1/12/2012. Jim Williams HONP-112 Week 3
|
|
- Lesley Johnston
- 5 years ago
- Views:
Transcription
1 Jim Williams HONP-112 Week 3 Set Theory is a practical implementation of Boolean logic that examines the relationships between groups of objects. Set theory has numerous real-life applications in computer systems design, as well as database searching (we will learn more about databases later, but will touch on search concepts today) A set consists of individual elements. A set is denoted by curly brackets and elements are separated by commas: {A,E,I,O,U} A set that has no elements is called the empty set, AKA the null set. {} 1
2 The Universal Set (or Universe ) contains all possible values of whatever type of objects we are studying. Sets can be infinite (i.e. {all real numbers}), or finite (i.e. {all letters of the alphabet}). We will only be studying finite (AKA "discrete") sets. We will use U to denote the universal set. Do not confuse this with the UNION symbol (later). Lets assume we have 2 sets A and B. B is a subset of A if and only if all the elements in B are also in A. Every set is a subset of the Universal Set. Example: {1,2,6} is a subset of {1,2,3,4,5,6} UNIVERSE A B A Venn Diagram can be used to graphically illustrate the relationship between sets. 2
3 UNIVERSE A B A UNION B contains all the elements that are either in A or B. The shaded areas illustrate the union. UNIVERSE A B A INTERSECT B contains only the elements that are in A and also in B. The shaded area illustrates the intersection. UNIVERSE A B A COMPLIMENT contains only the elements that are not in a given set. The shaded areas illustrate the compliment of A. 3
4 Union: Example: A B Intersection: Example: A B Compliment: ' Example: A' Define Universal Set = All U.S. Coins U={penny, nickel, dime, quarter, half-dollar, dollar} Set A = {penny, nickel} Set B = {nickel, dime, dollar} U={penny, nickel, dime, quarter, half-dollar, dollar} Set A = {penny, nickel} Set B = {nickel, dime, dollar} A B = {penny, nickel, dime, dollar} IMPORTANT: Notice that the set elements never repeat within a single set of any kind (see there is only one nickel element in the result set!) Do not forget this! 4
5 U={penny, nickel, dime, quarter, half-dollar, dollar} Set A = {penny, nickel} Set B = {nickel, dime, dollar} A B = {nickel} U={penny, nickel, dime, quarter, half-dollar, dollar} Set A = {penny, nickel} Set B = {nickel, dime, dollar} A' = {dime, quarter, half-dollar, dollar} U={penny, nickel, dime, quarter, half-dollar, dollar} Set A = {all denominations over 10 cents.} Set B = {all coins not silver in color} What is A B? A B? Try some more examples. 5
6 The UNION set operator functions in a similar manner to the Boolean OR logical operator. The INTERSECTION set operator functions in a similar manner to the Boolean AND logical operator. The COMPLIMENT set operator functions in a similar manner to the Boolean NOT logical operator. Given Set A, Set B The UNION applies a boolean OR to each element of each set. A result of True (1) for any of these cases qualifies the element to be included in the result set. Let s Look at an example Set A = {penny, nickel} Set B = {nickel, dime, dollar} Penny Nickel Dime Quarter Half D. Set A Set B Result Set Dollar The OR is applied to each element in set A and the corresponding element in set B Results with 1 are included in the result set. A B = {penny, nickel, dime, dollar} 6
7 Given Set A, Set B The INTERSECT applies a boolean AND to each element of each set. A result of True (1) for any of these cases qualifies the element to be included in the result set. Let s Look at an example Set A = {penny, nickel} Set B = {nickel, dime, dollar} Penny Nickel Dime Quarter Half D. Set A Set B Result Set Dollar The AND is applied to each element in set A and the corresponding element in set B Results with 1 are included in the result set. A B = {nickel} Given Set A The COMPLIMENT applies a boolean NOT to each element of the set. But, remember, that we also have to consider the entire universal set. This is because a NOT is a unary operator. In this context, it only operates on the elements of a single set. But there are elements in the universal set that are still NOT in A. (This type of compliment is the absolute compliment - which is the only type we are concerned with here). Let s look at an example 7
