Department of Mathematics Generic Syllabus
Boise State University Updated Fall 1998

Math 405
Abstract Algebra II
4 semester credits

Catalog Description

M 405 Abstract Algebra II (4-0-4)(F)(Offered on demand odd-numbered years) Sylow theorems, solvable groups, rings and ideals, rings of polynomials, factorization, fields and extensions, Galois Theory. PREREQ: M 301 and M 305.

Prerequisites

Linear algebra and abstract algebra I

Jurisdiction

This course is not currently controlled by a departmental committee and individual instructors may choose different textbooks. Exams, homework and grading system are left to the instructor.

Learning Objectives

As a theoretical senior level course, this course focuses on the aesthetic nature of mathematics and the view of mathematics as a language. The tools developed in this course are in the realm of logical deduction and induction and in general proof development.

Upon completion of this course, the students will have made substantial progress in:

Writing proofs of algebraic concepts.
Applying the Sylow theorems to the structure of a group
Using the fundamental isomorphism theorems to deduce structure and properties of rings and groups
Applying theory of quotient rings to create extension fields which contain roots of polynomials which were not present in the base field.
Use the fundamental theorem of Galois Theory to apply theorems about group composition to gain results about field composition.

1 Assessment of Learning Objectives

Students will be assessed by evaluating their ability to do problems based on the learning objectives. The problems will occur in several contexts;

Periodic problem sets for homework serve both as learning and assessment tools. Classroom activities may vary depending on students' performances on homework assignments.
Problems given on in-class examinations are designed to give students the opportunity to demonstrate their ability to apply rules and formulae to the solution of simpler problems and to demonstrate their ability to formulate proofs from the definitions of concepts given in the lectures.
Instructor optional take-home examinations designed to evaluate the students ability to solve more complicated and time consuming problems, and to extend the theory to areas which were not covered in the classroom.

Topics and Approximate Timeline


	Number of
Topic	Lectures
Sylow theorems and applications	8
Rings of polynomials	6
Factorization in integral domains	12
Extension Fields	8
Applications of field theory to geometric constructions	3
Field Automorphisms and Galois theory	12

Text

The last time the course was taught, the text was A First Course in Abstract Algebra, Fifth Edition by John Fraleigh, Addison Wesley Publishing.

Format, Student Activities, and Grades

Class meetings involve a combination of lecture, questions and discussion and sometimes small group activity. The particular mix is determined by the current instructor.

As in all mathematics courses, homework is an important part of the course.

The exams may be given in class or take-home. The students are given a letter grade based on points earned. The points are typically available as:


Homework	100
Two exams	200
Final exam	200
Total	500

Letter grades are based on a scale in which 90% of the 900 possible points guarantees an A, 80% a B, 70% a C, 60% a D, and less an F, with the instructor having the discretion to adjust these cut-offs if warranted.

File translated from T_EX by T_TH, version 1.56.