Northeastern State University

College of Mathematics, Science and Nursing

Department of Mathematics and Computer Science

Syllabus for MATH 3713 - Modern Algebra

PREREQUISITES: Math 3023 Discrete Mathematics and Math 2614 Calculus I or concurrent enrollment

CATALOG DESCRIPTION OF COURSE: Equivalences, congruences, logic, sets, groups, rings, and fields.

COURSE PURPOSE: This course has been designated as an approved liberal arts course. The course categorizes algebraic systems by investigating the structure, properties, and examples of groups, rings, integral domains and fields.

EXPECTED COURSE OUTCOMES: The student will be expected to achieve the following objectives:

  1. Define mapping and binary operation.

  1. Distinguish between relations and equivalence relations.

  1. Prove theorems using various techniques, including Mathematical Induction.

  1. Apply the elementary divisibility properties of number theory.

  1. Describe the properties and structure of groups, rings, integral domains and fields.

  1. List examples of groups, rings, integral domains and fields.

  1. Characterize subgroups and subrings.

INSTRUCTIONAL MATERIALS: (Required Textbook) Gilbert, Jimmie and Linda Gilbert. Elements of Modern Algebra (5th edition). Pacific Grove, California: Brooks/Cole, 2000.

INSTRUCTIONAL PROCEDURES: The expected course outcomes will be realized through a variety of instructional strategies. Those strategies include, but are not limited to, the following: lecture, expository-discussion, demonstration, and group activities. The instructor will integrate appropriate multi-media technology.

Modern Algebra

I. Fundamentals

  1. Logic

  1. Sets

  1. Mappings

  1. Properties of Composite Mappings

  1. Binary Operations

  1. Matrices

  1. Relations

II. Number Theory

  1. Mathematical Induction

  1. Divisibility

  1. Prime Factors and Greatest Common Divisor

  1. Congruence of Integers

  1. Congruence Classes

  1. Introduction to Coding Theory

III. Groups

  1. Definition of a Group

  1. Subgroups

  1. Cyclic Groups

  1. Isomorphisms

  1. Homomorphisms

IV. More on Groups, Rings, Integral Domains, and Fields

  1. Finite Permutation Groups

  1. Cayley's Theorem

  1. Definition of a Ring

  1. Integral Domains and Fields

ADA Compliance: If any member of the class feels that he/she has a disability and needs special accommodations , the instructor will work with you and the University's Office of Student Affairs to provide reasonable accommodations to ensure that you have a fair opportunity to perform in this class. Please advise the instructor of such disability and desired accommodations at the first class attended.

Inclement Weather/Disaster Policy:

The following are basic premises for the inclement weather policy at Northeastern State University:

1. Classes are expected to be held if at all possible.

2. It is the student's responsibility to receive the information when weather is questionable.

3. Neither students nor faculty are expected to risk life or limb.

4. Faculty members are obligated to hold classes if the University is not closed, unless the faculty member is unable to get to campus.

Policy: During times of inclement weather, decisions concerning day classes will be made by 6:00 a.m. in order for the media to be notified and for students to receive the announcement before they leave home. Decisions concerning night classes will be made by 3:00 p.m.

The following media will be notified regarding closing of the campus:

Radio Stations: Television Stations:
KRMG 740 AM Tulsa KJRH Channel 2 Tulsa

KAYI 107 FM Tulsa KOTV Channel 6 Tulsa

KTLQ 1350 AM Tahlequah KTUL Channel 8 Tulsa

KEOK 102 FM Tahlequah KFSM Channel 5 Fort Smith

KBIX 1490 AM Muskogee Cable Channel 96 Tahlequah

KMMY 97 FM Muskogee

KVOO 1170 AM Tulsa

The automated attendant message on 918-456-5511 will be modified to include information concerning campus operations during inclement weather.