8 Set A = {penny, nickel} Penny Nickel Dime Quarter Half D. Set A Result Set Dollar The NOT is applied to each element in the set we are taking the compliment of. Remember we are still doing this in relation to the universal set! Results with 1 are included in the result set. A' = {dime, quarter, half-dollar, dollar} Set A = {penny, nickel} Penny Nickel Dime Quarter Half D. Universe Set A Result Set Dollar The COMPLIMENT applies a NAND against each element of the universal set and the corresponding elements of the set we are taking the compliment of. The concept we have illustrated in our previous tables is also used in various other computer circuits, and is called BIT-MASKING. Given a sequence of bits, and a mask (also made up of some chosen sequence of bits), we can apply an AND mask, an OR mask, etc. We need not worry about what bit-masking is used for right now or why certain bit sequences may be chosen as a mask. But we should know HOW to apply a mask to a bit sequence. 8
9 Given a BIT sequence , and a MASK of : Seq Mask Result The resulting bit sequence results from applying an AND against each bit in the sequence, and the corresponding bit in the mask. Result is Given a BIT sequence , and a MASK of : Seq Mask Result The resulting bit sequence results from applying an OR against each bit in the sequence, and the corresponding bit in the mask. Result is Given a BIT sequence , and a MASK of : The AND mask results in The OR mask results in So, which type of MASK results in having more 1s in the resulting sequence? 9
10 We can better understand the relationship between Boolean Logic and Set Theory by using a database example. We will study databases in more depth later but just keep the concept in mind. Boolean searches are done against large databases in many situations (think of some). Databases usually use search operators that correspond with the standard Boolean operators of AND, OR, and NOT. BUT in the case of searches, they are applied to whether an item being searched for meets certain criteria. To understand this better, we need to think of search criteria in a different way. Keep in mind that each search criterion will really be creating a separate SUB that meets the criterion. When we search, we can apply boolean operators to connect criteria together in different ways. So what we are really doing is creating different subsets and applying set operators to them. 10
11 The OR search operator combines 2 or more subsets into a single larger subset. Example: Criterion 1: Customers from the zipcode. Criterion 2: Customers who have made a purchase within the past month. (Criterion 1) OR (Criterion 2) will create a single subset containing all customers from 07463, along with all the customers who have made a purchase within the past month, regardless of their zip code. The AND search operator selects the records that 2 or more subsets have in common into a single smaller subset. Example: Criterion 1: Customers from the zipcode. Criterion 2: Customers who have made a purchase within the past month. (Criterion 1) AND (Criterion 2) will create a single subset containing the customers from 07463, who also have made a purchase within the past month. The NOT search operator gives us all the records in a set that do not belong to a particular subset. Example: Criteria 1: Customers from the zip code. NOT (Criteria 1) will create a single subset containing the customers who are NOT from
12 In your college studies you will frequently need to look up books and articles in the library catalog, based on certain criteria (conditions). The following slides will illustrate some examples of this and hopefully clarify the relationship between boolean search operators and their corresponding behind the scenes set operations. Remember that in these examples the Universal Set is the entire library collection. Consider this: we want to find all books written by Stephen King within the past 5 years. What we are really doing: Set A: Books written by Stephen King. Set B: All books written within the past 5 years. If we want books that meet BOTH criteria, what we are looking for is the INTERSECTION between sets A and B. A library system may allow us to say something like: Author=Stephen King AND date >= But what if we wanted any book written by Stephen King, or any book (regardless of author) written within the past 5 years. What we are really doing: Set A: Books written by Stephen King. Set B: All books written within the past 5 years. If we want books that meet EITHER criteria, what we am looking for is the UNION of sets A and B. A library system may allow us to say something like: Author=Stephen King OR date >=
