WEEK 1, P.M. SCHEDULE
JUNE 13-17 2011
Utah Math Professor
Fernando Guevara Vasquez.
My office is
my phone number is
801-581-7467, and my email address is
"fguevara at math.utah.edu". These notes are posted at our
ACCESS Math home page,
The math portion of ACCESS is the first week, June 14-18, and the second week,
Erin Gavin (ejgavin"at"gmail.com)
is our ACCESS TA for the entire Summer session, and
is our special math-weeks TA. Cheryl is a Ph.D. student
in the Math Department.
Our theme for the first week will be codes and cryptography. Our
planned schedule is below, although
it could change as the week
progresses. The material here is based on previous ACCESS classes by Nick Korevaar, who is also teaching the morning cohort this week.
Monday June 13:
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:
We will walk to
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.
Introduction to the lab: your accounts,
email, internet, software; emailing Rosemary your
challenge problem solutions in a Microsoft Excel document, and emailing
Fernando your formula for the group assignment function. Fernando's problem is here:
to read the first chapter, pages 1-44, of "The Code Book" for tomorrow!
Tuesday June 14:
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 13 will help us. Everything we need to know is in
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,
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! Cheryl's presentation is here: dna.pdf.
An overview of public key cryptography.
Public key cryptography is a late 20th-century
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:
Wednesday June 15:
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!
are the notes: modulararithmetic.pdf.
learn about the amazing (and confusing at first)
Euclidean algorithm for finding gcd's and multiplicative
inverses in modular arithmetic.
Here are the notes:
Thursday June 16:
Continuing discussion of the number theory behind RSA cryptography.
We'll begin with a few volunteers showing some of
yesterday's homework problems on 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
Tom Davis notes on cryptography, which are a nice distillation of
historical cryptography ideas, culminating in RSA public key
Other good references are the latter chapters of "The Codebook", Wikipedia,
and the original breakthrough
Rivest, Shamir, Adleman.
Problem session on the genetic code problem: Each group should be
prepared to contribute!
"Genetic Codes," presentation by Biology Professor
Friday June 17:
1:00 - 4:30 p.m.
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,
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:
It may be easier for you to use these procedures: Davisconversion.mw to automate the encoding/decoding of a message into decimals.