Extra Material

Having covered Chapters 1 through 5, we're now have the basics tools necessary to talk about pretty much any "elementary" number theoretic results. Students will be responsible for presenting group projects that explore topics which they find interesting. In addition, we will also talk about an application of the ideas we've already discussed and an indication of what current number theorists spend time thinking about.

- Lecture 28: RSA Encyption
- Today we discussed the results of the second midterm, including how your raw score correlate to a letter grade. Students who received below a "C" were told how they could receive some "redemption" points to help pull up their grade, but the necessary work is due by Friday (unless otherwise scheduled with the instructor). Afterwards we discussed number theoretic encryption methods, including the modern-day workhorse known as RSA.
- Lecture 29: Analytic Number Theory and the Riemann Zeta Function
- Today we took a sneak peak at the kind of number theory which comes after a typical "elementary" course like ours. Much of our time was devoted to studying properties of the famous Riemann Zeta function. Along the way we saw the so-called Euler Product formula for $\zeta(s)$, and we used this to give a new proof of the infinitude of primes. We then discussed the kinds of properties of $\zeta(s)$ which mathematicians today are currently interested in.
- Lecture 30: Perfect, Amicable and Sociable Numbers
- During this lecture we discussed many classifications of classical numbers. These numbers included perfect, amicable, and sociable numbers. We discussed many different types of perfect numbers, restrictions on even and odd perfect numbers, sociable numbers and aliquot sequences.
- Lecture 31: Irrationality of Pi
- In today's class we discussed $\pi$, both its history as well as the mathematical properties it has.
- Lecture 32: Fibonacci Numbers
- In today's class we discussed the Fibonacci numbers.
- Lecture 33: Fermat's Last Theorem
- In today's class we discussed Fermat's Last Theorem.
- Lecture 34: Pythagorean Triples
- In today's class we discussed Pythagorean Triples.
- Lecture 35: Continued Fraction
- Today we discussed a variety of topics concerning continued fractions. This included finite and infinite continued fractions, convergents, as well as applications of each.
- Lecture 36: Integers as sums of squares
- In today's class we discussed integers as sums of squares.
- Lecture 37: Know/Don't Know Problem
- In today's class we solve a mathematical riddle.

page revision: 10, last edited: 10 Dec 2008 02:35