Math 632 is the second semester of a year long algebra sequence. In
the past, the full year has focused on group theory, including
normal subgroups, quotients, permutation groups, Sylow's theorems,
Abelian groups; field and Galois 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; bilinear
forms. Math 632 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 632 is designed to follow Math 631 (which in turn follows 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 beginning of the second semester, we will put particular
emphasis on the chapters concerning fields, Galois theory and the
structure theory of modules over a principal ideal domain. If time
permits, we will continue into the deeper commutative ring theory
and algebraic geometry.
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. Each will
constitute 25% of your course grade. The midterm will be given in
class on the Monday after the spring break (March 26). The final
will be given on Wednesday, May 16 12:30pm-2:30pm Location EMS
E129.
There will also be unannounced 1 or 2 problem quizzes throughout the
semester as well as graded homework. The quizzes+homework will
constitute 50% 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.
Homework
Homework will be assigned throughout the
course and some problems will be graded. 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...) See
http://www.math.hmc.edu/homework/.
First Homework Turn In: February 19
10.1: 8, 19, 21:
Second Homework Turn In: April 2
13.2: 18; 13.3: 3; 13.4: 4.
Third Homework Turn In: May 9
14.2: 15; 12.1: 9; 12.3: 5. and Extra Credit: 13.6: 13
Prereq: jr st, Math 631(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.
Important Dates
Monday, January 22
First class
Friday, February 2
Last day to add or change from a graded basis to audit or credit/no credit status.
Friday, February 16
Last day to drop or withdraw without a "W" on record
Friday, March 16
Last day to drop
March 17 - 25
Spring Break
Monday, March 26
Midterm Exam
Wednesday, May 9
Last day of class
Thursday, May 11
Study Day
Wednesday, May 16
Final Exam 12:30pm-2:30pm (In EMS E129)
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