13 But what if we didn t care for Stephen King s writing? So, we wanted to find any book NOT written by him. What we are really doing: Set A: Books written by Stephen King. If we want books that are NOT in set A, what we are looking for is the COMPLIMENT of set A. A library system may allow us to say something like: Author IS NOT Stephen King In real life most library searches are more complex. Example: Mystery books written in the past 5 years, but not by Stephen King. Set A: All Mystery Books. Set B: All Books written during the past 5 years. Set C: All Books written by Stephen King. A library system might let us do something like this: Category=Mystery AND Date >= 2007 AND Author IS NOT Stephen King. In set theory terms, this means: (A B) C' Know the three set operators Know how these are related to the three basic boolean operators. Use these concepts to solve set theory problems. Use these concepts to apply a given mask to a given bit sequence. Understand how these concepts are applied to boolean searching of databases. 13
1.1 - Introduction to Sets
1.1 - Introduction to Sets Math 166-502 Blake Boudreaux Department of Mathematics Texas A&M University January 18, 2018 Blake Boudreaux (Texas A&M University) 1.1 - Introduction to Sets January 18, 2018
More informationReview of Sets. Review. Philippe B. Laval. Current Semester. Kennesaw State University. Philippe B. Laval (KSU) Sets Current Semester 1 / 16
Review of Sets Review Philippe B. Laval Kennesaw State University Current Semester Philippe B. Laval (KSU) Sets Current Semester 1 / 16 Outline 1 Introduction 2 Definitions, Notations and Examples 3 Special
More information4.5 Notes Domain and Range
Algebra 1 4.5 Notes Domain and Range Name: Date: Class #: A relation is. The entire set of numbers that are put into a relation or function is called the After putting the numbers in the domain into the
More informationCS Bootcamp Boolean Logic Autumn 2015 A B A B T T T T F F F T F F F F T T T T F T F T T F F F
1 Logical Operations 1.1 And The and operator is a binary operator, denoted as, &,, or sometimes by just concatenating symbols, is true only if both parameters are true. A B A B F T F F F F The expression
More informationSet and Set Operations
Set and Set Operations Introduction A set is a collection of objects. The objects in a set are called elements of the set. A well defined set is a set in which we know for sure if an element belongs to
More information2 Sets. 2.1 Notation. last edited January 26, 2016
2 Sets Sets show up in virtually every topic in mathematics, and so understanding their basics is a necessity for understanding advanced mathematics. As far as we re concerned, the word set means what
More information2.1 Symbols and Terminology
2.1 Symbols and Terminology A is a collection of objects or things. The objects belonging to the are called the, or. - : there is a way of determining for sure whether a particular item is an element of
More informationSets MAT231. Fall Transition to Higher Mathematics. MAT231 (Transition to Higher Math) Sets Fall / 31
Sets MAT231 Transition to Higher Mathematics Fall 2014 MAT231 (Transition to Higher Math) Sets Fall 2014 1 / 31 Outline 1 Sets Introduction Cartesian Products Subsets Power Sets Union, Intersection, Difference
More informationWhat is Set? Set Theory. Notation. Venn Diagram
What is Set? Set Theory Peter Lo Set is any well-defined list, collection, or class of objects. The objects in set can be anything These objects are called the Elements or Members of the set. CS218 Peter
More information2 Review of Set Theory
2 Review of Set Theory Example 2.1. Let Ω = {1, 2, 3, 4, 5, 6} 2.2. Venn diagram is very useful in set theory. It is often used to portray relationships between sets. Many identities can be read out simply
More informationSET DEFINITION 1 elements members
SETS SET DEFINITION 1 Unordered collection of objects, called elements or members of the set. Said to contain its elements. We write a A to denote that a is an element of the set A. The notation a A denotes
More informationLab 6B Coin Collection
HNHS Computer Programming I / IPFW CS 11400 Bower - Page 1 Lab 6B Coin Collection You will create a program that allows users to enter the quantities of an assortment of coins (quarters, dimes, nickels,
More informationCOMS 1003 Fall Introduction to Computer Programming in C. Bits, Boolean Logic & Discrete Math. September 13 th
COMS 1003 Fall 2005 Introduction to Computer Programming in C Bits, Boolean Logic & Discrete Math September 13 th Hello World! Logistics See the website: http://www.cs.columbia.edu/~locasto/ Course Web
More informationDiscrete Math: Selected Homework Problems
Discrete Math: Selected Homework Problems 2006 2.1 Prove: if d is a common divisor of a and b and d is also a linear combination of a and b then d is a greatest common divisor of a and b. (5 3.1 Prove:
More informationTaibah University College of Computer Science & Engineering Course Title: Discrete Mathematics Code: CS 103. Chapter 2. Sets
Taibah University College of Computer Science & Engineering Course Title: Discrete Mathematics Code: CS 103 Chapter 2 Sets Slides are adopted from Discrete Mathematics and It's Applications Kenneth H.
