Course Guidelines Math 434
Dr. R. Beezer Spring 2006
Text   We will be using Contemporary Abstract Algebra (Fifth Edition) by Joseph A. Gallian. (Note that the book is now in a Sixth Edition, but we will still be using the Fifth Edition.) We will cover material from Chapters 12 through 23, and 32 - see the attached tentative schedule for the exact sections covered. A suggested optional text is Galois Theory (Second Edition) by Joseph Rotman (ISBN: 0387985417, $45 new, $35 used).
Home Page   Start at http://buzzard.ups.edu/courses.html to locate the WWW page for this course.
Office Hours   My office is Thompson 321G; the telephone number is 879-3564. Making appointments or simple, non-mathematical questions can be handled via electronic mail - my address is beezer@ups.edu. Office hours will be 11:00-11:50 on Monday, Wednesday and Friday. I will always be available during these times on a first-come, first-served basis. If these times are not convenient, please do not hesitate to make an appointment with me for another time. You are also welcome to drop by my office without an appointment at any time that I am in (good times to try are 2 P.M. to 4 P.M. on Monday, Wednesday and Friday, and most all of Tuesday). Office hours are your opportunity to receive extra help or clarification on material from class, or to discuss any other aspect of the course.
Homework   Homework will be assigned for each chapter (see list below), but will not be collected. (Some suggested problems from Rotman are also listed.) Of course, you are not limited to working just these assigned problems. Once per chapter we will have a problem session where we can discuss these problems. It is your responsibility to be certain that you are learning from the homework exercises. The best ways to do this are to work the problems diligently when assigned and to participate in the classroom discussion. If at this point you are still unsure about a problem, then a visit to my office is in order. Making a consistent effort outside of the classroom is the easiest way to do well in this course.
Mathematics not only demands straight thinking, it grants the student the satisfaction of knowing when he or she is thinking straight. - D. Jackson
Mathematics is not a spectator sport. - Anonymous
I hear, I forget.
I see, I remember.
I do, I understand.
    - Chinese Proverb
An education is not received. It is achieved.
       - Anonymous
Reading Questions   Once you have read the chapter prior to our in-class discussion, submit your responses to the reading questions via electronic mail as follows. Do not send your responses to my regular email address (beezer@ups.edu), but instead use the address I will announce in class. Your responses are due at 9 PM the night before we begin discussing a new chapter (these dates are noted on the attached tentative schedule), and will not be accepted late. Use a subject that is exactly like"RQ-X," where X is the number of the chapter. So for example, your first response will be titled: RQ-12. In the first line of your response, please put your real name, then answer the questions in order.
If a question asks for a computation, you can just give the answer, no need to show your work in the email. If the question is a yes/no answer, or asks "Why?" then give an explanation. Do your best with mathematical notation, but do not fret if it is a bit sloppy or weird, I can usually decipher any reasonable attempt. Please send only straight text - no attachments, no Word files, no graphics, no HTML if you can help it. Please pay careful attention to these procedures and deadlines.
Quizzes   There will be seven one-hour quizzes - see the attached sheet for tentative dates. These will occur on alternate Tuesdays and all but one will cover the content of two chapters. The lowest of your quiz scores will be dropped. The comprehensive final exam will be given at 8 AM on Wednesday, May 10. The final exam cannot be given at any other time, so be certain that you do not make any travel plans that conflict, and also be aware that I will allow you to work longer on the final exam than just the two-hour scheduled block of time.
Projects   You will participate in one research project on a topic related to the material in this course (interpreting this to mean both Math 433 and Math 434) as a way to demonstrate your progession towards becoming an independent scholar of mathematics. You may work in a group of size n, 1 £ n £ 3. My expectations for the quality and quantity of your work will be an, where a is some indeterminable constant of proportionality. Public presentations will be made as part of "Math Day" on a Saturday late in the semester (date has not been determined yet). More on this later, including suggestions on topics and due-dates.
Grades   Grades will be based on the following breakdown: Quizzes - 65%; Project - 5%; Reading Questions - 5%; Final - 25%. Homework, attendance and improvement will be considered for borderline grades. Scores will be posted on the Internet at http://buzzard.ups.edu/courses.html. A reminder about withdrawals - a Withdrawal Passing grade (W) can only be given during the third or fourth weeks of the semester, after that time (barring unusual circumstances), the appropriate grade is a Withdrawal Failing (WF), even if your work has been of passing quality. See the attached schedule for the last day to drop with an automatic `W' and please read Academic Handbook at http://www.ups.edu/x4727.xml#withdrawal about these often misunderstood grades.
Attendance   Daily attendance is required and expected, and is a pretty good idea.
Purpose   At this point in your college career, you should be well on your way to being an independent scholar, who appreciates the beauty of mathematics and understands the effort needed to master new and difficult ideas. Consistent with that, I will be giving you a fair degree of freedom to learn this material in a manner that suits you.
Read the book before the lectures, work the exercises diligently, tidy up your class notes each evening, and ask questions. Arriving late to class, or having conversations with others during class, not only disrupts your peers, but tells me you are not serious about your education. I will not routinely check attendance, but our class is small enough that I will notice when you are not here, and again this will be another way that you signal me about your commitment to the endeavor.
Many consider Galois Theory (the final branch of Abstract Algebra that we will concentrate on this semester) one of the most remarkable achievements in mathematics. The investment of your time and energy applied to studying the preparatory material will be amply repaid by a full understanding of the concluding material.
Homework Exercises (Gallian)
ChapPageComputationalTheoretical
12 234 2, 12, 20, 40, 45 18, 22, 27, 29, 43, 48
13 246 6, 11, 19 (see 16), 20 (see 13), 35, 60 14 (see 13), 24, 41, 46, 54, 55 (see 23)
14 260 5, 6ab, 22, 27, 29, 30, 34, 35, 42 (see 40), 45 10, 32, 39, 53
15 277 5, 6, 12, 15, 20, 21, 38 29, 30, 37, 40, 44, 54, 56
16 290 12, 13, 18, 22, 23 4, 8, 9, 21, 24, 30, 31, 40
17 307 8, 10, 11, 14, 21, 23 12, 19, 25, 30, 33
18 325 13, 14, 17, 19, 21 8, 10, 12, 27, 31, 32, 35
19 339 5, 6, 13, 15, 22 2, 8, 11, 19, 24, 27, 29, 30, 31
20 357 1-5, 7, 8, 9,13, 25, 26 21
21 369 8, 12, 14, 16, 24, 26 2, 4, 7, 9, 11, 18, 23
22 381 1, 6, 11, 20, 21, 26 5, 10, 18, 25
23 389 3, 4, 5, 7 8, 9, 14
32 560 2, 10, 11, 12, 18 7, 8, 23, 25







