Wednesday, January 22, 2014

First Class!

First Class!

- Discussion of course details:

- handout course
description

- Discussion of the many course features:

- In class activities.
- Homework
- Reading

- Portfolios
- Projects
- The Tool kit

- personal info sheet.

- Flatland as social commentary/satire.

- What is contemporary mathematics?
- Recent results on prime number problems.
- List of primes: 2,3,5,7,11,13,17,19,23, 29,31,...
- Some pairs are "twins" 3,5; 5,7; 11,13; 17,19; 29,31;...
- The twin prime conjecture: There are an infinite number of "twin primes."
- This has not been proven though there is much evidence to support the statement as being true.
- Recently there have been results that there are an infinite number of pairs of primes that are within a large fixed number of each other.
- FROM WIKIPEDIA:On April 17, 2013, Yitang Zhang announced a proof that
for some integer
*N*that is at most 70 million, there are infinitely many pairs of primes that differ by*N*.^{[1]}^{[2]}Zhang's paper was accepted by*Annals of Mathematics*in early May 2013.^{[3]}Terence Tao subsequently proposed a Polymath project collaborative effort to optimize Zhang’s bound;^{[4]}as of November 28, 2013, Thomas Engelsma claims to have reduced the bound to N = 576.^{[5]}

- Counting activity: How many pencils? Next class: How
many Leprechauns?