# MAT 112 Integers and Modern Applications for the Uninitiated

## IndexIndex

$$=\quad$$ is equal to
function
integers
ordered pair
sets
$$\#\quad$$ cardinality
$$\A\quad$$ set of characters, Item
$$\cspace\quad$$ space, Item
$$\fdiv\quad$$ quotient
$$\fmod\quad$$ remainder
$$\gcd\quad$$ greatest common divisor
$$\ge\quad$$ is greater than or equal to
$$\gexp{b}{-1}{\bullet}\quad$$ inverse
in group
with respect to $$\bullet$$
$$\gexp{b}{0}{}=1$$
$$\gexp{b}{n}{\otimes}\quad$$ exponentiation in $$(\Z_p^\otimes,\otimes)$$
$$\gexp{b}{n}{\star}\quad$$ exponentiation in group
$$\gexp{b}{n}{}\quad$$ exponentiation of integers
$$\glog{b}{a}{\otimes}\quad$$ discrete logarithm in $$(\Z_p^\otimes,\otimes)$$
$$\glog{b}{a}{\star}\quad$$ discrete logarithm in group
$$\gt\quad$$ is greater than
$$\in\quad$$ is element of
$$\le\quad$$ is less than or equal to
$$\lt\quad$$ is less than
$$\mid x\mid\quad$$absolute value
$$\N\quad$$ set of natural numbers, Item
$$\ne\quad$$ is not equal to
function
integers
ordered pair
sets
$$\not\in\quad$$ is not element of
$$\not\subseteq\quad$$ is not subset of
$$\oplus\quad$$ modular addition, Item
$$\otimes\quad$$ modular multiplication, Item
$$\PP\quad$$ set of prime numbers, Item
$$\subseteq\quad$$ is subset of
$$\W\quad$$ set of whole numbers, Item
$$\Z\quad$$ set of integers, Item
$$\Z_n=\{0,\dots,n-1\}$$, Item
$$\Z_n^\otimes=\{1,\dots,n-1\}$$, Item
$$\{\,\}\quad$$ empty set
$$\{\cdot,\cdot,\cdot,\cdot,\ldots\}\quad$$ roster form with ellipsis
$$\{\cdot,\cdot,\cdot,\cdot\}\quad$$ roster form
$$\{\cdot\mid \cdots\}\quad$$ set builder
$$C\quad$$ encoding function
$$C^{-1}\quad$$ decoding function
$$f^{-1}\quad$$ inverse function
$$n!\quad$$factorial
abelian
absolute value
algorithm
acknowledgments
associative property, Item
inverse
algorithm
absolute value
base $$10$$ to base $$2$$
base $$10$$ to base $$b$$
discrete logarithm
division
negative integers
positive integers
Eierkuchen
Euclidean
even or odd
exponentiation
fast in groups
naive for integers
naive in groups
factorial
forty-two
four powers
with let_:=
gcd
maximum
repeated squaring
sum of two integers
sum up to
Alice
Ant Attack
arithmetic
clock
ASCII
associative
binary operation
multiplication, Item
base
in group
base 10
expansion
base 2
counting
expansion
base b
expansion
representation
binary
binary operation
associative
commutative
identity element
inverse element
video
black and white
blackboard bold
Bob
Bézout’s Identity
easy case
Bézout’s identity
modular inverse
Caesar ciphers
calculator long division
cardinality
Cartesian product
empty set
same
cardinality of a set
Cartesian product
cardinality
image
chapter
dependencies
character
$$\cspace$$ space, Item
encoding
set of, Item
check digit
checkpoint
are these commutative ?
are these groups ?
binary operation
definition of associativity
definition of commutativity
definition of identity
definition of inverse
discrete logarithm
find inverses
group axioms
is there an identity ?
is this a group ?
