AMAT 326: Classical Algebra Fall 2013
|Class hours||MWF 12:351:30pm|
|Office||Earth Science 120B|
|Office hours||M 11:30am12:30pm and WF 1:30pm2:30pm|
|Email address||bgoldfarb at albany.edu|
About the course:
The text is
A Concrete Introduction to Higher Algebra, by Lindsay Childs,
During the first class I will be explaining the contents of the book and setting up goals.
We will start by learning properties of integers including the Division Theorem and operations in various bases. The main purpose of this stage is to learn to use induction and other techniques to prove facts about integers. Next we will develop Euclid's Algorithm and use it to solve Bezout's identities, apply it to study congruences and congruence classes. There are many beautiful applications of this material such as sieves for finding prime numbers. We will generalize the methods to other rings and prove Fermat's and Euler's Theorems in that setting. Applications of these theorems include RSA codes and study of 2-pseudoprimes. We will review matrix algebra and apply earlier material to error-correcting codes.
Exams: There will be two midterm tests.
Reading/Homework/Quizzes/Tests: Read the sections we cover in class immediately after each lecture. Homework problems from the text will be posted and updated here, on this web page. You don't have to turn in solutions. However, the quizzes which will be usually given every (non-test) week will consist of one/two/three problems very similar to those in the homework due that week. Each quiz will be worth 5 points. There will be one or two homework assignments, better described as projects, that will be graded, also out of 5 points. Out of all quizzes and graded projects, only the best 10 grades will matter. This is designed so that I don't have to give make-up quizzes. Unless there is a very unusual and meticulously documented situation which forces one to miss many quizzes, no make-ups will be given.
Homework assignments: To see the homework assigned during the corresponding week, follow the link on the left. To see the solution of the quiz or the test given that Friday, follow the link on the right.
Grades: The course letter grades will be based on a curve obtained from quiz and test scores according to the following scheme:
The following information is added to satisfy the Minimum Contents of a Class Syllabus requirements. The prerequisite for this course is A MAT 113. The course is A-E graded. Attendance is critical to success in the class.