Course: Abstract algebra, Math 417, Section F13/F14 Time: MWF 2-2:50. Location: 345 Altgeld Hall Instructor:Chris Leininger Phone: 265-6763 Email: clein (at) illinois.edu Office: 366 Altgeld Hall Office hours: TBA
Math 417 is an introduction to abstract algebra. The main objects of
study are groups, which are abstract mathematical objects
that reflect the most basic features of many other mathematical
constructions you are likely familiar with. Rather than beginning
our discussion with groups, we will instead
spend some time discussing more familiar
algebraic structures, namely fields, polynomials, and vector spaces.
After sufficient motivation, we define groups and begin their
systematics study. If time permits, we will discuss some deeper
connections between group theory, fields and polynomials.
The goal of the course is to introduce the students to abstract
mathematical thinking through the study of these simple, beautiful
mathematical constructions, and to explore the relationship to other
areas of mathematics.
The text for this course is an expansion of the instructors lecture
notes, available here:
I will not cover everything from these lecture notes in class, and I will
assume that you have read everything from the sections covered,
even if they were not discussed in class. This is crucial since class
time is extremely limited. As an additional
reference, one can use
Frederick M. Goodman, Algebra: Abstract and Concrete (Edition 2.6), SemiSimple Press Iowa City, IA.
(available online free here).
or the book at the bookstore:
John B. Fraleigh, A First Course in Abstract Algebra
Grades will be based on
Weekly homework (15%): This will be assigned at the
beginning of the week, covering the material for that week, and will generally be due the following Monday, with a few exceptions (as posted).
This will be graded by the grader.
Quizzes(5%): There will be short quizzes periodically throughout the semester.
This is to check that you know the absolute basics of what we are doing in class. It will typically
cover very recent material, or if reading was assigned, it may cover that.
Three in-class midterms (10%,20%,20%):
These will be held September 13, October 18, and November 15solutions.
Final exam (30%):
This will be a 3
hour exam held 8:00--11:00 am, Friday, December 15.
There will be a take home portion of the final exam, handed out on
the last day of class, due by Wednesday, December 20, noon.
Assignments (please report any errors/mistakes to me)
Note: Illegible work will be returned, ungraded.
All assignments will come from this text.
HW1: Do all problems from section 1.1, 1.2, and 1.3. Turn in problems
1.1.1, 1.2.2, 1.2.3, 1.2.4, 1.3.1, 1.3.2. Due Friday 9/1, beginning of
class.
HW2: Do all problems from section 1.4 and 1.5. Turn in problems
1.4.2, 1.4.3, 1.4.4, 1.5.2, 1.5.3, 1.5.4. Due Friday 9/8, beginning of class.
HW3: Do all problems from section 2.1, 2.2 and turn them all in
(i.e. problems 2.1.1, 2.1.2, 2.2.1, 2.2.2). Due Monday, 9/18,
beginning of class.
HW4: Do all of the problems from section 2.3 and all problems
from section 2.4. Turn in problems 2.3.3, 2.3.4, 2.3.6, 2.4.3, 2.4.5.
Due Monday, 9/25, beginning of class.
HW5: Do all problems from sections 2.5, 2.6. Turn in 2.5.1, 2.5.4, 2.6.4, 2.6.7, 2.6.8, 2.6.9.
Due Monday, 10/2, beginning of class.
HW6: Do all problems from 3.1, 3.2, and the first five from 3.3. Turn in 3.1.1, 3.2.1, 3.2.2, 3.2.4, 3.2.6, 3.3.1, 3.3.3. Due Monday, 10/9, beginning of class.
HW7: Do the rest of the problems from section 3.3 and all problems from 3.4. Turn in 3.3.6, 3.3.8, 3.3.13, 3.3.15, 3.4.1, 3.4.2.
Due Friday 10/13.
HW8: Do and all problems from section 3.5. Turn in problems 3.5.1, 3.5.4, 3.5.6.
Due Monday, 10/23, beginning of class
HW9: Do all problems from section 3.6.
Turn in problems 3.6.1, 3.6.3, 3.6.4, 3.6.6, 3.6.8, 3.6.9, 3.6.13.
Due Monday, 10/30, beginning of class.
HW10: Do all of the problems from section 3.7 and problems 4.1.1-4.1.5.
Turn in problems 3.7.1, 3.7.2, 3.7.7, 4.1.2, 4.1.4. Now due Wednesday,
11/8, beginning of class.
HW11: Do the rest of the problems from Section 4.1 and all the
problems from Section 4.2. Not to be turned in, but you will be
responsible for the content on Midterm 3.
HW12: Do all problems from Section 4.3. Turn in 4.3.1, 4.3.4, 4.3.8, 4.3.9, 4.3.10, 4.3.12 (you may use 4.3.7 without proving it). Due Wednesday, 12/6, beginning of class. This is the last
homework assignment that will be collected.
HW13: Do all problems from Chapter 5. These problems will not be collected.
Week 14: Read Sections 5.1-5.3. There will be super-quizzes on both Monday and Friday of this week.
Week 15: Reread entire text! There will be a super-quiz on the last day of class.
Other things
The first midterm, on 9/13, will cover everything from Chapter 1. That
is the Wednesday of the third week of class!
The reviews are at the end of each section in the form of the "You
should..." list.
The second midterm, on 10/18, will cover everything from Chapter 2 and Sections 3.1-3.4.
The third midterm, on 11/15, will cover 3.5-3.7, 4.1, 4.2.