Number Theory
NO DECIMALS ALLOWED!
Why Number Theory?
There are lots of scenarios where calculations and values need to
be presented in integer values
Time: (Hours, Minutes, Seconds, Milliseconds, et
Algorithms
HOW TO DO A THING
(AND CALCULATE IF IT IS WORTH DOING)
Algorithms are NOT code
Code is a particular implementation of the an
Algorithm and can vary between different
programming & developme
Logic II
TAKING THE OPERATIONS LARGE SCALE
Before we continue
Make sure you have reviewed all the material from
Logic I before continuing on to this lesson.
Have any notes on the symbols and operation
Number Theory Applications
BONUS MATERIAL
Number Represntation
DECIMAL AND BINARY REVIEW
Review: Expressing a Value in Decimal
Express the value of the Roman Numeral MDCCLXXVI in Decimal
M is one thou
Boolean Algebra Project
Levi Kilgore
1. What is a Boolean Variable?
Boolean algebraisasetofrulesandoperationsforworkingwithvariableswhosevalues
areeither0or1.Thevalue1correspondstoTintherulesofproposi
Number Theory Lecture
Discrete Math
A small explanation about truth tables.
Find the truth table of (p v q) ^ (p v r)
We have three variables (p, q and r are the variables; If a variable is repeated,
Combinatorics Lecture
Discrete Math
Combinatorics: This is counting, and counting big numbers.
Product Rule (Multiplication Principle): If you have to select one element of a set,
and a bunch of sets,
Discrete Math
Logic 1 Lecture
This session is being recorded, and it will be posted as an announcement later
tonight or tomorrow morning. At the same time, I type a lot of notes, and the notes
will be
Sequences, Summations and Matrices
Discrete Math
Sequences: List of numbers, organized by positions.
A1 = 2
A2 = 4
A3 = 7
A4 = 0
A5 = 3
A6 = 10
Note: Sequence An contains more numbers in the list, but
6.2.2
[(76 mod 7) (58 mod 7)] mod7
Step 1: To find mod 7 think about a clock. If the number is positive it goes clockwise, if it is
negative it goes counter clockwise.
So, we are going to start a numb
Simple Truth table for 2 propositions (p, q):
Conjunction and Disjunction of 2 propositions (p, q)
Conditional and Biconditional Statements for 2 propositions (p, q)
Examples for compound statements w
B: (P ^ Q ^ R) v (P ^ Q ^ R)
C: (P v Q v R) ^ (P v Q v R) ^ (P v q v R)
P Q R P Q R (P^Q^R) (P^Q^R) G v H (PvQvR) (PvQvR)
T
T
T
T
F
F
F
F
T
T
F
F
T
T
F
F
T
F
T
F
T
F
T
F
F
F
F
F
T
T
T
T
F
F
T
T
F
F
T
1.1|Fundamentals:Logic
Test in WEEK 1 : LOGIC
2
FEB
STATUS
1
Isthestatement,"Donotpassgo."alogicalproposition?
10Points
YesanditisTrue
YesanditisFalse
No,itisnotalogicalproposition.
2
Isthestatement,"
Set Theory
APPLYING LAWS OF LOGIC TO GROUPS
A GROUP IS A SPECIAL TYPE OF SETWE WONT GO OVER THOSE HERE
Why Set Theory?
Applying logic to entire
groups
Players on a Team
Players part of Offense
Injured
Number Theory
NO DECIMALS ALLOWED!
Why Number Theory?
There are lots of scenarios where calculations and values need to
be presented in integer values
Time: (Hours, Minutes, Seconds, Milliseconds, et
Combinatorics
YOU LEARNED TO COUNT AS A CHILD
NOW LEARN TO COUNT LIKE AN ADULT!
What we already know
Cardinality
Count how many elements belong to a set
Length of a Sequence
Is the sequence Finite
Logic I
THE FOUNDATION OF ALL MATHEMATICS
AND
THE KEY TO THE LANGUAGE OF MACHINES
Why we start with Logic
THE MOST CRITICAL SKILL TO FUTURE
TECHNOLOGY DRIVEN COURSES
LOGIC REQUIRES NO PRE-REQUISITE MA
Sequences, Summations, and
Matrices
INDEXED DATA STRUCTURES
Why These Topics?
While sets are a good way to view collections of data in the
abstract actual implementation on computing devices
requires
Functions
THEY DO A THING
Why Functions?
Functions serve an important role in both
mathematics and programming
Calculations that are plug and chug operations will
be presented as functions
You will