Day 11: Heart of Mathematics

Last time: Prime numbers; finding them using the Sieve of Eratosthenes; that there are infinitely many (and a proof that there are!).
Today:
- Assignment 1 is due. I'll try to be gentle!
- Reminder:
  - Project Assignment 1: by Friday, 9/20, pick your partner(s) (you can go alone!) for the poster project; it would also be nice if you have a topic, but that's not required!
- Project idea: Sections 2.4 and 2.5 (clock arithmetic, secret codes). Sections we skip are fertile ground for posters....
- Prime Numbers:
  - Starting from the idea of decomposing (or factoring) natural numbers using division, we find primes using the Sieve of Eratosthenes (but only finitely many!). There are infinitely many -- they just don't stop! The proof was discovered by Euclid over 2000 years ago.
    Even though primes seem to appear irregularly amongst the natural numbers, primes become sparser and sparser as the natural numbers get bigger and bigger. It's just that there's always another one!
  - Let's look at these exercises:
    - I.2, 7, 9, 10, 19
    - II.7
    - II.10
Next time: those pesky irrational numbers....

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