More informationMath 202 Test Problem Solving, Sets, and Whole Numbers 19 September, 2008
Math 202 Test Problem Solving, Sets, and Whole Numbers 19 September, 2008 Ten questions, each worth the same amount. Complete six of your choice. I will only grade the first six I see. Make sure your name
More informationn! = 1 * 2 * 3 * 4 * * (n-1) * n
The Beauty and Joy of Computing 1 Lab Exercise 9: Problem self-similarity and recursion Objectives By completing this lab exercise, you should learn to Recognize simple self-similar problems which are
More informationCSC Discrete Math I, Spring Sets
CSC 125 - Discrete Math I, Spring 2017 Sets Sets A set is well-defined, unordered collection of objects The objects in a set are called the elements, or members, of the set A set is said to contain its
More information(Refer Slide Time: 00:01:30)
Digital Circuits and Systems Prof. S. Srinivasan Department of Electrical Engineering Indian Institute of Technology, Madras Lecture - 32 Design using Programmable Logic Devices (Refer Slide Time: 00:01:30)
More informationPAIRS AND LISTS 6. GEORGE WANG Department of Electrical Engineering and Computer Sciences University of California, Berkeley
PAIRS AND LISTS 6 GEORGE WANG gswang.cs61a@gmail.com Department of Electrical Engineering and Computer Sciences University of California, Berkeley June 29, 2010 1 Pairs 1.1 Overview To represent data types
More informationSETS. Sets are of two sorts: finite infinite A system of sets is a set, whose elements are again sets.
SETS A set is a file of objects which have at least one property in common. The objects of the set are called elements. Sets are notated with capital letters K, Z, N, etc., the elements are a, b, c, d,
More information(Refer Slide Time: 0:19)
Theory of Computation. Professor somenath Biswas. Department of Computer Science & Engineering. Indian Institute of Technology, Kanpur. Lecture-15. Decision Problems for Regular Languages. (Refer Slide
More information2.2 Set Operations. Introduction DEFINITION 1. EXAMPLE 1 The union of the sets {1, 3, 5} and {1, 2, 3} is the set {1, 2, 3, 5}; that is, EXAMPLE 2
2.2 Set Operations 127 2.2 Set Operations Introduction Two, or more, sets can be combined in many different ways. For instance, starting with the set of mathematics majors at your school and the set of
More informationintroduction to Programming in C Department of Computer Science and Engineering Lecture No. #40 Recursion Linear Recursion
introduction to Programming in C Department of Computer Science and Engineering Lecture No. #40 Recursion Linear Recursion Today s video will talk about an important concept in computer science which is
More informationSEVENTH EDITION and EXPANDED SEVENTH EDITION
SEVENTH EDITION and EXPANDED SEVENTH EDITION Slide 2-1 Chapter 2 Sets 2.1 Set Concepts Set A collection of objects, which are called elements or members of the set. Listing the elements of a set inside
More information61A LECTURE 6 RECURSION. Steven Tang and Eric Tzeng July 2, 2013
61A LECTURE 6 RECURSION Steven Tang and Eric Tzeng July 2, 2013 Announcements Homework 2 solutions are up! Homework 3 and 4 are out Remember, hw3 due date pushed to Saturday Come to the potluck on Friday!
More informationCS 2316 Individual Homework 1 Python Practice Due: Wednesday, August 28th, before 11:55 PM Out of 100 points
CS 2316 Individual Homework 1 Python Practice Due: Wednesday, August 28th, before 11:55 PM Out of 100 points Files to submit: 1. HW1.py For Help: - TA Helpdesk Schedule posted on class website. - Email
More information2.1 Sets 2.2 Set Operations
CSC2510 Theoretical Foundations of Computer Science 2.1 Sets 2.2 Set Operations Introduction to Set Theory A set is a structure, representing an unordered collection (group, plurality) of zero or more
