ACCESS-UGS 1430
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University of Utah University of Utah map University of Utah directory College of Science Math Department Nick Korevaar's home page Alla Borisyuk's home page Darci Taylor's home page |
JUNE 15-19, 2009
Welcome! I'm Utah Math Professor Nick Korevaar. My office is LCB 204, my phone number is 801-581-7318, 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/ACCESS2009
The math portion of ACCESS is the first week, June 15-19, and the fifth week, July 13-17. Ashley Miller is our ACCESS TA for the entire summer session, and Darci Taylor is our special math-weeks TA. Darci is a Ph.D. student in the Math Department, specializing in mathematical biology. Math Professor Alla Borisyuk will be helping this week, and leading week 5.
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 15:
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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 in a Microsoft Excel document. Details here: June15.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 16:
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8:30-10:30 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. |
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10:45-11:15 a.m. JTB 120 |
After we've solved our substitution cipher Darci has a different 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 on Thursday, before Jon's presentation, especially since part of your week 1 project is to solve this problem and explain your work! |
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11:20-noon JTB 120 |
"An overview of public key cryptography," a presentation led by Nick. Public key cryptography is a late 20th-century conceptual breakthrough that has allowed the internet to be used for secure transactions. We'll be working for most of the rest of week 1 to understand the number theory behind the most widely used public key system: RSA cryptography. Here are the notes for Nick's presentation: overview.pdf. |
Wednesday June 17:
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8:30-12:00 a.m. JTB 120 |
We'll discuss and work with the modular arithmetic (also sometimes called "clock" or "remainder" or "residue" arithmetic) which underlies RSA cryptography. Alla will lead
our study of the
operations of addition, subtraction, multiplication, using the
multiplicative inverse (don't say "dividing"!) in
modular number systems.
Remember prime numbers, greatest common divisors, and
all the arithmetic surrounding these ideas that you thought you'd never see again? Well, surprise! Here are Alla's notes:
modulararithmetic.pdf We'll learn about the amazing (and confusing at first) Euclidean algorithm for finding gcd's and multiplicative inverses in modular arithmetic. Nick's class notes on the Euclidean Algorithm are here: Euclid.pdf. Then, after all this work, we'll realize that modular addition and multiplication don't work well as one-way 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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12:30-2:30 p.m. Sill Center |
New Student Orientation. Special session for ACCESS women. Lunch will be provided. |
Thursday June 18:
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8:30-9:40 JTB 120 |
We'll continue the discussion of the number theory behind RSA cryptography. Nick's notes on power functions in modular arithmetic are here: modularpowers.pdf. In addition to the latter chapters of "The Codebook" and Wikipedia, 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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9:50-10:20 JTB 120 |
Problem session on the genetic code problem: Each group should be prepared to contribute! The specific assignment is bio.pdf. |
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10:30-noon JTB 120 |
"Genetic Codes," presentation by Biology Professor Jon Seger. |
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12:30-1:30 p.m. Crocker Science House |
ACCESS welcome luncheon |
Friday June 19:
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8:30-noon PC-Lab 1735 |
We'll finish the number theory behind RSA cryptography 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: assignment1.pdf |
The method least squares for linear fits, and using ln-ln data to find power laws: leastsquares.mws
National height-weight data, and the Maple commands you'll need for your project: bmi.mws
Your ACCESS height-weight data: htwts09.mws