Fall
2013 
Mtg
# 
Agenda For Class Meeting
(What is Planned / What Happened) 
Homework Assignment/Tasks
(To be completed before the next class
meeting) 

AUG
19 



[1] 
Activity
Getting a
Little Discrete
examples of Discrete Math topics, background information

Assignment
Getting
There ASAP


[2] 
Activity
Game of
Sprouts
how to play, rules
Notes Graph Theory Basics:
Vocabulary &
Counting
vertex, edge, degree, strategies for counting 
Question
How Many Moves?
Is it possible to predict the maximum number of moves that can be
played in a Sprouts game based on how many vertices at the start of the
game?

 introduce game by having a student come up and play



AUG
26 
[3] 
Activity
Analyzing The Game of Sprouts
quantifiable differences,
collecting data, looking for patterns, describing patterns

Research
Leonard Euler
write 3 sentences about Euler's life and why he is considered one of
the greatest mathematicians

 preview the week
 ask if anyone got the answer to the question "How many Moves?"
 frame the activity as to get a glimpse of how mathematicians work in
analysis...emphasis on quantifiable differences...and sometimes we have
to look for more than just the obvious
 interesting number of available vertices as a quantifiable
difference...does this lead anywhere?
 find patterns in the columns  pretty easy
 find relationships among the columns...some are easy, some not so
easy  Algebra to the rescue
 introduce the adjective "complete"  what do you think it means?
show some examples
 look at the pattern for complete graphs in respect to the
relationship between number of vertices & number of edges  is there a
simple way to move ahead in the pattern without knowing the previous??
** might be a nice connection point to Pascal's Triangle

[4] 
Activity
The Euler
Characteristic
quantifiable
differences, pieces, regions, looking for patterns
Notes
Describing Structures in Graphs
adjacent, planar, complete

Crossword
Talking Graph Theory
facts about Euler, graph theory vocabulary

 begin working at the structure of graphs  ask students
to draw graphs that are planar
 Review/Discuss Euler's life and achievements with the
assistance of these videos
An Evening with Leonard Euler:
http://www.youtube.com/watch?v=hDV26x6n_Q
The Euler Identity (New Ageish):
http://www.youtube.com/watch?v=zApx1UlkpNs
Euler Biography (CloudBiography):
http://www.youtube.com/watch?v=Ty6ejK1rAkg
 have students draw a graph that is planar with between 8
and 15 vertices and at least 20 edges but no more than 40
edges
 practice counting  have students count vertices &
edges
 introduce the idea of regions or trapped space 
quantify these
 Euler "saw" a relationship here....what was it?
 motivate the Euler Characteristic by having

[5] 
Notes The
"Essence" of a Graph
equivalent representations,
isomorphisms,
planar
Activity
Water Puzzle
draw a graph that represents the game

Research
The FourColor Problem
6 sentences (who, what, where, when, why,
how)

 start with a picture of K4 drawn
with and without edges crossing then a picture of K4 with
edges crossing  now ask "Are the graphs different?" and
remind students to look for/identify quantitative
differences between the graphs
 sane number of edges, same number of vertices, same
adjacency relationships...hmmm, so the only difference is
the position of the vertices and how the edges were drawn 
so essentially the structure of the graphs are identical 
the DNA or the fingerprint
 introduce the term Isomorphic and relate to the term
Equivalent  give examples of each
 move to the Isomorphic applet at
http://webspace.ship.edu/deensley/discretemath/flash/ch7/sec7_3/isomorphism.html
 while working through the applet, focus students on
looking at structures  i.e the number of vertices, the
degree of the vertices, adjacencies, and triangles  these
features will help in determining if two graphs are
isomorphic
 return to the K4 example and discuss the concept of
planar in light of isomorphic graphs  make sure to define
planar as a graph that cannot be drawn without edges
crossing
 determining whether a graph in nonplanar is difficult,
but there are two classic examples of nonplanar graphs,
namely K5 or greater or K3,3
 make the connection with the idea of looking for these
structures within graphs as a way to decide if the graph is
planar or not by using the applet at
http://webspace.ship.edu/deensley/discretemath/flash/ch7/sec7_3/planargraphs.html
 time permitting, discuss how these graphs get used? what
is the practical reason for studying graphs? by introducing
the Water Puzzle and how a graph can "map" the game
 *** might be a good way to transition to game theory