Homework Exercises (Rotman)
ChapProblems
12 1, 5, 7, 8
13 10, 11, 13, 16
14 31, 33, 37
15 27, 29
16 40, 45
17 53, 58, 64, 65
18
19 68, 69, 71
20
21
22
23 Appendix C
32
Tentative Daily Schedule


Monday Tuesday Wednesday

Friday

Jan 16
MLK Day

Jan 17
Syllabus
Chapter 12

Jan 18
Chapter 12
RQ Due

Jan 20
Chapter 12

Jan 23
Chapter 13
RQ Due

Jan 24
Problem Session

Jan 25
Chapter 13

Jan 27
Chapter 13

Jan 30
Problem Session

Jan 31
Quiz: 12 & 13

Feb 1
Chapter 14
RQ Due

Feb 3
Chapter 14

Feb 6
Chapter 15
RQ Due

Feb 7
Problem Session

Feb 8
Chapter 15

Feb 10
Chapter 15

Feb 13
Problem Session
Last day to drop

Feb 14
Quiz: 14 & 15

Feb 15
Chapter 16
RQ Due

Feb 17
Chapter 16

Feb 21
Chapter 17
RQ Due

Feb 22
Problem Session

Feb 23
Chapter 17

Feb 25
Chapter 17

Feb 27
Problem Session

Feb 28
Quiz: 16 & 17

Mar 1
Chapter 18
RQ Due

Mar 3
Chapter 18

Mar 6
Chapter 19
RQ Due

Mar 7
Problem Session

Mar 9
Chapter 19

Mar 10
Chapter 19
Mid-Term
Monday Tuesday Wednesday

Friday

Mar 20
Problem Session

Mar 21
Quiz: 18 & 19

Mar 22
Chapter 20
RQ Due

Mar 24
Chapter 20

Mar 27
Chapter 21
RQ Due

Mar 28
Problem Session

Mar 29
Chapter 21

Mar 31
Chapter 21

Apr 3
Problem Session

Apr 4
Quiz: 20 & 21

Apr 5
Chapter 22
RQ Due

Apr 7
Chapter 22

Apr 10
Chapter 23
RQ Due

Apr 11
Problem Session

Apr 12
Chapter 23

Apr 14
Chapter 23

Apr 17
Problem Session

Apr 18
Quiz: 22 & 23

Apr 19
Chapter 32
RQ Due

Apr 21
Chapter 32

Apr 24
Chapter 32

Apr 25
Problem Session

Apr 26
Chapter 32

Apr 28
Chapter 32

May 1
Problem Session

May 2
Quiz: 32

May 2
Housekeeping

Final Examination
8:00 AM, Wednesday, May 10


File translated from TEX by TTH, version 3.71.
On 09 Jan 2006, 14:21.