Abstract Algebra I
M466, Fall 2017
Lecture: MWF 10:00-10:50, Engineering E206.
Abstract algebra is a fundamental subject in mathematics. Its theory was developed in the 1800s when people realized that many different types of problems could be solved in the same way using underlying algebraic structures. It has applications in many fields such as cryptography and chemistry. The first main topic of this course will be group actions. We will analyze the structure of groups by seeing how they act on geometric objects, vector spaces, or other groups. Group actions have applications in combinatorics, chemistry and mechanical engineering. The second main topic will be ideals in rings. We will focus on quadratic fields, quadratic rings and quadratic forms. This material is key for understanding number theory and algebraic geometry, which in turn lead to applications in cryptography and error-correcting codes.
Prerequisite: M360 or M366 or M369 or equivalent experience.
Goodman, Algebra: Abstract and Concrete.
2) Judson, Abstract Algebra: Theory and Applications.
3) Garrett, Abstract Algebra.
4) Ash, Abstract Algebra: The Basic Graduate Year.
5) Wilkons, Abstract Algebra Lecture Notes.
6) Clark, Quadratic forms, chapter I.
7) Dummit and Foote: chapter 4.
The course grades will be computed as follows:
60% exams; 40% homework/projects.
See syllabus for details. Borderline grades will be decided on the basis of class participation.
Homework: Homework is the most important part of this class. Doing homework problems is crucial for doing well in this class. The process of doing homework will help you solve unfamiliar problems on the tests. The homework problems will help you develop skills in algebraic computation and logical reasoning. I will only grade homework which is neat, legible, and stapled. I encourage you to brainstorm the problems in groups and write up your solutions independently.
Project: There are many amazing topics and applications of abstract algebra which we will not have time to cover fully. Each person will do a poster presentation. This gives everyone a chance to explore a new topic.
There will be midterms in class on Monday 9/25 and Monday 11/13.
The poster is due at the CSU math department poster session.
The final exam is Thursday December 14, 4:10-6:10 pm.
There are no makeups for missed exams, regardless of the reason for absence. You must take the final examination at this time scheduled by the university; no final exams will be given earlier. Examinations will not be rescheduled because of travel arrangements. It is your responsibility to schedule travel appropriately.
CSU Honor Pledge:
Academic integrity is important to me.
Paraphrasing the words of Greg Dickinson, Director of Graduate Studies; Professor, Dept. of Communication Studies:
Plagiarism is the unauthorized or unacknowledged use of a person's academic or scholarly work. Regardless of how it occurs, plagiarism is a theft of intellectual property.
Academic integrity means having a true educational experience. It involves doing your own reading and studying. It includes regular class attendance, careful consideration of all class materials, and engagement with the class and other students. Academic integrity lies at the core of our common goal: to create an intellectually honest and rigorous community.
Because academic integrity is so central to our mission as students, teachers, scholars, and citizens, we will ask you (but not require you) to sign the CSU Honor Pledge when completing all major assignments.
"I have not given, received, or used any unauthorized assistance."
If you plagiarize in your work you could lose credit for the plagiarized work, fail the assignment, or fail the course. Each instance of plagiarism, classroom cheating, and other types of academic dishonesty will be addressed according to the principles published in the CSU General Catalog (see page seven, column two: http://www.catalog.colostate.edu/FrontPDF/1.6POLICIES1112f.pdf).
Help: Help is always available if you have trouble with homework or lecture material. If your classmates can't answer your question, come ask me! Office hours are (tentative) Wed 11-12, Thurs 1-2 or by appointment in Weber 205A.