# Course

Course Summary
Credit Type:
Course
ACE ID:
NNCS-0670
Organization's ID:
MATH1110
Location:
Hybrid
Length:
16 hours
Dates Offered:
Credit Recommendation & Competencies
Level Credits (SH) Subject
Lower-Division Baccalaureate 2 Applications of Finite Fields
Description

## Objective:

The course objective is to introduce basic concepts of the finite field number systems.

## Learning Outcomes:

• compute the Euclidean algorithm for integers;
• recognize the properties of groups, rings, and integral domains;
• construct prime finite fields;
• compute characteristics of polynomials and their reverses;
• perform the Division and Euclidean algorithm for polynomials;
• recognize properties of extension fields;
• produce finite fields using shift registers, primitive elements, and primitive polynomials;
• identify minimal polynomials;
• compute conjugates and cyclotomic cosets of a field;
• construct finite fields to coding theory using the Peterson tables;
• perform modulo arithmetic;

## General Topics:

• Division and Modulo arithmetic
• Euclidean algorithm and division algorithms for integers and polynomials
• Groups, rings, and integral domains
• Prime finite fields and extension fields
• Polynomials and minimal polynomials
• Primitive elements and primitive polynomials
• Logarithms
• Conjugates and cyclotomic cosets
• Peterson tables
Instruction & Assessment

## Instructional Strategies:

• Computer Based Training

• Examinations
• Quizzes

## Minimum Passing Score:

70%
Supplemental Materials