More informationUAB CIS High School Programming Contest. March 18, 2017 OFFICIAL HIGH SCHOOL CONTEST QUESTIONS
UAB CIS High School Programming Contest March 18, 2017 OFFICIAL HIGH SCHOOL CONTEST QUESTIONS Each problem in this packet contains a brief description, followed by three example test cases of a successful
More informationTHE SET ANALYSIS. Summary
THE SET ANALYSIS Summary 1 Why use the sets... 3 2 The identifier... 4 3 The operators... 4 4 The modifiers... 5 4.1 All members... 5 4.2 Known members... 6 4.3 Search string... 7 4.4 Using a boundary
More information2. Sets. 2.1&2.2: Sets and Subsets. Combining Sets. c Dr Oksana Shatalov, Fall
c Dr Oksana Shatalov, Fall 2014 1 2. Sets 2.1&2.2: Sets and Subsets. Combining Sets. Set Terminology and Notation DEFINITIONS: Set is well-defined collection of objects. Elements are objects or members
More informationMath Week in Review #5
Math 141 Spring 2006 c Heather Ramsey Page 1 Math 141 - Week in Review #5 Section 4.1 - Simplex Method for Standard Maximization Problems A standard maximization problem is a linear programming problem
More informationChapter 9 Graph Algorithms
Introduction graph theory useful in practice represent many real-life problems can be if not careful with data structures Chapter 9 Graph s 2 Definitions Definitions an undirected graph is a finite set
More informationBasic Geospatial Analysis Techniques: This presentation introduces you to basic geospatial analysis techniques, such as spatial and aspatial
Basic Geospatial Analysis Techniques: This presentation introduces you to basic geospatial analysis techniques, such as spatial and aspatial selections, buffering and dissolving, overly operations, table
More informationCombinatorics Prof. Dr. L. Sunil Chandran Department of Computer Science and Automation Indian Institute of Science, Bangalore
Combinatorics Prof. Dr. L. Sunil Chandran Department of Computer Science and Automation Indian Institute of Science, Bangalore Lecture - 5 Elementary concepts and basic counting principles So, welcome
More informationROCHESTER COMMUNITY SCHOOL MATHEMATICS SCOPE AND SEQUENCE, K-5 STRAND: NUMERATION
STRAND: NUMERATION Shows one-to-one correspondence for numbers 1-30 using objects and pictures Uses objects and pictures to show numbers 1 to 30 Counts by 1s to 100 Counts by 10s to 100 Counts backwards
More informationCSPs: Search and Arc Consistency
CSPs: Search and Arc Consistency CPSC 322 CSPs 2 Textbook 4.3 4.5 CSPs: Search and Arc Consistency CPSC 322 CSPs 2, Slide 1 Lecture Overview 1 Recap 2 Search 3 Consistency 4 Arc Consistency CSPs: Search
More informationWhat is a Set? Set Theory. Set Notation. Standard Sets. Standard Sets. Part 1.1. Organizing Information
Set Theory What is a Set? Part 1.1 Organizing Information What is a Set? Set Notation A set is an unordered collection of objects The collection objects are also called members or "elements" One of the
More informationDr. Relja Vulanovic Professor of Mathematics Kent State University at Stark c 2008
MATH-LITERACY MANUAL Dr. Relja Vulanovic Professor of Mathematics Kent State University at Stark c 2008 1 Real Numbers 1.1 Sets 1 1.2 Constants and Variables; Real Numbers 7 1.3 Operations with Numbers
More informationGrade 4. Number Strand. Achievement Indicators. 1. Represent and describe whole numbers to , pictorially and symbolically.
Number Strand Outcomes 1. Represent and describe whole numbers to 10 000, pictorially and symbolically. Grade 4 Achievement Indicators Read a four-digit numeral without using the word and (e.g., 5321 is
More informationMath 7 Notes - Unit 4 Pattern & Functions
Math 7 Notes - Unit 4 Pattern & Functions Syllabus Objective: (3.2) The student will create tables, charts, and graphs to extend a pattern in order to describe a linear rule, including integer values.
