A Course Syllabus

for

Math 3720

Algebraic Structures

(Two Semester Hours Credit)

in the

Department of Mathematics and Computer Science

of the

COLLEGE OF SCIENCE AND TECHNOLOGY

Catalog Description: Basic mathematical systems: groups, rings, and fields. Prerequisite: Math 2410.

UNIVERSITY OF CENTRAL MISSOURI

Warrensburg, Missouri

2008-2009 I. Purpose of the Course

This course will provide an introduction to certain basic algebraic systems, and will enable the student to broaden and develop his/her facility in mathematical abstraction.

II. Objectives and Desired Student Competencies

Upon completion of this course, the student will be able to:

A. Have a fundamental knowledge of one and two operation systems and some of their major theorems and their proofs. B. Understand the concepts of groups, rings, integral domains and fields. C. Use the topics treated in this course to proceed to more advanced mathematical concepts.

III. Course Content Outline

Texts: Elements of Modern Algebra, by Gilbert and Gilbert, PWS-Kent Publishing Co., 6th ed., 2005.

A. Introduction to group theory 1. Basic definitions and terminology 2. Permutation groups 3. Homomorphisms and Isomorphisms 4. Cyclic groups 5. The theorems of Cayley and Lagrange

B. Rings, Integral Domains and Fields 1. Basic definitions and terminology 2. The field of quotients of an integral domain

C. Ideals and Quotient Rings 1. Ring homomorphisms 2. Prime and maximal ideals

IV. Grading and Evaluation

Student evaluation is based on written assignments, regular examinations, special projects and a comprehensive final examination.

A sample grading scale: A 90-100% B 80-89% C 70-79% D 60-69% F 0-59% TEACHER EDUCATION

1. Conceptual Framework information

Belief Statement The Central educator is a competent, caring, reflective practitioner committed to the premise that all can learn.

Mission As a cornerstone of the institution for over 130 years, the University of Central Missouri's Teacher Education Program develops teachers and other school professionals who are well grounded in theory, display competence in content knowledge and instructional strategies, and possess the dispositions to ensure success for all learners. The Teacher Education Program prepares individuals as professional educators for an ever-changing, culturally diverse population. Faculty and candidates provide support and service to schools in meeting their present and future challenges by developing communities that learn through research and scholarly activities. Educator preparation is a campus-wide responsibility, a commitment that reflects the honor and worth of serving a vital profession.

2. Course Objectives - In your Course Objectives section, please include the MoSTEP and/or content area standards and student outcomes that are covered in the course. This can be accomplished by listing the objectives in your own words and citing the relevant standard, or by including the entire standard as a course objective. For example: Upon completion of the course, the student will be able to (a) describe four major philosophical models of human behavior, (b) use a variety of strategies to record and graphically display classroom behavior and social skills, (c) conduct a functional behavioral assessment, and (d) select appropriate interventions to improve active engagement in learning, prosocial behavior, and self-efficacy. (MoSTEP 1.2.6) or MoSTEP 1.2.6 The preservice teacher uses an understanding of individual and group motivation and behavior to create a learning environment that encourages positive social interaction, active engagement in learning, and self-motivation.