Course

Course Summary
Credit Type:
Course
ACE ID:
NNCS-0670
Organization's ID:
MATH1110
Organization:
National Cryptologic University
Location:
Hybrid
Length:
Self-paced (16 hours)
Dates Offered:
Credit Recommendation & Competencies
Level Credits (SH) Subject
Lower-Division Baccalaureate 2 Introduction to Finite Fields and Their Applications
In the lower-division baccalaureate/associate degree category, 2 semester hours in introduction to finite fields and their applications
Description

Objective:

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

Learning Outcomes:

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

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

Methods of Assessment:

  • Examinations
  • Quizzes

Minimum Passing Score:

70%
Supplemental Materials