Syllabus for Math 5210 – Abstract Algebra
Section 101

Spring 2012

Prerequisite: Math 3110 or permission of the instructor.

Text: Abstract Algebra (3^rd Edition) by David S. Dummit & Richard M. Foote ISBN: 978-0-471-43334-7 (Used cost approx. $45 -- you can go to AddAll.com for prices)
You may also find Abstract Algebra: The Basic Graduate Year by Robert Ash helpful (it's available free online or for $15 as a Dover paperback).

Web Page: My webpage is located here: https://mathsci.appstate.edu/~cookwj and
our course webpage is located here: https://mathsci.appstate.edu/~cookwj/courses/math4720-spring2012.

Meeting times: Tuesday & Thursday 11:00am – 12:15pm in Walker Hall room 314 (unless otherwise announced).

Final Exam: The final exam will be held on Tuesday, May 8^th from 9:00am to 11:30am in Walker 314 (our regular classroom).

Lecturer:

Name:	Dr. William (Bill) Cook
Office:	Walker Hall 347
Office hours:	Monday & Wednesday 9:00am – 11:00pm Tuesday 10:00am – 11:00am Thursday 9:00am – 11:00am
Phone:	(828) 262-2367
Email:	cookwj@appstate.edu
Webpage:	https://mathsci.appstate.edu/~cookwj

Technology: You are welcome to use any technology at your disposal to complete out of class assignments. No calculators or other computer technology will be allowed on exams or quizzes.

Course Topics: The course catalog says, “A study of ring and field theory, including integral domains, ideals, polynomial rings, vector spaces, and algebraic field extensions.” Our semester will break up into 3 parts: Group Theory, Ring Theory, & Module Theory.

• Group Theory: We will begin by reviewing chapters 1 – 3 (basic group theory) focusing on a few new examples and ideas which aren't covered in 3110. Then we will discuss group actions and the Sylow theorems (Chapter 4). Time permitting we will discuss selected topics from chapters 5 & 6.
• Ring Theory: We will begin by reviewing the definition of a ring and some basic concepts (Chapter 7). Then discuss factorization theory - studying Euclidean domains, Principal Ideal Domains, & Unique Factorization Domains (Chapter 8). We will then specialize and focus on polynomials rings (Chapter 9).
• Module Theory: We will begin by studying basics about (ring) modules (parts of Chapter 10). Time permitting we will classify modules over a PID and then apply this result to group theory (classifying finitely generated abelian groups) and linear algebra (rational and Jordan canonical forms).

Your term grade will be based on the results of your tests and final project as well as your scores on quizzes, homework, and class participation. Here is more information about the individual components of your grade:

Tests: There will be two tests. The first test will primarily cover group theory and the second ring theory. Each test will make up 25%. The dates of the tests listed in the tentative course schedule may change. The actual dates will be announced in class.

Homework & Quizzes: I will post a list of suggested homework problems from the text – these will not be collected. Even though these homework problems will be not collected, working out all of the suggested problems is strongly recommended. Please ask questions about problems with which you have had difficulty. I will regularly assign sets of homework problems to be turned in for a grade. We may have a few quizzes (if needed). I encourage you to work on your homework with your classmates. However, you must write up your solutions yourself. Do NOT copy your collaborators work and turn it in as your own. The homeworks and quizzes will make up 25% of your term grade.

Participation & Final Project: After the second test, everyone will pick out a topic for further study and make a (brief) proposal. I will look over and approve proposals for projects and then suggest some problems/issues for you to consider. You will type up your project (minimum 5 pages). This should include some background, proofs of some basic facts, and several worked out representative homework problems. Your paper will be due toward the end of the semester. We will then use the final class periods (as well as the final exam period itself) for presentations. Your proposal, paper, presentation, and overall class participation will make up 25% of your term grade.

In summary, here are the components of your term grade with corresponding weights:

Component	Weight
Tests	25% x 2 = 50%
Homework & Quizzes	25%
Final Project, Presentation & Participation	25%

Differences between 5210 and 4720: This course is dual listed with Mat 4720. We have the same meeting times. However, your exams will include extra problems (most likely given as a take-home portion of the exam) and most homework assignments will include additional problems just for 5210 students. (Don't you feel special?)

Grades will be assigned based on the standard +/- system. (92-100 = A, 90-91 = A-, 88-89 = B+, 82-87 = B, 80-81 = B-, …, 60-61 = D-, 0-59 = F)

Attendance: Don't miss class (this may hurt the class participation component of your grade). If you miss class, you are responsible for the material covered during your absence. If you miss a quiz, test/exam, or assignment, you must bring in documentation proving that you absence is excusable or otherwise receive a zero. If a make-up quiz/test/exam is granted, it must be made up before the next quiz/test/exam.

Help! If you need help, please come to my office hours. If you are in Walker Hall and my office door is open, please feel free to stop by and ask questions – even if it's not during my regular posted office hours.

Fine Print: Copies of the academic integrity code, disability services information, religious observance policies can be found at https://academicaffairs.appstate.edu/syllabi