gallian. ISBN Number: 0-618-5147-6.
Class meeting times: TBA
Purpose: This is an elective upper-division course for those students wanting to get an in depth look at the topics that fall under the general heading of abstract algebra.
Course objectives: Where Math 460 studied abstract groups exclusively, Math 461 focuses primarily on Field Theory – ending with a mixed bag of historically significant results from abstract algebra in general, and tailored to the desires if the individual student.
In field theory, we look at vector spaces, extension fields, finite fields, and
end with a look at geometric constructions.
Students typically find this last topic quite fascinating, as we do
proofs on which numbers are constructible with straight-edge and compass, the
use these results to prove that we cannot trisect angles or square
circles. False proofs for these last two
still show up every few years, and actually get published occasionally! We also prove the insolvability of the quintic.
Under general topics students can choose, time permitting, from studies of Sylow theorems, symmetry groups. Caley digraphs, algebraic coding theory, and Galois theory.
Methods of instruction: New material will be introduced primarily through lecture. However, it is intended that there be a very active discourse at all times between students and instructor. Students should interrupt a lecture at any point where they do not understand what is being said, or whenever they wish to contribute to what is being said. Frequently, students will be asked to present solutions to assigned work in front of the class. This is a time to constructively criticize each other’s work. Past classes have shown that often much can be learned by viewing other student’s misconceptions, as well as by seeing them do things right. It’s a good confidence builder, and students shouldn’t be frightened by the thought that their work may be incorrect if asked to produce it for the class. As a general rule, each class period will begin with a question and answer session. In upper division math classes, every homework problem is crucial to the course, and students should not leave an assignment until they are certain they can produce the results to each problem accurately.
Methods of evaluation: Students will be assigned homework routinely, with homework cumulatively counting for 40% of the final course grade. No late homework will be accepted for any reason whatsoever. There is an expectation that students will work cooperatively on homework. Students unable to work out a schedule where they can work together with other students can work with me in office hours. The often lengthy results required in abstract algebra proofs necessitate that that hour examinations be based very heavily on homework results. With this in mind, it should be the goal of every student to have each homework result mastered prior to examination time.
Four hour exams, equally weighted, will comprise the remaining 60% of a student’s cumulative grade. The first of these will be an exam covering review material for the course. The last will be given during the scheduled final exam period. It will not be cumulative, and weighted the same as the previous three hour exams. No makeup exams will be given for any reason whatsoever. Students who know of a conflict in advance must make arrangements to take the exam prior to its being given to the rest of the class. Students who miss an exam for unforeseeable reasons, such as last minute illness or emergencies, will need to make arrangements with the instructor on an individual basis to find a reasonable way to make up for the missed exam.
The minimum score for each grade is : A 92; A- 89; B+ 86; B 82; B- 79; C+ 76; C 72; C- 69; D+66; D 60. Grades below 60 will be scored as F. For those students required to get a 2.0 or better in this course, it should be noted that a grade of C- is insufficient. A grade of at least C must be achieved.
Disability statement: If course adaptations or accommodations are needed because of a disability, if you need to make me aware of emergency medical information, or if you need special arrangements in case of building evacuation, please contact me as soon as the need arises. Please, make your request in writing if it involves my intervention in the case of a medical emergency.
FERPA Statement: By FERPA regulations, information regarding a student cannot be given to anyone without the student's written permission. Information cannot be given out over the phone, even to the student, or to any e-mail account other than the student's LC WarriorMail account.