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
- rsa encryption
- traveling salesman problem
- secondary schools
- discrete mathematics
Date of Defense 2002-04-12 Availability unrestricted AbstractThis 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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