This course will be an introduction to ring and field theory. A ring is an algebraic system with two operations (addition and multiplication) satisfying various axioms, the basic example being the integers. We will see that many properties of the integers are shared by other broad classes of rings (for example polynomial rings). In particular we will explore the general notion of unique factorization and formulate conditions under which a ring has this property. Later in the course we will apply some of the results of ring theory to construct and study field extensions. If time permits we will outline the main results of Galois theory which studies the structure of the extension generated by the roots of a polynomial in terms of an associated group.Syllabus
We will cover Chapters 16--26 of the textbook.Class log
There will be weekly homework, due at the beginning of Wednesday's class. (First homework due Wednesday 2/6/13.)Homework sets
There will be two midterm exams and one final exam.
The first midterm is Wednesday 2/27/13, 7:00PM--8:30PM, in LGRT 173. There is a review session for the first midterm on Tuesday 2/26/13, 7:00PM-8:30PM, in LGRT 173. Please try the review questions here before the review session.
The second midterm is Wednesday 4/3/13, 7:00PM--8:30PM, in LGRT 173. There is a review session for the second midterm on Tuesday 4/2/13, 7:00PM-8:30PM, in LGRT 173. Please try the review questions here before the review session.
The final exam is Friday 5/3/13, 4:00PM-6:00PM, in LGRC A301. There is a review session for the final exam on Thursday 5/2/13, 7:00PM-8:30PM, in LGRT 173. Please try the review questions here before the review session.
Calculators, notes, and the textbook are not allowed on exams and quizzes. You should bring your student ID (UCard) to each exam.Grading
Your course grade will be computed as follows: Homeworks and quizzes 30%, Midterm exams 20% each, Final exam 30%.