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 Zhu Wang's home page |
JUNE 14-18 2010
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/ACCESS2010
The math portion of ACCESS is the first week, June 14-18, and the sixth week, July 19-22. Brenna Blackburn (brenna.blackburn"at"utah.edu) is our ACCESS TA for the entire summer session, and Zhu Wang is our special math-weeks TA. Zhu is a Ph.D. student in the Math Department and Brenna is an undergraduate Math major.
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 14:
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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. I'll hand out copies of these notes: June14.pdf, June14.doc. |
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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 PC-Lab 1735. If you want to explore the rest of campus from your computer, use the interactive campus map. |
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10:30-noon PC-Lab 1735 |
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 for the group assignment function - Nick's problem is here: groups.mws. groups.pdf. Don't forget to read the first chapter, pages 1-44, of "The Code Book" for tomorrow! |
Tuesday June 15:
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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 10 will help us. Everything we need to know is 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 the "genetic code" most of you learned as a "fact" in biology. Here's the background for the problem, Cracking_the_Code.pdf, and your precise group assignment, bio.pdf. Utah evolutionary biology Professor Jon Seger, who will be presenting on Thursday, created the Cracking_the_Code document. We're hoping each group is ready to contribute to a discussion of solutions on Thursday, before Jon's presentation! |
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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 16:
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8:30-11:10 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; 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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11:20-11:50 a.m. JTB 120 |
Math course advising with Angie Gardiner, Math Department director of undergraduate services, and ACCESS 1992 cohort member. |
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12:00-1:00 p.m. Bandstand |
ACCESS welcome lunch at the Fort Douglas Officer's Circle Bandstand. this is also close to the Crocker Science House. |
Thursday June 17:
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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 18:
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8:30-11:50 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 from last year (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.
Here is the RSA public key information: publickeys.mws, publickeys.doc |
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12:00-12:45 p.m. The Den, Union |
Women's Resources Center orientation. Lunch will be provided. |