More informationIntroduction to Rational Functions Group Activity 5 STEM Project Week #8. AC, where D = dosage for a child, A = dosage for an
MLC at Boise State 013 Defining a Rational Function Introduction to Rational Functions Group Activity 5 STEM Project Week #8 f x A rational function is a function of the form, where f x and g x are polynomials
More information11/22/2016. Chapter 9 Graph Algorithms. Introduction. Definitions. Definitions. Definitions. Definitions
Introduction Chapter 9 Graph Algorithms graph theory useful in practice represent many real-life problems can be slow if not careful with data structures 2 Definitions an undirected graph G = (V, E) is
More informationChapter 2: Sets. Diana Pell. In the roster method: elements are listed between braces, with commas between the elements
Chapter 2: Sets Diana Pell 2.1: The Nature of Sets Set: any collection of elements. Elements: objects of the set. In the roster method: elements are listed between braces, with commas between the elements
More informationChapter 9 Graph Algorithms
Chapter 9 Graph Algorithms 2 Introduction graph theory useful in practice represent many real-life problems can be slow if not careful with data structures 3 Definitions an undirected graph G = (V, E)
More informationCMPSCI 250: Introduction to Computation. Lecture #1: Things, Sets and Strings David Mix Barrington 22 January 2014
CMPSCI 250: Introduction to Computation Lecture #1: Things, Sets and Strings David Mix Barrington 22 January 2014 Things, Sets, and Strings The Mathematical Method Administrative Stuff The Objects of Mathematics
More informationProject 1: How to Make One Dollar
Project Objective: Project 1: How to Make One Dollar Posted: Wednesday February 16, 2005. Described: Thursday February 17, 2005. Due: 11:59PM, Sunday March 6, 2005. 1. get familiar with the process of
More informationChapter 9 Graph Algorithms
Chapter 9 Graph Algorithms 2 Introduction graph theory useful in practice represent many real-life problems can be if not careful with data structures 3 Definitions an undirected graph G = (V, E) is a
More informationUML CS Algorithms Qualifying Exam Spring, 2004 ALGORITHMS QUALIFYING EXAM
NAME: This exam is open: - books - notes and closed: - neighbors - calculators ALGORITHMS QUALIFYING EXAM The upper bound on exam time is 3 hours. Please put all your work on the exam paper. (Partial credit
More informationCS1 Lecture 31 Apr. 3, 2019
CS Lecture 3 Apr. 3, 209 HW6 due Fri. Q3: think carefully about overlaps draw pictures Think dimension by dimension three D problems if they don t overlap in x, they don t overlap» Express this in terms
More informationFundamental Mathematical Concepts Math 107A. Professor T. D. Hamilton
Fundamental Mathematical Concepts Math 107A Professor T. D. Hamilton January 17, 2007 2 Contents 1 Set Theory 7 What is a set?.......................................... 7 Describing a Set.........................................
More information9/19/12. Why Study Discrete Math? What is discrete? Sets (Rosen, Chapter 2) can be described by discrete math TOPICS
What is discrete? Sets (Rosen, Chapter 2) TOPICS Discrete math Set Definition Set Operations Tuples Consisting of distinct or unconnected elements, not continuous (calculus) Helps us in Computer Science
More information1 of 7 7/15/2009 3:40 PM Virtual Laboratories > 1. Foundations > 1 2 3 4 5 6 7 8 9 1. Sets Poincaré's quote, on the title page of this chapter could not be more wrong (what was he thinking?). Set theory
More informationArrays and Files. Jerry Cain CS 106AJ November 1, 2017 slides courtesy of Eric Roberts
Arrays and Files Jerry Cain CS 106AJ November 1, 2017 slides courtesy of Eric Roberts Once upon a time... Ken Iverson and APL In the early 1960s, a computer scientist named Ken Iverson invented the APL
More information1 Sets, Fields, and Events
CHAPTER 1 Sets, Fields, and Events B 1.1 SET DEFINITIONS The concept of sets play an important role in probability. We will define a set in the following paragraph. Definition of Set A set is a collection
More informationTuesday, November 5, 2013 Name: Per:
Learning Objective Tuesday, November 5, 01 Name: Per: We will solve and interpret 1 problems using a Venn Diagram and set theory. Activate Prior Knowledge If we look at the following set of numbers 1-0,
More informationPrerequisites: Read all chapters through Chapter 4 in the textbook before attempting this lab. Read through this entire assignment before you begin.
Assignment Number 5 Lab Assignment Due Date: Wednesday, October 3, 2018 LAB QUESTIONS Due Date: Email before Monday, October 8, 2018 before 5:00 PM CS 1057 C Programming - Fall 2018 Purpose: write a complete
More informationMAT 090 Brian Killough s Instructor Notes Strayer University
MAT 090 Brian Killough s Instructor Notes Strayer University Success in online courses requires self-motivation and discipline. It is anticipated that students will read the textbook and complete sample
More informationMath 7 Notes - Unit 4 Pattern & Functions
Math 7 Notes - Unit 4 Pattern & Functions Syllabus Objective: (.) The student will create tables, charts, and graphs to etend a pattern in order to describe a linear rule, including integer values. Syllabus
More informationChapter 3. Set Theory. 3.1 What is a Set?
