Basic Course Information
Abstract algebra is one of the cornerstones of modern mathematics. It has enjoyed wide-ranging applications to both pure and applied sciences : people have found extensive use of abstract algebra in number theory, geometry (which led to modern algebraic geometry), topology (which led to algebraic topology), and of course, theoretical and mathematical physics. On more practical side, abstract algebra has become an indispensable tool for many computer scientists.
The biggest thesis in undergraduate abstract algebra is the following :
Not all zeros of every quintic real polynomial can be expressed in terms of radicals.
To prove this theorem, one has to understand various concepts that go into a proof of this theorem such as : groups (normal subgroups, factor groups, abelian and simple groups), rings (ideals, Euclidean rings, and unique factorization rings), and fields (algebraic extensions, finite fields). In this course, we will focus on groups. Subsequent concepts and the proof of the theorem will be covered in Algebra II and graduate course in algebra.
Abstract Algebra, 2nd Edition by John A. Beachy & William D. Blair
Homework 20%
Midterm 1 25%
Midterm 2 25%
Final 30%
<>Homework will be collected every Monday unless told otherwise in
class. The assignments will be posted on the web. I encourage
you to work with other students in the class when solving the homework
problems, but you should write them up on your own. To receive credit
for homework, it must be handed in on time. In case of a legitimate
conflict that you know of before hand, you may see the instructor to
make appropriate arrangements. No late homework will be accepted.
ACADEMIC CONDUCT:
Academic honesty and mutual respect (student with student and
instructor with student) are expected in this course. Mutual respect
means being on time for class and not leaving early,
being prepared to give full attention to class work, not reading
newspapers or other material in class, not using cell phones or pagers
during class time, and not looking at another student's work during
exams. Academic misconduct, as defined by the Student Judicial Code,
will not be treated lightly.
CAAR STATEMENT:
If you have specific physical, psychiatirc, or learning disabilities
and
require accomodations, please let your instructor know early in the
semester so thatyour learning needs may be appropriately met. You will
need to provide documentation of your disability to the CAAR (Center
for Access Ability Resources) Office located in the Health Services
Building, 4th floor.