Western Washington University, Winter 2016
Math 401: Introduction to Abstract Algebra
Class Meetings:MTRF 1 – 1:50 pm, Old Main 587
Instructor:Dr. Stephanie Treneer
206 Bond Hall
stephanie.treneer[at]wwu.edu
(360) 650-3468
Office Hours:MTRF 12—12:50, or by appointment
Prerequisites:Math 204; Math 302 or Math 309
Textbook:A First Course in Abstract Algebra, 7th ed. By John B. Fraleigh
Course Overview: This course is an introduction to group theory. We will aim to cover parts I through III of the textbook, which include the basic properties of groups and the maps between them (isomorphisms and homomorphisms). We will consider many examples in an effort to make the abstract notions more concrete.
Class time: A weekly schedule can be found here. I strongly encourage you to read each chapter before we cover it in class. In this way you will already be somewhat familiar with the topic, and we can focus our class time on refining our understanding and discussing problems.
Course Objectives:The successful student will demonstrate:
1)Knowledge of the group axioms, and familiarity with various examples including cyclic, dihedral, unit and permutation groups.
2)The ability to compute orders of elements and cosets of a subgroup and knowledge of the relationships between these notions and the order of a group via Lagrange’s Theorem.
3)Knowledge of the definition of an isomorphism between groups and the properties it preserves.
4)Knowledge of the definition of a homomorphism between groups and the properties it preserves.
5)Knowledge of the definition of a normal subgroup and its relationship to both factor groups and homomorphisms.
6)Knowledge of the definition of a direct product of groups.
7)Knowledge of the structure theorem for finite abelian groups and ability to determine all possible finite abelian groups of a given order.
Homework: I will assign and collect weekly homework. I will assign some computational exercises that I won’t collect, along with more conceptual problems that I will collect. The best preparation for working on the conceptual problems is to first do the computational problems to get a feel for the objects we are working with. You may work together to figure out the problems, but the written solutions you turn in must be your work, in your own words. They must be written in complete sentences, following the rules of English grammar. Your work will be graded for clarity and completeness, as well as correctness. If I have trouble reading or understanding a solution, you will get less credit. I strongly encourage you to type your homework if your handwriting is difficult to read. This is a good opportunity to learn LaTeX!
Exams: There will be two midterm exams, and a final exam. Each exam will be closed-book and closed-notes. The exam are tentatively scheduled for January 28, and February 25. Makeup midterm exams will only be considered in the case of illness or emergency, and you must let me know of your situation prior to the exam. The final exam is comprehensive, and is on Wednesday, March 16 from 8—11 am. The date and time of the final will not be changed, so you should plan your spring break travel so as not to interfere with the exam.
Grading: Your grade for the course will be based on exams and homework as follows:
30% Homework
20% eachExams
30%Final Exam
Academic Integrity: Don’t cheat! In this course, cheating includes, but is not limited to, copying writing assignment solutions from other students or the internet. Please consult this collection of integrity resources for further information.
Accommodation: If you are in need of special accommodation for this course, you should first visit disAbility Resources for Students (DRS, Old Main 120) to register your eligibility, and then submit the necessary requests online. Please also feel free to talk with me early in the quarter to let me know how I can be of assistance.