Chapter 3 Set Theory 3.1 What is a Set? A set is a well-defined collection of objects called elements or members of the set. Here, well-defined means accurately and unambiguously stated or described. Any
More informationGateway Regional School District VERTICAL ARTICULATION OF MATHEMATICS STANDARDS Grades K-4
NUMBER SENSE & OPERATIONS K.N.1 Count by ones to at least 20. When you count, the last number word you say tells the number of items in the set. Counting a set of objects in a different order does not
More informationGateway Regional School District VERTICAL ALIGNMENT OF MATHEMATICS STANDARDS Grades 3-6
NUMBER SENSE & OPERATIONS 3.N.1 Exhibit an understanding of the values of the digits in the base ten number system by reading, modeling, writing, comparing, and ordering whole numbers through 9,999. Our
More informationEngr. Joseph Ronald Canedo's Note 1
Engr. Joseph Ronald Canedo's Note 1 IP Addressing & Subnetting Made Easy Working with IP Addresses Joseph Ronald Cañedo Introduction You can probably work with decimal numbers much easier than with the
More informationLab 7: Change Calculation Engine
Lab 7: Change Calculation Engine Summary: Practice assembly language programming by creating and testing a useful cash register change calculation program that will display results on an LCD display. Learning
More informationFull file at
Java Programming: From Problem Analysis to Program Design, 3 rd Edition 2-1 Chapter 2 Basic Elements of Java At a Glance Instructor s Manual Table of Contents Overview Objectives s Quick Quizzes Class
More informationUsing a percent or a letter grade allows us a very easy way to analyze our performance. Not a big deal, just something we do regularly.
GRAPHING We have used statistics all our lives, what we intend to do now is formalize that knowledge. Statistics can best be defined as a collection and analysis of numerical information. Often times we
More informationObjectives/Outcomes. Introduction: If we have a set "collection" of fruits : Banana, Apple and Grapes.
1 September 26 September One: Sets Introduction to Sets Define a set Introduction: If we have a set "collection" of fruits : Banana, Apple Grapes. 4 F={,, } Banana is member "an element" of the set F.
More informationIntroduction. Sets and the Real Number System
Sets: Basic Terms and Operations Introduction Sets and the Real Number System Definition (Set) A set is a well-defined collection of objects. The objects which form a set are called its members or Elements.
More informationUNIVERSITY OF WATERLOO DEPARTMENT OF ELECTRICAL AND COMPUTER ENGINEERING ECE 250 ALGORITHMS AND DATA STRUCTURES
UNIVERSITY OF WATERLOO DEPARTMENT OF ELECTRICAL AND COMPUTER ENGINEERING ECE 250 ALGORITHMS AND DATA STRUCTURES Final Examination Instructor: R.E.Seviora 9-12 AM, Dec 14, 2002 Name (last, first) Student
More informationMath Week in Review #5. A proposition, or statement, is a declarative sentence that can be classified as either true or false, but not both.
Math 166 Fall 2006 c Heather Ramsey Page 1 Math 166 - Week in Review #5 Sections A.1 and A.2 - Propositions, Connectives, and Truth Tables A proposition, or statement, is a declarative sentence that can
More informationModule 6. Campaign Layering
Module 6 Email Campaign Layering Slide 1 Hello everyone, it is Andy Mackow and in today s training, I am going to teach you a deeper level of writing your email campaign. I and I am calling this Email
More informationNotebook Assignments
Notebook Assignments These six assignments are a notebook using techniques from class in the single concrete context of graph theory. This is supplemental to your usual assignments, and is designed for
More informationDatabase Management System Prof. Partha Pratim Das Department of Computer Science & Engineering Indian Institute of Technology, Kharagpur
Database Management System Prof. Partha Pratim Das Department of Computer Science & Engineering Indian Institute of Technology, Kharagpur Lecture - 01 Course Overview (Refer Slide Time: 00:45) Welcome
More informationMath 110 FOUNDATIONS OF THE REAL NUMBER SYSTEM FOR ELEMENTARY AND MIDDLE SCHOOL TEACHERS
2-1Numeration Systems Hindu-Arabic Numeration System Tally Numeration System Egyptian Numeration System Babylonian Numeration System Mayan Numeration System Roman Numeration System Other Number Base Systems
More informationProblem One: A Quick Algebra Review
CS103A Winter 2019 Solutions for Week One Handout 01S Problem One: A Quick Algebra Review In the first week of CS103, we'll be doing a few proofs that will require some algebraic manipulations and reasoning
More information1. POSITION AND SORTING Kindergarten
MATH CURRICULUM KINDERGARTEN 1. POSITION AND SORTING Kindergarten A. Position and Location 1. use the words inside and outside to describe the position of objects. 2. use the words over, under, and on
More informationCS103 Handout 42 Spring 2017 May 31, 2017 Practice Final Exam 1
CS103 Handout 42 Spring 2017 May 31, 2017 Practice Final Exam 1 We strongly recommend that you work through this exam under realistic conditions rather than just flipping through the problems and seeing
More informationComputer Graphics Prof. Sukhendu Das Dept. of Computer Science and Engineering Indian Institute of Technology, Madras Lecture - 14
Computer Graphics Prof. Sukhendu Das Dept. of Computer Science and Engineering Indian Institute of Technology, Madras Lecture - 14 Scan Converting Lines, Circles and Ellipses Hello everybody, welcome again
More informationDublin Unified School District Suggested Pacing Guide for Grade 2 Text: Scott Foresman-Addison Wesley envision Math
Trimester 1 8 Topic 1: Understanding Addition and Subtraction 1 1-1: s: Writing Addition Sentences, 1 1-2: s: Stories About Joining AF 1.0,, 1 1-3: s: Writing Subtraction Sentences, 1 1-4: s: Stories About
More informationSlides for Faculty Oxford University Press All rights reserved.
