Course Section 1 Content Section 1 Content Left Section 1 Content Right Credit Type: Course ACE ID: NNCS-0670 Version: 4 Organization's ID: MATH1110 Organization: National Cryptologic University Location: Hybrid Length: 16 hours Minimum Passing Score: 70 ACE Credit Recommendation Period: 8/1/2024 - 7/31/2027 5/1/2021 - 7/31/2024 11/1/2017 - 4/30/2021 10/1/2013 - 9/30/2016 Credit Recommendation & Competencies Section 2 Content Section 2 Content Left Section 2 Content Right Level Credits (SH) Subject Lower-Division Baccalaureate 2 Applications of Finite Fields Description Section 3 Content Section 3 Content Left Section 3 Content Right 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 Section 4 Content Section 4 Content Left Section 4 Content Right Instructional Strategies: Computer Based Training Methods of Assessment: Examinations Quizzes Supplemental Materials Section 5 Content Section 5 Content Left Section 5 Content Right Equivalencies Section 6 Content Section 6 Content Left Section 6 Content Right Button Content Rail Content 1 Other offerings from National Cryptologic University View All Courses College Credit Opportunities Page Content