Instructor: Marlow Anderson, Palmer 140, 389-6543, manderson@ColoradoCollege.edu,

Text: "A First Course in Abstract Algebra: Rings, Groups and Fields", by Marlow Anderson & Todd Feil, Prindle, Weber & Schmidt.

This course is a second block continuation of MA321: Abstract Algebra I, as taught by Dave Roeder and Marlow Anderson in Block 3 of this academic year.

This course will begin by looking more deeply in the theory of commutative rings, by picking up Chapters 14 and 15 on the Unique Factorization Problem, and then the theory of ideals, in Chapters 20 and 21.

We will then cover Sections VII & VIII in the book, where we will meet the ideas of field extensions, with the goal in mind of proving the impossibility of the three great construction problems of the ancient Greeks: Squaring the Circle, Duplicating the Cube, and Trisecting the Angle. The fact that it takes the abstract algebraic approach in order to lay to rest these ancient unsolved problems is one of the great mathematical triumphs of the abstract method.

Once we have accomplished this goal, we will look at the additional topics in Section IX. Depending on how much time is available, we may expand section 45 on Frieze Groups, to look at the group of all plane symmetries, a topic of great interest to geologists, artists etc.