Description: This course is an introduction to the modern abstract
theory of algebra and algebraic structures. The primary focus is on
the theory of groups, which are “abstract groups of composable
transformations;” key examples include the symmetries of a geometric
figure, and the permutations of a set. Our focus is on constructing
groups, understanding their structure, and developing techniques for
classifying them.
At the end of the course we also begin the study of rings and
fields, which are “abstract number systems” in which there are
abstract versions of the four arithmetic operations: addition,
subtraction, multiplication, and (in the case of fields) division.
Lectures: Lectures will be held in person. Written notes for the
lectures will be made available. Please see the links in the
schedule below.
Homework: There will be 11 homework assignments whose due days
(usually Fridays) are listed in the schedule. Homework must be
submitted on paper in class. There is no homework due on weeks when
there is an exam.
Exams: There will be two midterm exams and a final exam. The
midterm exams will be held in class on Friday, September 29 and
Friday, November 3. The final exam will be held Wednesday, December 13, 8:00–11:00am in 169 Davenport Hall.
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Assessment: Grades will be based on homework (25%), two midterm
exams (22% each), and the final exam (31%). The two lowest homework
scores will be dropped. Grade cutoffs will never be stricter than
90% for an A- grade, 80% for a B-, and so on. Individual exams may
have grade cutoffs set more generously depending on their
difficulty.
Homework assignments should be submitted on paper in class on
the due date. If you are unable to come to class, you may turn in
your homework to James Pascaleff’s mailbox in 250 Altgeld Hall.
This mailbox will be checked at Noon on the due date, so you
should have your homework in the box by that time.
Late homework will not be accepted, but the lowest two scores are
dropped, so you may miss one or two assignments without penalty.
Missed exams: If you need to miss an exam (for reasons such as
illness, accident, or family crisis), please let the instructor know
as soon as possible, so that arrangements can be made.
Collaboration and Academic Integrity: For homework assignments,
collaboration is permitted and expected, but you must write up your
solutions individually and understand them completely. On exams, no
collaboration is permitted.
Disability accommodations: Students who require special
accommodations should contact the instructor as soon as
possible. Any accommodations on exams must be requested at least one
week in advance and will require a letter from DRES.