ACCESS-UGS 1430
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 College of Science Math Department Nick Korevaar's home page |
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JUNE 11-15, 2007
Hi! I'm Professor Nick Korevaar. My office is LCB 204, my phone number is 581-7318, and my email address is korevaar@math.utah.edu You can find ACCESS information (like these notes), by following links from my home page, at http://www.math.utah.edu/~korevaar
The math portion of ACCESS is the first week, June 11-15, and the fourth week, July 2-6. Meagan McNulty is our ACCESS TA for the entire summer session, and Jen Guajardo is our special math-weeks TA; both Meagan and Jen are math graduate students.
Our theme for the first week will be codes and cryptography. Our planned schedule is below, although it could change as the week progresses.
Monday June 11:
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8:30-9:45 a.m.
JTB 120 |
Introductions, and the forming of study groups. Rosemary Gray has a challenge for you! |
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9:45-10:15 a.m. |
We will walk to the Union to get pictures taken for your University I.D.'s, and then over to Marriott Library and PC-Lab 1735. If you want to explore the rest of campus from your computer, use the interactive campus map. |
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10:15-noon PC-Lab 1735 |
Introduction to the lab: set up accounts, email, internet; introduction/review to Microsoft Word for word processing. We will download Monday's notes: MonJune11.doc. If you want to look at these notes from a non-microsoft place, try MonJune11.pdf. We may also experiment with the mathematical software known as Maple, by playing with the document MapleExpls.mws; (Open MapleExpls.pdf if you want to look but not play.) |
Tuesday June 12:
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8:30-10:15 a.m. PC-Lab 1735 |
An introduction to historical cryptography: Caesar Shifts and other
substitution ciphers, as described
in "The Code Book". Please read chapter 1 (pages 1-44) before class.
Simon Singh tells the story of how Mary Queen of Scots lost her head,
not understanding how easy it is to break substitution
ciphers with frequency analysis. There will be a cipher for us to solve,
and MAPLE 8 will help us. The files we need are in
Tuesdaydocs
After we've solved our substitution cipher Meagan has a different, but related code-breaking problem for you....we'd like each group to work out the logic which led from experimental data to the "genetic code" most of you learned as a "fact" in biology. Jon Seger, who will be presenting on Thursday, thought up this fine problem for you (actually he found it in an advanced biology text book), and we're hoping each group is ready to contribute to a discussion of solutions by the start of Jon's presentation...Please bring a written explanation of your work too (to help your explanation, although we won't collect it). Here is the problem! Cracking_the_Code.pdf |
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10:30-noon JTB 120 |
"Clock arithmetic," a presentation led by Jen. We used the handout modular1.pdf (with more to come on Wednesday). |
Wednesday June 13:
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8:30-12:00 a.m. JTB 120 |
Jen will continue our discussion of modular addition and multiplication. We'll learn about the amazing (and confusing at first) Euclidean algorithm for finding gcd's and multiplicative inverses. Here are the notes we've been using, including answers to all examples and exercises... modularnotes.pdf. |
Thursday June 14:
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8:30-10:15 JTB 120 |
"Modular powers and the RSA algorithm", lecture and discussion
led by Nick. The RSA algorithm uses power functions in modular
arithmetic, to
encrypt (and decrypt) message packets. We'll explore the number
theory behind this algorithm, which goes way way back
before the digital age - about 270 years. Here are the class notes
(without the answers to exercises and examples):
modularpowers.pdf
Useful modern-day sources about RSA are chapters 6-7 of "The Code Book", the Tom Davis notes on cryptography , and the breakthrough paper by Rivest, Shamir, Adleman. You might also want to look at Alice and Bob's actions, sketched out: alicebob.pdf |
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10:30-noon JTB 120 |
"Genetic Codes," lecture by Biology Professor Jon Seger. |
Friday June 15:
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8:30-noon PC-Lab 1735 |
Project work in the MARRIOTT computer lab. Here's the assignment:
project1.mws,
project1.pdf.
The first thing we'll do is go over the Maple Code you'll be using
and modifying: The .pdf with commands still in is
RSAverbose.pdf.
The file to download from Maple 8 is
RSA.mws
Here are the public keys: publickeys.doc |