Continue to make vertex-edge graphs, making one alteration at a time.  You should have at least a page full of them.  Use this work to answer the following questions:

1. What happens when you add a vertex? Is this always true?  Why?
2. What happens when you add an edge? Is this always true? Why?
3. What happens when you add a face? Is this always true? Why?
4. Do you notice any special relationships between the number of vertices, edges and faces?

Use examples to illustrate each answer.

See attached assignment description

Use an affine cipher to encrypt the quotation of your choice.

Your affine cipher must have a multiplier and a shift.  Remember what we talked about in class – use a “good” multiplier.  A multiplier of 6, for example, won’t work.  Ask a classmate if you don’t remember what makes a multiplier good.  For class on Monday, bring a printout of your CIPHERTEXT without the rest of the spreadsheet.  The page should have your name on it and the multiplier and shift you used to encrypt it.

During class, you will trade and decrypt each others’ quotes using the inverse of the shift, then the inverse of the multiplier.

I encrypted this message using an affine cipher with a multiplier of 17.

L E A U O L P Q D G Y P L M C Q U L G E N G U P A D Z Q D L P A N L E A N U K Q D G L

You will need to use a completed MOD26 multiplication table to find out how to decrypt this message.  (Remember that our alphabet starts at 0!)

For next class, bring a printed (and stapled) copy of your excel spreadsheet that shows your solution.

Use excel to change this CIPHERTEXT to PLAINTEXT. It was encoded using a +21 shift.

Why is the study of math so important?  A famous scientist said:

R C Z M Z O C Z N Z I N Z N A V D G P N M Z V N J I H P N O N O Z K D I