[6] 
Audio Clip
Solving or Proving? The 4Color Problem
Activity
Coloring Maps
Four Color
Problem, algorithms

Activity
Coloring Maps
Four Color
Problem, algorithms

 ask for the who, what, where,
when, how, why for their 4color problem homework and write
on the board  verify & correct where necessary
 introduce the audio clip and
Keith Devlin
 as the clip plays, check
off/correct the w, w, w, w, h, & w written on the
board
 dntart with a picture of K4 drawn
with and without edges crossing then a picture of K4 with
edges crossing  now ask "Are the graphs different?" and
remind students to look for/identify quantitative
differences between the graphs
 sane number of edges, same number of vertices, same
adjacency relationships...hmmm, so the only difference is
the position of the vertices and how the edges were drawn 
so essentially the structure of the graphs are identical 
i.e. the DNA, the fingerprint


SEP
02 

LABOR DAY HOLIDAY 
[7] 
Activity
Tracing a Graph
Seven Bridges of Königsberg & Eulerian paths,
necessary & sufficient conditions

Research
The Traveling Salesman Problem
6 sentences (who, what, where, when, why,
how)

 spend a few minutes reviewing: count
the number of vertices, count the number of edges (count
degrees), adjacent vertices, nonadjacent vertices, planar
 sane number of edges, same number of vertices, same
adjacency relationships...hmmm, so the only difference is
the position of the vertices and how the edges were drawn 
so essentially the structure of the graphs are identical 
i.e. the DNA, the fingerprint

[8] 
Notes/Video
Movement in Graphs:
Paths & Circuits
path, circuit, necessary &
sufficient conditions


[9] 
Notes
Traveling Salesman Problem & Algorithms
Nearest Neighbor, Cheapest Link,
strategies, establishing simple repeatable
steps/clear process

Activity
TSP in Florida
find Hamiltonian circuits using the Nearest Neighbor algorithm
first then the Cheapest Link algorithm



SEP
09 
[10] 
Review
TSP in Florida
Discuss
TSP Applications
routing, construction

Read
Splitting Terrorist Cells

 start with a "quiz" on Canvas that refers to the
homework assignment from the weekend
 project the distance matrix and demonstrate how to apply
the Cheapest Link algorithm


[11] 
Discuss
Connectivity in Graphs
how to measure, bridges, cut vertices, pieces,
applications

Crossword
Graph Theory Vocabulary Review

 review vocab
 reintroduce new vocab & practice
 use campus connection as example for discussion  how
to connect
 find Hamiltonian or Euler path?  find the hamiltonian
 How well connected? no bridges and no cut verticies 
yay
 how many edges to remove before causing problems? 2 
how bad a problem?
 after removing 1 edge, go from zero bridges to YIKES!
 How long will the entire construction job take? the sum
of all the times is 31, but does the structure of the graph
indicate shorter?

[12] 
Review
Graph Theory Fundamentals
Cheapest Link & Nearest Neighbor algorithms, planar, paths, circuits, complete,
adjacent, isomorphic

Sample Test Questions
Graph Theory Fundamentals
[Solutions]

 distribute copies of last year's test and provide about
10 minutes for students to work on answering the questions
without any assistance

 students allowed to use all materials (notes, hw,
classwork, iPads, computers)
 remind students about the hw assignemtn

[13] 
Test
Graph Theory Fundamentals
Collect Homework & Classwork

Assignment
Sudokus
 A Glimmer of Algorithms

 allow the entire period for the test
 students allowed to use all materials (notes, hw,
classwork, iPads, computers)
 remind students about the hw assignemtn


SEP
16 
[14] 
Discussion
Navigating Sudoku Using Algorithms
practice the sudoku algorithm discussed in class
Video/Activity
Getting There Efficiently
Dijkstra's Algorithm

Assignment
Finding the Shortest Path in Graphs [Numb3rs]
complete
questions #14

 start by making sure that everyone understands the goal
of a sudoku and the parameters that must be satisfied 
also note that sudokus are not mathematical...the numbers
could be replaced with letters or pictures...so it's more of
a logic puzzle
 solicit one or two students to explain how they start a
sudoku  have them tell what to do first using a sudoku
projected on the board
 invite students to follow the 8 step algorithm to work
through the sudoku  which quadrant to start with?
 spend time to work through at least 2 quadrants 
emphasize that repeating the same procedure over and over 
eventually it should lead to a solution or pretty darn close
to a solution
 show the start of NUMB3RS episode "Money for Nothing"
until Charlie has talked about Dijkstra's Algorithm and the
possible paths out of LA show up on the computer screen
 project the hw assignment and work through #1 together

[15] 
Notes
Examining Dijkstra's Byproduct
subgraphs,
trees, spanning trees
Activity
Modeling: Getting Things Done
flow, directed
edges & digraphs, modeling

Assignment
Turner Construction
find the least
amount of time it will take to complete the construction project

 review homework  complete #3 on the board
 "what are the chances that you'll have to find a
hijacked semi in your professional life?"...so let's talk
about a related idea that might be more "realistic" 
construction industry anyone? remember the construction of
SLC and the aux gym?
 Like many things in life, there is usually a sequence to
how things happen  sometimes some things can happen in
parallel, other times it must be sequential  sometimes a
combo of both
 Turner Construction  draw a graph that represents the
construction process
 introduce directed edges and digraphs
 how to quantify the weeks  start with week 0 or week
1?  how to represent in the graph
 How long will the entire construction job take? the sum
of all the times is 31, but does the structure of the graph
indicate shorter?

[16] 
Review
Turner Construction
critical paths, flow analysis
Notes
Navigating Flow in Graphs
source, sink, quantifying capacity, max flow

Assignment
Finding the Flow
map the max
flow for a digraph

 continue/finish discussion of Turner Constructions  emphasize critical paths, the analysis the graph allows
for evaluating slowdowns, etc.
 introduce flows in networks by using the conveyor belt
analogy with this video:
 discuss what other real life phenomenon are examples of
flow  include electricity and discuss why it cannot be
stored
 show the start of NUMB3RS episode "Blackout"  need to
edit the beginning but focus on Charlie's examination of the
network to identify the next substation to target if the
goal is a cascading failure of the network
 use the NUMB3RS handout to work through an example of
determining maximum flow  be sure to define source & sink
 introduce hw assignment

[17] 
Notes
Navigating Flow in Graphs [Numb3rs]
quantifiable differences, starting backwards, exclusionary approach

Assignment
How Much Can You Flow?
develop an
algorithm to determine the maximum flow in a digraph

 work through the hw modeling an algorithmic approach to
determining the max flow  emphasize finding quantitative
differences between the verices and use those to determine
flow through individual vertices  working backwards from
the sink
 introduce/explain hw assignment / start in class


SEP
23 

FACULTY INSERVICE
DAY 
[18] 
Video
Applications of Graphs & Algorithms
work flow &
queues

Assignment
Connecting the Campus

 preview the week
 review hw from the weekend  remind of sink, source,
establishing bounds, quantifying vertices with flow in &
flow out, reverse analysis
 watch For All Practical Purposes Episode #3 starting
with the Bell Laboratories piece on connectivity  stop
video along the way to make connections
 show/discuss NUMB3RS handout Critical Maths from "End of
Watch"  highlight space race need to identify critical
paths, cooking a meal example, & share experience of Pizza
Hut 5 minute guarantee with an 8 minute oven
 explain hw assignment / start in class

[19] 
Activity
Increasing Electricity Flow

Sample Test Questions
More Graph Theory & Algorithms
[Solutions]

 indicate that one of the two activities will be selected
as a 5point possible for the hw
 introduce/explain Increasing Electricity Flow
activity  students will have 25 minutes in class to work
together to provide a solution
 regroup as a class and discuss
 distribute old quiz and answer the multiplechoice &
true/false questions
 remind students to prepare for tomorrow's test

[20] 
Test
More Graph Theory & Algorithms
Collect Homework & Classwork

Assignment
Prove that the number xxx is a prime number.

 allow the entire period for the test
 students allowed to use all materials (notes, hw,
classwork, ipads, computers)
 remind students about the hw assignemtn


SEP
30 
[21] 
Notes
Getting Into Algorithms
multiplication & division, efficiency, prerequisites, Rubik
Cubes, divisibility

Research
The Sieve of Eratosthenes

 preview the week
 start with soliciting ways to multiply 142 and 58  be
sure to highlight at least 4 options (traditional, repeated
addition, partitioning into smaller/easier multiplications
and addition, lattice multiplication, and peasant's
multiplication)
 engage in discussion with questions about prerequisite
knowledge (times tables), how these algorithms are similar
(lattice & traditional), etc.
 give special attention to Peasant's because of the
simplicity and relative quickness of it's method  tie into
Rubiks Cube
 transition into algorithms for determining if a number
is prime by introducing divisibility rules
 tease out the divisibility algorithm for multiples of 3
 connect to the partitioning algorithm for multiplication

[22] 
Notes
Setting the Stage for Number Theory
partitioning & factoring, uniqueness of prime factorization, sifting
for primes

Research
Goldbach's Conjecture
Who? What?
Where? When? Why? How?

 have "infinity" playing as students settle into to class
 start by formally defining prime and divisible 
provide examples & stress that we are only talking about
positive integers
 transition to discussing the Sieve of Eratosthenes  an
algorithmic way to find prime numbers
 will we eventually run out of prime numbers? gut feeling
no because there are infinite positive natural numbers, but
how do we know for sure the primes don't fizzle out?
 introduce the video Lecture 7: Numbers of Prime
Importance (from Zero to Infinity: A History of Numbers)
 stop video to emphasize why 1 is not considered a prime
number
 stop video to provide concrete numerical example of
showing the existence of prime numbers beyond a finite list
 end class by discussing the idea of finding patterns in
primes  look at the Sieve table to see that primes must
end in a 1, 3, 7, or 9, what about spacing  then define
Twin Primes

https://www.youtube.com/watch?v=iFuR97YcSLM

[23] 
Video Getting
Primed for Number Theory
distribution of primes, π(n)
function, establishing bounds, natural log, comparing quantities

Research
Mersenne Primes
Who? What?
Where? When? Why? How?

 start by discussing Goldbach's Conjecture  who, what,
where, when, why, and how  be sure to include discussion
of $1,000,000 prize
 work through several examples  30=13+7+5+3+2
 emphasize the idea of partitioning  breaking a
quantity into smaller quantities  a way to find out about
the "nature" of the number, similar to in chemistry and
distillation
 introduce and show the video Lecture 9: The Prime Number
Theorem and Riemann
 stop to highlight/explain the function
π(n)  emphasize
that it's a function like functions in algebra but the
difference is there is no quick and easy plug and chug way
of getting the values
 mathematicians have been trying to figure out a formula
for this function with the hopes that it will give us
insight/the ability to predict where prime numbers are, i.e.
how they are distributed
 breakthrough was that n divided by the natural log of n
served as an upper bound for
π(n)  but how close does this upper bound get
to the actual value of
π(n)
 end class with discussion of taking into account size of
numbers when discussing how close

[24] 
Video
Getting to "Know" Numbers
divisibility, visualizing patterns, proof,

Research
Perfect Numbers & Pentagonal Numbers

 finish discussion about comparing numbers via ratios
 ask about Mersenne numbers  write the pattern on the
board and see how well it works
 go to the GIMPS website online and highlight how the
program works and how big these numbers are/how many digits
 introduce video The Primes from Mathematics Illustrated
 stop after the introduction of figurative numbers
 end class by discussing figurative numbers


OCT
07 
[25] 
Notes Figurative Numbers:
Patterns Galore
triangular, square, pentagonal, Gauss & partitions, Collatz
conjecture

Research
Fibonacci
6 sentences (who, what, where, when, why,
how)

 start class by reviewing the prior week and giving some
examples of questions types that could be asked on the test
 review vocabulary  prime, composite, odd, even
 reintroduce figurative numbers  numbers that are
generated by arranging objects into regular polygons
 triangular numbers: 3, 6, 10, 15, 21,...  draw shape
on board and then increase the number of edges on each side
 look for pattern to how many new vertices get added at
each juncture
 square numbers: 4, 9, 16, 25, 36,...  draw shape on
board and then increase the number of edges on each side 
look for pattern to how many new vertices get added at each
juncture
 pentagonal numbers: 5, 12, 22, 35, 51,...  draw shape
on board and then increase the number of edges on each side
 look for pattern to how many new vertices get added at
each juncture
 show how the patterns can be reversed back to include 1
and 0 for each type of number
 now look for patterns that exist among the sets of
numbers  i.e. square numbers and triangular numbers,
pentagonal numbers and triangular numbers, etc.
 Gauss  Prince of Mathematics  theorem that every
positive integer can be written as the sum of at most
3 triangular numbers  some sense that triangular numbers
are in a way like prime numbers except for the uniqueness

[26] 
Notes Sequences:
Gauss & Fibonacci
recursive definitions, partial sums
Activity
Generating Sequences in Excel

Crossword
Number Theory Review

 historical notes on Gauss  the famous adding up
integers punishment story
 introduce Fibonacci numbers  highlight the idea of a
recursive pattern/definition
 look at partial sums of Fibonacci numbers  any
patterns?
 transition to laptop cart etiquette  how to remove and
not remove / how to replace and not replace
 login using BCP credentials  if you want to save work,
several options: on your BCP network drive, personal USB
drive, email to yourself
 Microsoft Excel  explain that a spreadsheet is a bunch
of individual calculators that can talk to each other, etc.
 establish columns with headings Triangular, Square,
Pentagonal, Fibonacci  introduce Excel commands/language
while generating these number sequences

[27] 
Notes Number
Symbols & Zero
counting methods, number systems, alternative bases
Activity
Generating Sequences in Excel

Sample Test Questions
Number Theory Basics & Algorithms [Solutions]

 start with slide showing triangular numbers and
Fibonacci numbers using Roman Numerals  discuss the nature
of Roman Numerals / positional? how many symbols necessary?
grouping? compare with Arabic numerals
 discuss counting  onetoone correspondence / the idea
of keeping track by grouping (use a shepard and sheet
analogy with small pebbles) /
 using a deck of cards, count the cards emphasizing
grouping first in the traditional 10s / then recount the
cards using base 6 grouping
 go to the GIMPS website online and highlight how the
program works and how big these numbers are/how many digits
 emphasize the idea of partitioning  breaking a
quantity into smaller quantities  a way to find out about
the "nature" of the number
 return to
 label a column Collatz  introduce the =if( function to
check
 end class by distributing number grid  complete by
identifying triangular, Fibonacci, etc.

[28] 
Test Number Theory Basics & Spreadsheets
Collect Homework & Classwork

Assignment
Avoiding Friday the 13th

 allow the entire period for the test
 students allowed to use all materials (notes, hw,
classwork, ipads, computers)
 remind students about the hw assignment


OCT
14 
[29] 
Activity
Using Modular Arithmetic:
Friday the 13th
modeling
repeating cycles, finding congruences

Assignment
Predicting the Future

 direct students to the pdf for this activity
 depending on time and level of student, use the chart to
develop the idea of repeating cycles


FROSH SERVICE DAY / PSAT / SENIOR WORKSHOPS 

OCTOBER BREAK  Classes Do Not Meet 


OCT
21 
[30] 
Notes
Into the Mod: Check Digit Applications
algorithms, congruence, ISBN10 & ISBN13 numbers

Research
UPC Number Check Digits

 solicit ISBN numbers and ask to
read all but the last digit / do the magic on the board
 solicit UPC numbers and ask to read all
but the last digit  UPC have 5 and 5 inside the barcode
and 1 on each end / do the magic on the board

[31] 
Notes/Activity
Sneaky Scrambling Algorithms
counting methods, scrambling via modular
arithmetic & geometry

Read
Cryptography: Secret Writing pp 1128

 end with rectangular transposition challenge  offer to
answer questions about the method / depending on
amount of time available, offer extra credit points for the
first correct solution

[32] 
Notes Only Two
Options: Transposition & Substitution
scrambling vs. replacing, algorithms, reversibility

Read
Cryptography: Secret Writing pp 2956

 start with second rectangular transposition challenge 
very similar enciphering method as the previous example
 explain expectations for the reading homework  you are
responsible and there will be questions on the test that are
drawn from the reading, but it's your responsibility to read
 highlight the idea of "stock phrases" on p14  give
example of at BCP the phrase "Go Bells" is often used at the
conclusion of talks/etc. so a message between BCP students
might end with "Go Bells"  this gives enemies something to
look for/a way into the system / connect this to the Enigma
Machine and the allies using "Hail Hitler" as the in for
breaking German messages
 highlight the only two actions that can be performed,
namely scrambling or replacing / pp1718
 show the NSA recruitment advertisement and highlight
that they are not looking for experts in Calculus :)
 return to the scramble MHRNRRKBEOUTYSEOC and reveal that
the message is NUMBERTHEORYROCKS  the scramble is not
random, but generated by using both addition and
multiplication in mod 17
 begin a process of trying to figure out what was added
and multiplied to generate the scramble  why focus on
unique letters vs. nonunique?

