Identifier

etd-0417102-115228

Degree

Master of Science (MS)

Department

Mathematics

Document Type

Thesis

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.

Date

2002

Document Availability at the Time of Submission

Release the entire work immediately for access worldwide.

Committee Chair

Bogdan Oporowski

DOI

10.31390/gradschool_theses.1537

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