ACCESS-UGS 1430
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 College of Science Math Department Nick Korevaar's home page |
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JUNE 9-13, 2008
Hi! I'm Utah Math Professor Nick Korevaar. My office is LCB 204, my phone number is 581-7318, and my email address is korevaar"at"math.utah.edu. These notes are posted at our ACCESS Math home page, http://www.math.utah.edu/~korevaar/ACCESS2008
The math portion of ACCESS is the first week, June 9-13, and the fifth week, July 7-11. Nessy Tania is our ACCESS TA for the entire summer session, and Erin Chamberlain is our special math-weeks TA. Nessy is a Ph.D. student in the Math Department, specializing in mathematical biology. Erin just received her Ph.D. in Algebra, and will be a Postdoctoral Instructor at BYU this fall.
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 9:
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8:30-9:45 a.m.
JTB 120 |
Introductions; Lisa Batchelder wants to talk to you about T-shirts, Rosemary Gray has a puzzle for you to solve, and we'll give each of you copies of The Code Book, by Simon Singh. |
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9:45-10:15 a.m. |
We will walk to the Union to get your University I.D.'s and bus passes (make sure you bring an official picture I.D., like a driver's license or passport!), 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, and emailing Rosemary your challenge problem solutions. Details here: June9.doc If there's time, you can play with a mathematical analog of Microsoft Word, the software program MAPLE....we'll be using this software in both Math weeks. You can open the following file from MAPLE: MapleExpls.mws. Don't forget to read the first chapter, pages 1-44, of "The Code Book" for tomorrow! |
Tuesday June 10:
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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 is a cipher for us to solve,
and MAPLE 8 will help us. Everything we need is at
Tuesdaydocs.
After we've solved our substitution cipher Nessy has a different but actually 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. Here's the problem: Cracking_the_Code.pdf. Utah Biology Professor Jon Seger, who will be presenting on Thursday, thought up this fine problem for you (actually he found and modified it from 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. |
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10:30-noon JTB 120 |
"Clock arithmetic," a presentation led by Erin. (Follow her link to copies of our class notes.) This material is a subset of classical number theory, and is the starting point for the amazing RSA public key cryptography system we will be talking about for the rest of the week. |
Wednesday June 11:
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8:30-12:00 a.m. JTB 120 |
Erin 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. Then, after all this work, we'll realize that modular addition and multiplication don't work well as encryption functions. Luckily for internet security, powers do! And, all of our work on addition and multiplication will be key in understanding this. |
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1:00-2:00 p.m. Crocker Science House |
ACCESS welcome luncheon |
Thursday June 12:
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8:30-10:15 JTB 120 |
Erin will finish leading us through the Euclidean algorithm and multiplicative inverses in modular arithmetic. Then Nick will discuss "Modular powers and the RSA algorithm." Here are the class notes. We also used these handwritten ones. Useful modern-day sources about RSA are chapters 6-7 of "The Code Book", the Tom Davis notes on cryptography , and the original breakthrough paper by Rivest, Shamir, Adleman. |
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10:30-noon JTB 120 |
"Genetic Codes," presentation by Biology Professor Jon Seger. Did you solve the Tuesday problem? |
Friday June 13:
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8:30-noon PC-Lab 1735 |
We'll finish the last bit of number theory and then work through the Davis notes example of RSA encryption together, letting MAPLE do the math steps. The Maple document you need to open is RSA.mws. (To see what this looks like with the commands filled in, see RSAverbose.pdf We'll also use the Alice and Bob diagram. After we understand RSA, groups will begin their week 1 project work in the MARRIOTT computer lab - here's the assignment: project1.pdf |