Course

Course Summary
Credit Type:
Course
ACE ID:
NCCS-0675
Organization's ID:
MATH4335
Organization:
National Cryptologic University
Location:
Hybrid
Length:
16 weeks (48 hours)
Dates Offered:
Credit Recommendation & Competencies
Level Credits (SH) Subject
Graduate 3 Applied Combinatorics in Mathematics
In the graduate degree category, 3 semester hours in applied combinatorics in mathematics.
Description

Objective:

The course objective is to introduce cryptomathematicians to enumeration, generating functions and recursions, random mappings, permutations, and Mobius inversion in partially ordered sets with applications. Selected topics in graph theory block designs, and combinatorial algorithms will also be introduced.

Learning Outcomes:

  • apply the basic concepts of graph theory
  • design and apply various algorithmic approaches for combinatorial optimization
  • construct optimal algorithms for various well-known problems
  • formulate and validate various methods of enumeration
  • analyze and apply generating functions and recurrence relations
  • test application of appropriate inversion techniques
  • research, formulate and defend presented research on synthesized combinatorial topic

General Topics:

  • Enumeration
  • Recurrence
  • Generating functions
  • Inversion
  • Graph theory
  • Combinatorial optimization
  • Designs
Instruction & Assessment

Instructional Strategies:

  • Classroom Exercise
  • Learner Presentations
  • Lectures
  • Practical Exercises

Methods of Assessment:

  • Other
  • Presentations
  • exercise sets

Minimum Passing Score:

80%
Supplemental Materials