WEEK 1 A.M. SCHEDULE
JUNE 13-17 2011
Welcome to the "U"! I'm
Utah Math Professor
My office is
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
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
Monday June 13:
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
Nick your formula, related to Rosemary's problem.
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 will help us. The documents we need are in
After solving the substitution cipher problem above via frequency analysis, we'd like you to exercise your thinking abilities in different
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),
Jon Seger's slides), which include more discussion and the experimental results you'll be using in your precise group assignment,
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.
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:
ACCESS welcome lunch at the Crimson View room in the Student Union.
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 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
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:
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 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: