Instructor: Prof. Brooke Shipley
Class hours:
The course meets MWF 9:00- 9:50am Addams Hall 307
Email: bshipley@math.uic.edu
Office:SEO 508
Office hours: Monday 3-4pm, Wednesday 1-2pm, Friday 11am -12 noon
Math Learning center (4th Fl. East SEO): tutors/student groups available
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.
Text: Joseph A. Gallian,
Contemporary Abstract Algebra, Seventh edition.
(Homework problems will be assigned from the seventh edition. Other than this, earlier editions of the book are very similar.)
Homework: Homework is due on Wednesdays at the beginning of class (or in my mailbox (Shipley) in SEO 304 by 8:30am). 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 (roughly in week 5 and 12). These will be announced at least two weeks in advance. Make-up midterms are only available before the midterms occur (for absences for emergencies the grade will usually just be dropped).
Academic Honesty: Students are expected
to be thoroughly familiar with the University's policy on academic integrity.
See: http://www.uic.edu/ucat/catalog/GR.shtml#qa
The University has
instituted serious penalties for academic dishonesty. We encourage
you to work with your classmates on homework problems, but you must write
solutions to the problems on your own. 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