Title page for ETD etd-0417102-115228


Type of Document Master's Thesis
Author Boyd, Aimee Beth
URN etd-0417102-115228
Title Discrete Mathematics Topics in the Secondary School Curriculum
Degree Master of Science (M.S.)
Department Mathematics
Advisory Committee
Advisor Name Title
Bogdan Oporowski Committee Chair
Frank Neubrander Committee Member
James Oxley Committee Member
Keywords
  • cryptograhy
  • rsa encryption
  • traveling salesman problem
  • secondary schools
  • discrete mathematics
Date of Defense 2002-04-12
Availability unrestricted
Abstract
This thesis discusses two topics of discrete mathematics in a manner suitable for presentation at a secondary-school level. The introduction outlines the benefits of including discrete mathematics in the secondary-school curriculum. The two chapters which follow include detailed treatment of the two selected topics: the Traveling Salesman Problem and RSA encryption.

The discussion of the Traveling Salesman Problem consists of introduction to the problem through several real-life scenarios, followed by a discussion of various methods for solving the problem. We discuss exact and approximate algorithms together with their computational complexity and practical limitations.

The discussion of RSA encryption begins with an introduction to the necessary background in number theory, which includes the Chinese Remainder Theorem, Bezout's Equation, and Fermat's Little Theorem. Following this is a discussion of encryption and decryption techniques, which are illustrated through an example that is accessible to any student with a basic scientific calculator.

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