[33] 
Notes/Activity
Going Backwards: Unscrambling
modular arithmetic & inverse operations

Assignment
Solving Equations in Modular Arithmetic

 assign every student two numbers
 they will be responsible for the letters in those
positions in the plaintext message
 display a message on the board
with corresponding position values  ask students as a
group to encipher the message by scrambling the positions
using an affine scramble / once students have determined
where their letters will be moved, have them come up to the
board and write their letter...no students should be
fighting for the same box!
 model one or two letters for them
 verify the scramble using the Excel
spreadsheet
 repeat the process but this time
give the students a message in its enciphered form & provide
the enciphering keys (additive and multiplicative)  ask
students to decipher the message
 emphasize that going backwards is more difficult that
going forwards


OCT
28 

OPEN HOUSE
HOLIDAY 
[34] 
Activity
Modular Arithmetic
Messages
congruence, avoiding negatives, finding remainders

Crossword
History
of Secret Writing

 begin by working through the homework assignment 
assume that only a handful of students even attempted the
assignment
 use the assignment to instruct key points for
working in modular arithmetic: avoid negatives, avoid
division, values should not exceed remainder values, etc.
 use remaining class time for students to work on
deciphering the message while practicing solving modular
equations  offer extra points to the first person or team
to correctly decipher the message

[35] 
Activity
Going Backwards: Inverses
multiplicative inverses

Sample Test Questions
Modular Arithmetic & Introduction to Secret Writing [Selected Solutions] 
 begin by discussing the previous day's challenge 
assign each group an equation to solve and then
brainsorm how to use those answers to reveal the message
 focus on equation #9 and highlight the fact that it took
a long time (many additions of the mod) before arriving at a
value that was a multiple of the coefficient of x  but IS
there an easier and/or more efficient way of finding the
solution?
 working through the homework assignment 
assume that only a handful of students even attempted the
assignment
 use the assignment to instruct key points for
working in modular arithmetic: avoid negatives, avoid
division, values should not exceed remainder values, etc.
 use remaining class time for students to work on
deciphering the message while practicing solving modular
equations  offer extra points to the first person or team
to correctly decipher the message

[36] 
Test
Modular Arithmetic & Introduction to Secret Writing
Collect Homework & Classwork

Read
Cryptography: Secret Writing pp 5790

 allow the entire period for the test
 students allowed to use all materials (notes, hw,
classwork, ipads, computers)
 remind students about the hw assignment


NOV
04 
[37] 
Notes
Mathematics of Substitution: Forwards
methods for scrambling the alphabet, onetoone correspondence,
cipher charts vs. code systems

Read
Cryptological Mathematics pp 2734

 start class by asking students to decipher the message
"Did you do your reading this weekend" that was enciphered
using a monoalphabetic substitution where the keyword
'MEAT' was used to scramble the alphabet
 after about 5 minutes of time present Ceasar ciphers
(alphabet shifting) & give an example on the board / discuss
how this is not very securecomplicated
 compare/contrast Ceasar vs. Keyword vs. Modular methods
for scrambling the alphabet  then present the idea of a
polyalphabetical substitution to reduce the "Wheel of
Fortune" effect
 end class with Cement Truck joke/punchline  give time
to find patterns

[38] 
Activity
Automating Substitution Ciphers
text & chart referencing functions, number to text conversions,
uppercase vs. lowercase

Assignment
Monoalphabetic Ciphers

 anually create a substitution chart by typing one
letter per cell
 encipher 'bellarmine' manually making the distinction
between upper & lower case as presented in the text
reading
 introduce the idea of having the spreadsheet
"automatically" do the substitution  present the vlookup
and hlookup functions
class by asking students to decipher the message
"Did you do your reading this weekend" that was enciphered
using a monoalphabetic substitution where the keyword
'MEAT' was used to scramble the alphabet
 after about 5 minutes of time present Ceasar ciphers
(alphabet shifting) & give an example on the board / discuss
how this is not very securecomplicated
 compare/contrast Ceasar vs. Keyword vs. Modular methods
for scrambling the alphabet  then present the idea of a
polyalphabetical substitution to reduce the "Wheel of
Fortune" effect
 end class with Cement Truck joke/punchline  give time
to find patterns

