Math 632 is the second 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; bilinear forms.
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 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.
Often the course uses the book by Artin. This book was chosen as
our textbook this year, in part, because of the emphasis on linear
algebra and matrices, which is a cornerstone in any mathematician's
education. For the second semester, we will first finish some odds
and ends that we left out in Math 631 (Fall 2005). We will then
move onto the core material in Chapters 10, 11 and 12. An
application of these three chapters to canonical forms of matrices
will follow from the structure theory of finitely generated modules
over a principal ideal domain. If time permits, we will either
backtrack to Chapters 7 (Bilinear Forms) and 8 (Linear Groups), or
continue onto Chapters 13 (Fields) and 14 (Galois theory). The
choice of these two options will depend on a class vote.
Algebra by: Michael Artin.
Published by Prentice Hall 1991
Upper Saddle River, New Jersey 07458
ISBN: 0-13-004763-5
Examinations
Your grade in Math 632 will be determined by two exams. The first
(March 14) will be in class and will constitute 50% of your grade.
The second exam will serve as a cumulative take-home final. A
portion of the problems will be taken directly from problems
assigned in class. No make-up exams, 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
March 14 (Tuesday) 2:00pm-3:15pm in EMS W109 (In Class Exam)
Counts for 50% of your course grade.
3:15pm-3:45pm Tuesday and Thursday
12:00pm-2:00pm Wednesday
Important Dates
January 24
First class
February 3
Last day to add or change from a graded basis to audit or credit/no credit status.
February 17
Last day to drop or withdraw without a "W" on record
March 14
Midterm Exam
March 17
Last day to drop
March 19-26
Spring break
May 11
Last day of class
Prerequisites
Math 631 or consent of instructor. In general, students should be advised that in
Math 632 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.
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