Course Course Summary Section 1 Content Section 1 Content Left Section 1 Content Right Credit Type: Course ACE ID: NNCS-0670 Organization's ID: MATH1110 Organization: National Cryptologic University Location: Hybrid Length: Self-paced (16 hours) Dates Offered: 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 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 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: 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 Section 4 Content Section 4 Content Left Section 4 Content Right Instructional Strategies: Computer Based Training Methods of Assessment: Examinations Quizzes Minimum Passing Score: 70% Supplemental Materials Section 5 Content Section 5 Content Left Section 5 Content Right Section 6 Content Section 6 Content Left Section 6 Content Right Button Content Rail Content 1 Other offerings from National Cryptologic University Accelerated Basic Ukrainian Structure for Russian Analysts (NNCS-5208) Advanced Cryptologic Korean I (NNCS-0668) Advanced Cryptologic Korean III (NNCS-0699) Advanced Korean History (NNCS-5180) Advanced Spanish Structure I (NNCS-0679) Advanced Spanish Structure II (NNCS-0680) Advanced Spanish Workshop I (NNCS-0632) Advanced Spanish Workshop ll (NNCS-0651) Advanced Technical ELINT Analysis and Radar Concepts (NNCS-0004) Advanced Urdu Refresher (NNCS-0710) View All Courses Page Content