[39] 
Activity
Automating Substitution Ciphers: Generating Alphabets
number to text conversions, replicating patterns using mod



[40] 
Activity
Automating Substitution Ciphers: Backwards
text & chart referencing functions

Video
CodeBreakers: Bletchley Park's Lost Heroes



NOV
11 
[41] 
Quiz
CodeBreakers: Bletchley Park's Lost Heroes
Activity
Affine Ciphers
additive vs. multiplicative, keys, modular inverses

Read Cryptological Mathematics
pp 7681


[42] 
Activity
Polyalphabetical Ciphers
keys, modular patterns, Enigma Machine

Assignment
Polyalphabetic Ciphers


[43] 
Notes
How Secure Is Your Cipher System?
brute force &
key options, strategies for breaking

Read
Cryptological Mathematics
pp 103108


[44] 
Notes
Increasing Complexity & Subtle Twists
Hill
Ciphers/matrix algebra, steganography

Research
RSA Encryption
6 sentences (who, what, where, when, why,
how)



NOV
18 
[45] 
Notes 
Understanding Public Key Encryption: RSA
modular arithmetic, primes, finding inverses, public and private
keys 
Sample Test Questions
Cipher Systems
& Spreadsheets [Selected
Solutions]

 preview the week  remind students about being prepared
for the test
 begin by discussing the problem of key exchanges  how
do you make sure that both parties have access to the same
keys?
 move into the ides of a public key  a way for people
to send you a secure message where how to encipher is public
but the how to decipher is private
 use an example of Joe wants to send the letter J to you
 you instruct hum to use mod 527 and key 7  takes the
letter J, converts to number, then uses multiplication in
the form of exponents where the number 10 will be
multiplied 10 times in a row  this generates a large
number which is then reigned in by converting to its mod 527
equivalence, so that Joe send you the number 175 which
represents his original letter J / invite students to join
in the process
 how do you go backwards? solicit from students their
enciphered letter values  let them know the plan is to
raise the number they sent to the 343 power!  yikes a
ridiculously huge number...how can you compute that? luckily
you just want to know what the remainder is after dividing
by 527
 using an Excel spreadsheet, show how the modulu
congruence can be used to compute the remainder without
having to get that big number  stress the algorithmic
approach of this
 verify that the reverse process is working correctly by
checking the values from the solicited student
numbers/original letters
 transitiion to the Youtube video

 end class with Cement Truck joke/punchline  give time
to find patterns

[46] 
Test
Cipher Systems & Spreadsheets
Collect Classwork & Homework

Assignment
Design Your Own Cipher System (example)

must have
substitution and transposition

not more
than 6 steps in complexity

originality/creativity (5pts max)

communication/presentation (5pts max)


[47] 
Cipher System Project 
Introduction & Information
scope, expectations, guidelines, specifications 
Cipher System Project 
[48] 
Cipher System Project 
Organizational Workday
organize homepage, synthesize ideas for substitution &
transposition, establish timeline/key dates, assign responsibilities 
Cipher System Project 



DEC
09 
[54] 
Notes Overview of Game Theory
quantifying strategies, zerosum, minimax theorem, Nash Equilibrium 

[55] 
Activity TwoPlayer Games: Strategies
collecting data, looking for patterns 
Activity
Sprouts Strategy
Is there a winning strategy for the game of Sprouts?

[56] 
Activity TwoPlayer Games: Winning Strategies
rules that drive strategies, combinatorial analysis, Grundy's Game 

[57] 
Activity The Prisoners' Dilemma
rules that drive strategies, combinatorial analysis 
Sample
Final Exam 

DEC
16 
[58] 
Semester
Reflection 
Study/Prepare
for
Final Exam 

SEMESTER EXAMS  SOCIAL SCIENCE &
MATHEMATICS 

SEMESTER EXAMS  ENGLISH & RELIGIOUS STUDIES 

SEMESTER EXAMS  LANGUAGE & SCIENCE 
