Mathematics: From Number Theory to Encryption

This is a leisurely paced, but mathematically rigorous introduction to elementary number theory. Students will learn proof techniques like `indirect proof’ and `induction’. (Some past participants have found these skills useful to gain fast acceptance into the Math Honors concentration at the University of Tennessee.) The methods of logical reasoning employed in this area go back to the ancient G(r)eeks and still represent core skills for all aspects of modern mathematics.

Number theory studies the properties of natural numbers, like divisibility, primes, modular arithmetic, and so-called diophantine equations: one application is to find a method that produces all right triangles with integer sides.

We will also choose a collection of topics beyond these basics from our book. In particular, this will include the RSA method, which is key to encryption (for instance keeping credit card information secure during transmission over the internet).

In the evenings, students will have the opportunity to study the material for themselves, but with competent help available. This will include projects on encryption and its modern applications.

A student choosing this topic should have completed 2 years of high school algebra. In particular, calculus is NOT required; however for students that do know calculus, a project is available that establishes an amazing connection between calculus and prime numbers.

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