Instructor: Prof. Brooke Shipley
Class hours:
The course meets MWF 1-1:50, 311 BSB
Email: bshipley@math.uic.edu
Office:SEO 508
Office hours: 9:30 -11:30am Monday and 3-4 Wednesday
Grader Office hours: 1-3pm Thursday, SEO 735, Marcy Robertson (volunteer TA)
Math Learning center hours (4th Fl. East SEO)
Purpose of Course: The aim of the course is to introduce students to the basic abstract algebraic structures such as groups, rings and fields. Students will be expected to read the text and comprehend proofs, as well as to do problems involving both computations and proofs.
Prerequisites: Grade of C or better in Math 215.Grading:
Midterm Exams(2) 40%
Homework 20%
Final Exam 40%
Homework: Homework is due on Friday at the beginning of class (or in my mailbox (Shipley) in SEO 304 by 11am). No late homework accepted. Only legible writing will be graded. Several lowest grades will be dropped.
The listed homework does not cover all of the important topics of the course and it does not allow for enough practice. It is suggested that you do as many of the odd numbered problems as you can. Their solutions can be found in the back of the text book.
Midterms: There will be two midterms (FRIDAY, FEBRUARY 15 (end of week 5) and roughly in week 12). These will be announced at least two weeks in advance. There will be no make-up midterms after the exams occur (for excused absences the grade will just be dropped).
Academic Honesty: Students are expected
to be thoroughly familiar with the University's policy on academic integrity.
See page 56 of the 2001-2003 Undergraduate Catalog. The University has
instituted serious penalties for academic dishonesty. We have encouraged
you to work with your classmates on homework. Regarding
homework, quizzes, hour exams, and the final examination:
Copying work to be submitted
for grade, or allowing your work to be submitted for grade to be copied,
is considered academic dishonesty.
Students with Disabilities: It is University policy that students with disabilities who require accommodations for access and participation in this course must be registered with the Office of Disability Services (ODS); phone number 312-413-2103.
Course Topics
A brief review of sets, mappings,
equivalence relations and properties of integers.
Groups: Subgroups, homomorphisms, cyclic
groups, permutations, matrix groups, cosets,
Lagrange's Theorem, normal subgroups and factor groups.
Rings: Integral domains, homomorphisms,
ideals, factor rings, polynomial rings, factorization of polynomials.
(If time permits: Fields: Finite extensions and their connection with polynomial rings,
construction of finite extensions, application to geometric constructibility problems.)
Chapters 1-4, all pages; Ch. 5, p.94-105; Ch 6, p.120-128; Ch 7, p.137-142;
Chapter 8, p.153-157; Ch 9, p.177-184; Ch 10, p.199-207; Ch. 11, 217.
Chapter 12,13, 14, 15 all pages; Ch 16, p.291-294; Ch 17, p.303-313
Chapter 20, p.352-357; Ch 21, p.369-374