Math 460 Syllabus

Fall 2009


Schedule and notes:


Course number and title:  Math 460  Abstract Algebra 1

Credit Hours: Three (3)

Semester: Fall 2009

Prerequisites:  Math 175 and Math 300 or permission of instructor

 

Instructor:  Dr. Craig M. Steenberg:  Office: MLH 302:  Phone: 792 2343:  e-Mail: csteenbe@lcsc.edu
 

Office hours: OPEN: MW:  9:00 - 11:30.  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, 7th ed.”, by Joseph A Gallian.  ISBN: 0547165099

Class meeting times:  TTh: 10:30 - 11:45.  Admin 206

 

Purpose:  This is a required course for mathematics majors, and an upper-division elective for mathematics minors.  It covers those elements of mathematics necessary to the study of abstract algebra, such as the properties of integers, modular arithmetic, mathematical induction, and functions.  It then provides students with an in-depth look at abstract group theory, beginning with basic definitions, and going on to a study of groups, subgroups, normal subgroups, group isomorphisms, and a proof of the fundamental theorem of finite abelian groups. 

 

Course objectives:  The primary objective of this course is to give students a firm understanding of finite group theory, to include its applications outside of theoretical mathematics.  As soon as we prove Caley’s theorem (that every finite group is isomorphic to a group of permutations), the course will be dedicated entirely to the study of permutation groups.  The course ends with a proof of the fundamental theorem of finite abelian groups: Every finite abelian group is a direct product of cyclic groups of prime-power order. 

 

Because every result in finite group theory involves examining a finite (although possibly very large) number of cases, computers have proven to be an invaluable tool in the study of abstract group theory.  While no prior computer experience is necessary for this class, we will be generating certain computer algorithms, most of which can be executed quite nicely on a Voyage 200.  Students are encouraged to have their own Voyage 200.  These calculators are available from the Division of Natural Sciences for a fee of $30 per semester.

 

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 Mail account.

 

Cell phone use:   Cell phones should be shut off at all times during class sessions.  The use of cell phones during examinations will be considered to constitute academic dishonesty and appropriate actions will be taken.