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 Brittany Banish's home page |
JUNE 13-17 2011
Welcome to the "U"! 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". In case you're reading a printout and want to follow on-line links later, the URL for this page is http://www.math.utah.edu/~korevaar/ACCESS2011
Britney Erickson (britney.erickson"at"utah.edu) is our ACCESS TA for the entire summer session, and Brittany Bannish, a Ph.D. student in the Math Department, is our week 1 math TA.
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 13:
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8:30-10:00 a.m.
JTB 120 |
Introductions; Lisa Batchelder wants to talk to you about T-shirts and pass out checks; Rosemary Gray has a puzzle for you to solve, to which I'll be adding a twist; and the Math Department is pleased to give each of you complimentary copies of The Code Book, by Simon Singh. We'll hand out copies of these notes: June13.pdf, June13.doc. Here is the "twist": groups.mw. groups.pdf. |
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10:00-10:30 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 MAC-Lab 1008. If you want to explore the rest of campus from your computer, use the interactive campus map. |
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10:30-noon MAC-Lab 1008 |
Introduction to the lab: your accounts, email, internet, software; emailing Rosemary your challenge problem solutions in a Microsoft Excel document, and emailing Nick your formula, related to Rosemary's problem. Don't forget to read the first chapter, pages 1-44, of "The Code Book" for tomorrow! |
Tuesday June 14:
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8:30-10:30 a.m. Mac-Lab 1008 |
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 will help us. The documents we need are in Tuesdaydocs |
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10:45-11:15 a.m. JTB 120 |
After solving the substitution cipher problem above via frequency analysis, we'd like you to exercise your thinking abilities in different ways by considering one of the most fundamental historical code breaking successes ever: we'd like each group to use experimental data and logic to deduce significant portions of the "genetic code" most of you learned as a "fact" in biology. Here are the details: dna.pdf (Britt's slides from class), Cracking_the_Code.pdf ( Jon Seger's slides), which include more discussion and the experimental results you'll be using in your precise group assignment, bio.pdf. Jon is an evolutionary biology Professor here at the U. who will be presenting to us. We're hoping each group is ready to contribute to a discussion of solutions in the half hour before before Jon's presentation on Thursday! Each group will write up a more formal explanation of their results as part of the group projects that will be due next week Thursday at midnight. |
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11:20-noon JTB 120 |
An overview of public key cryptography. 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 our notes for this discussion: overview.pdf. |
Wednesday June 15:
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8:30-11:50 JTB 120 |
We'll discuss and work with the modular arithmetic (also sometimes called "clock" or "remainder" or "residue" arithmetic) which underlies RSA cryptography; we'll
get comfortable with the
operations of addition, subtraction, multiplication, and 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 the notes: modulararithmetic.pdf.
Next, we'll learn about the amazing (and confusing at first) Euclidean algorithm for finding gcd's and multiplicative inverses in modular arithmetic. Here are the notes: Euclid.pdf. |
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12:00-1:00 p.m. Union |
ACCESS welcome lunch at the Crimson View room in the Student Union. |
Thursday June 16:
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8:30-9:40 JTB 120 |
Continuing discussion of the number theory behind RSA cryptography. We'll begin with a few volunteers showing some of yesterday's homework problems on gcd's and multiplicative inverses via the Euclidean algorithm. Then we'll move on to power functions in modular arithmetic, with these class notes: modularpowers.pdf. We'll also use the Tom Davis notes on cryptography, which are a nice distillation of historical cryptography ideas, culminating in RSA public key cryptography. Other good references are the latter chapters of "The Codebook", Wikipedia, 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! |
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10:30-noon JTB 120 |
"Genetic Codes," presentation by Biology Professor Jon Seger. |
Friday June 17:
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8:30-11:50 PC-Lab 1009 |
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.mw. To see what this looks like with the commands filled in,
see RSAverbose.pdf.
We'll also use the
Alice and Bob diagram from previous years (so the date is wrong
on the document). After we understand RSA,
groups will begin their week 1 project work in the
MARRIOTT computer lab - Here is the precise project assignment
for week 1:
project1.pdf. In case you want to automate the Davis table part of the project, try using these procedures:
Davisconversion.mw.
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12:00-12:45 p.m. The Den, Union |
Women's Resources Center orientation. Lunch will be provided. |