Day 9: Mat115

Last time: RSA encryption

Next time: 3.2: Comparing the Infinite

Today:

Warning: exam 1 is coming up Wednesday of next week. It will cover chapters 1 and 2.
Hand in problems 2.4
Problems 2.3 returned: graded II.22 and I.2
Questions/Comments on old stuff?
Next time David Freeman (UC Grad Student) will lead class. Please come prepared to discuss section 3.2 with him!

From 2.5: Let's start with a review of RSA, and then, in groups, we will send and receive messages

Use p=7, q=11, e=13, d=37 (or, if you're feeling very adventurous come up and I'll help you pick your own!)

Use the numbers 1-26 for the alphabet, a-z, and 27 for a space:

A	B	C	D	E	F	G	H	I	J	K	L	M	N	O	P	Q	R	S	T	U	V	W	X	Y	Z	SPACE
1	2	3	4	5	6	7	8	9	10	11	12	13	14	15	16	17	18	19	20	21	22	23	24	25	26	27

Encode your messages letter-by-letter.
Send a secret message -- a word or phrase of length at least 8 -- to another group, and see if they can decode it.
Use your calculators! I can help with any calculations that you need to do....

Today we begin chapter 3: To Infinity, and Beyond!
- Infinity - so mysterious...
  Q: Are mathematicians trying to take all the fun out of it by studying it?! A: Of course not! We relish the mind-blowing mystery. And there's plenty of fun to be had....
  
  William Blake (from Auguries of Innocence):
  To see a World in a Grain of Sand
  And a Heaven in a Wild Flower,
  Hold Infinity in the palm of your hand
  And Eternity in an hour.
- We start with the idea of number (e.g. What does "2" mean?).
- What is infinity? Is it a number? Is it just one thing?
- What is a one-to-one correspondence, and how is it useful?
- Let's look at some problems:
  - III.16
  - II.6, II.9
  - IV.22

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