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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