Modern Algebra.
Fall 2006
Math 631

Dr. Willenbring

1  Course Description

Math 631 is the first semester of a year long algebra sequence. In the past, the year has focused on group theory, including normal subgroups, quotients, permutation groups, Sylow's theorems, abelian groups; field theory; linear algebra over general fields, ring theory, including ideals, quotient rings, euclidean rings, polynomial rings, unique factorization; modules, including vector spaces, linear transformations, canonical forms; galois theory. Math 631 is often taken by both graduate students and undergraduate students. See the Undergraduate or Graduate Bulletin where the above information has been taken from. Note that Math 631 is designed to follow Math 531, and the material in Math 632 is designed to precede the Math 731-732 sequence.
We are using the book by Dummit and Foote. This book was chosen as our textbook this year, in part, because of the broad range of topics when compared to other algebra books at this same level. For the first semester, we will aim at the first 5 chapters of Part I, which cover group theory (including the Sylow theorems and semidirect products). If time permits, we will continue into Part II (Ring theory) this semester.

2  Course Details

Class time
3:30pm-4:45pm Monday and Wednesday in EMS E495A
Textbook
Dummit, David S.; Foote, Richard M. Abstract algebra. John Wiley & sons, Inc.; Third Edition; (2003); Hardcover 944 pages; ISBN: 0471433349
Examinations
There will be both a midterm exam and a final exam. The final will constitute one sixth of your course grade and will be given in class on December 20 (Wednesday) 3:00pm-5:00pm Location TBA.
The midterm consists of two parts: (1) a take home exam, and (2) an interview to be scheduled with the instructor. During the interview the solutions to the take home test and homework problems will be discussed. The combination of the two parts will constitute one third of your course grade.
There will also be unannounced 1 problem quizzes throughout the semester. The quizzes will constitute one sixth of your course grade.
No make-up exams or quizzes, except in severe situations such as illness. Students will be allowed to complete examinations or other requirements that are missed because of a religious observance.
Midterm
Due October 16 (Monday)
Student-Professor Interviews during the week of Oct. 23-27. Make appointments ASAP!
Counts for one third of your course grade.
Final
December 20 (Wednesday) 3:00pm-5:00pm Location TBA
Counts for one sixth of your course grade.
Homework
Homework will be assigned throughout the course and will constitute one third of your course grade. You will want to do a very careful and thorough write-up of these. The standard rules for neatness will apply (name in upper right corner with date and course number, stapled, write on one-side only, no more than one problem per page, no paper torn out of notebook, etc...)
First Homework Turn In:
September 25
0.1.7 (page 4); 0.2.2 (page 7); 0.3.10 (page 11); 1.1.25 (page 22);
Second Homework Turn In:
November 6
1.6.17 (page 40); 2.4.15 (page 65); 2.5.11 (page 71);
Third Homework Turn In:
December 11
4.4.19 (page 138); 4.5.29 (147); 4.6.4 (page 151).
You should also make sure that you can do:
Week 1
1.1: 8, 25;
Week 2
1.2: 9-13; 1.3: 7, 16; 1.4: 1, 11.
Week 3
1.6: 1, 10; 1.7: 2, 22; 2.1: 8, 14.
Week 4
2.2: 5, 13; 2.3: 3, 23; 2.4: 9, 15.
Week 5
2.5: 9, 11; 3.1: 1, 9, 26, 35, 43.
Week 6
Take Home Exam
Week 7
3.2: 7, 9, 16, 22; 3.3: 2, 7, 9.
Week 8
3.4: 1, 4, 5; 3.5: 3, 6, 7, 10, 12;
Week 9
4.1: 4, 5, 10; 4.2: 4, 8, 14;
Week 10
4.3: 21, 25, 33; 4.4: 18, 19.
Week 11
4.5: 3, 11, 12, 16, 29; 4.6: 1-6.
Week 12
7.1: 1, 14, 25, 26, 27; 7.2: 3, 4, 5, 6, 13.
Week 13
7.3: 1, 11, 21, 24, 26; 7.4: 19, 31, 33, 34, 37.
Week 14
7.5: 4, 5; 7.6: 1, 2, 4, 5, 6.
Week 15
7.6: 8, 9, 10, 11.
Contact Information
 
Web Page:
http://www.uwm.edu/~jw/
email:
j w a t u w m d o t e d u
Phone:
(414) 229-5112
Office:
EMS E461
Office Hours:

2:00pm-4:00pm Tuesday and by appointment.
Prerequisites
Prereq: jr st, Math 531(P) or consent of instructor, or graduate standing. In general, students should be advised that in Math 631 we assume that you know what a mathematical proof is and how to read and write one.
Attendance
Attendance is required, and will be occasionally monitored. Absences due to illness require a medical excuse on Physician's letterhead, signed by the physician, which must be submitted before any alternate arrangements for the exam will be considered. There is no provision for absences due to vacations and other social activities. In general, missing classes is a bad idea. Please arrive promptly.
Disabilities
If you have any disability, please feel free to contact me for any help or accommodation which you may need.
Statement of Sexual Harassment
Sexual harassment is reprehensible and will not be tolerated by the University. It subverts the mission of the University and threatens the careers, educational experience, and well being of students, faculty, and staff. The University will not tolerate behavior between or among members of the University community which creates and unacceptable working environment. The draft policy on discriminatory conduct, including sexual harassment, can be found at
http://www.uwm.edu/Dept/uc/briefings/S-47-Mar05rev.pdf
Statement of Academic Misconduct
The university has a responsibility to promote academic honesty and integrity and to develop procedures to deal effectively with instances of academic dishonestly. Students are responsible for the honest completion and representation of their work, for the appropriate citation of sources, and for respect of others' academic endeavors. Further information can be found at http://www.uwm.edu/Dept/Acad_Aff/policy/academicmisconduct.html.
Posted room changes
or class cancelations will be on Official Department Letterhead
Course Evaluation Policies
are posted here: 
http://www.uwm.edu/Dept/SecU/acad%2Badmin_policies/S52.5.htm


File translated from TEX by TTH, version 3.61.
On 27 Nov 2006, 15:01.