operation table
repeated squaring
clock arithmetic
code
codes
coding theory
codomain
colors
darker
grey
interactive
lighter
video
commutative
binary operation
group
multiplication, Item
complexity analysis
composite
function
integer
compound statement
conjecture
twin prime
conversion
base 10 to base 2
base 10 to base b
base 2 to base 10
base b to base 10
character to number
image to numbers
text to number
countably infinite set
counterexample
counting in base 2
cryptography
Caesar ciphers
Diffie Hellman key exchange
ElGamal encryption system
frequency analysis
public key
substitution ciphers
symmetric key
cubed
darker colors
decimal
expansion
representation
decoder disc
interactive
decoding function $$C^{-1}$$
definition
difference
Diffie Hellman key exchange
diagram
interactive
video
color mixing
example
how it works
digital signatures
discrete logarithm
algorithm
video
distributive
distributive property
div
divides
other formulations
divisibility
division
algorithm
negative integers
positive integers
calculator long
long
negative integers
divisor
domain
Eierkuchen
ElGamal encryption system
diagram
interactive
video
ellipses
empty set
cardinality
encoding
character
function $$C$$
text to number
equal
function
integers
ordered pair
sets
Eratosthenes, sieve of
Euclidean algorithm
video
Euclid’s theorem
evaluation
Eve
even
example
expansion
base 10
base 2
base b
decimal
exponent
in group
exponentiation
algorithm
fast in groups
naive for integers
naive in groups
fast in groups
in groups
integers
properties
expression
factor
factorial
algorithm
Factoring the Time
false
fast exponentiation
algorithm
fifty shades of grey
finite set
for all
there exists
frequency analysis
full
function
composite
video
equal
video
graph
video
identity
video
inverse
video
invertible
trapdoor
video
gcd
algorithm
video
given any
graph
function
greatest common divisor
video
grey
group
hex triplet
identity
binary operation
function
modular
multiplicative, Item
if ( if_then )
image
Cartesian product
of an element under a function, Item
to numbers
interactive
strategy
video
in
infinite
countably, set
set
infinitude of primes
input, Item
instruction
if ( if_then )
let ( let_:= )
repeat ( repeat_until )
return
integer
composite
even
exponentiation
negative
odd
operation
positive
prime
set of, Item
interactive
algorithm
(naive) exponentiation
base $$10$$ to base $$2$$
base $$10$$ to base $$b$$
division of negative integers
division of positive integers
eighth power
Euclidean
fast exponentiation
sum
Cartesian product
colors
decoder disc
Diffie Hellman key exchange
ElGamal encryption system
function
invertible
image to numbers
sieve of Eratosthenes
inverse
binary operation
function
in group
modular
multiplicative
uniqueness
with respect to binary operation
invertible function
ISBN
iteration
let
let ( let_:= )
lighter colors
log
logarithm
discrete
long division
mod
operation
modular
arithmetic
multiplication, Item
multiple
multiplication
associative property, Item
natural number
set of, Item
negative integers
non-negative
number
line
of elements in a set
of subsets
to text
odd
operation
binary
integers
mod
order of
order of operations
ordered pair
equal
output, Item
perfect square
pixel
placeholder
positive integer
power
of group element
of integer
preimage, Item
prime
factorization
infinitude
set of, Item
twin
conjecture
video
video
problem
product
Cartesian
proof
public key cryptography
diagram
quotient
remainder
repeat ( repeat_until )
repeated squaring
algorithm
representation
base 2
base b
binary
return ( return )
RGB
hex triplet
video
root
roster form
set
-builder notation
countably infinite
empty
equal
finite
infinite
of characters, Item
of integers, Item
of natural numbers, Item
of primes, Item
of whole numbers, Item
roster form
special
subset
well-defined
sieve of Eratosthenes
interactive
strategy
video
SLOs
space
special sets
square
perfect
root
squared
statement
compound
strategy
calculator long division
comparing shades of grey
image to numbers
modular inverse
numbers to text
sieve of Eratosthenes
text to number
student learning outcomes
subset
number of
substitution ciphers
sum
symmetric key cryptography
text to number
strategy
then ( if_then )
theorem
Euclid’s
there exists
trapdoor function
triplet
true
twin prime
conjecture
video
Unicode
uniqueness
identity
inverse
until ( repeat_until )
variable
video
algorithms
assignment let
associativity
base 10 to base 2
base 10 to base b
binary operations
caesar cipher
cardinality
cardinality of Cartesian products
clock arithmetic
colors
commutativity
compute mod
conditional if_then
decoder disc
Diffie Hellman
color mixing
example
how it works
discrete logarithm
division algorithm
ElGamal encryption system
encoding
Euclidean algorithm
exponentiation (of integers)
fast exponentiation
frequency analysis
function
composite
equal
graph
identity
inverse
gcd
greatest common divisor
groups
examples
multiplicative
identity
image to numbers
infinite sets
integers
definition and statements
inverses
ISBN
long division
loop repeat_until
membership and equality
naive exponentiation
number of subsets
operation mod
other substitution ciphers
prime
factorization
infinitude
twin
quotients and remainders
repeated squaring
algorithm
roster form
set builder
sets (definition)
sieve of Eratosthenes
special sets
subsets
symmetric key cryptography
variables
well-defined
whole number
set of, Item
witness
xkcd
1 to 10
Alice and Bob
Certainty
Code Talkers
Forgot Algebra
Loop
Mnemonics: order of operations
privacy opinions
Protocol
random number
Su Doku