Oxford University Press 2013 Slides for Faculty Assistance Preliminaries Author: Vivek Kulkarni vivek_kulkarni@yahoo.com Outline Following topics are covered in the slides: Basic concepts, namely, symbols,
More information9. MATHEMATICIANS ARE FOND OF COLLECTIONS
get the complete book: http://wwwonemathematicalcatorg/getfulltextfullbookhtm 9 MATHEMATICIANS ARE FOND OF COLLECTIONS collections Collections are extremely important in life: when we group together objects
More information6. Relational Algebra (Part II)
6. Relational Algebra (Part II) 6.1. Introduction In the previous chapter, we introduced relational algebra as a fundamental model of relational database manipulation. In particular, we defined and discussed
More information2.NS.2: Read and write whole numbers up to 1,000. Use words models, standard for whole numbers up to 1,000.
UNIT/TIME FRAME STANDARDS I-STEP TEST PREP UNIT 1 Counting (20 days) 2.NS.1: Count by ones, twos, fives, tens, and hundreds up to at least 1,000 from any given number. 2.NS.5: Determine whether a group
More informationMicrosoft Excel 2010 Handout
Microsoft Excel 2010 Handout Excel is an electronic spreadsheet program you can use to enter and organize data, and perform a wide variety of number crunching tasks. Excel helps you organize and track
More informationDiscrete Mathematics
Discrete Mathematics Lecture 2: Basic Structures: Set Theory MING GAO DaSE@ ECNU (for course related communications) mgao@dase.ecnu.edu.cn Sep. 18, 2017 Outline 1 Set Concepts 2 Set Operations 3 Application
More informationComputer Algorithms-2 Prof. Dr. Shashank K. Mehta Department of Computer Science and Engineering Indian Institute of Technology, Kanpur
Computer Algorithms-2 Prof. Dr. Shashank K. Mehta Department of Computer Science and Engineering Indian Institute of Technology, Kanpur Lecture - 6 Minimum Spanning Tree Hello. Today, we will discuss an
More informationSets. Mukulika Ghosh. Fall Based on slides by Dr. Hyunyoung Lee
Sets Mukulika Ghosh Fall 2018 Based on slides by Dr. Hyunyoung Lee Sets Sets A set is an unordered collection of objects, called elements, without duplication. We write a A to denote that a is an element
More informationGrade 1 ISTEP+ T1 #1-4 ISTEP+ T1 #5
Unit 1 Establishing Routines 1 a D Count by 5's to 40. (Lessons 1.4, 1.7, and 1.11) 1 b D Count by 2's to 40. (Lessons 1.9-1.13) 1 c D Begin ongoing digit-writing practice. (Lessons 1.1-1.6) (Lessons 1.4,
More informationSection Sets and Set Operations
Section 6.1 - Sets and Set Operations Definition: A set is a well-defined collection of objects usually denoted by uppercase letters. Definition: The elements, or members, of a set are denoted by lowercase
More informationSimplifying Expressions
Unit 1 Beaumont Middle School 8th Grade, 2017-2018 Math8; Intro to Algebra Name: Simplifying Expressions I can identify expressions and write variable expressions. I can solve problems using order of operations.
More informationSituation 3. Parentheses vs. Brackets. Colleen Foy
Situation 3 Parentheses vs. Brackets Colleen Foy Prompt: Students were finding the domain and range of various functions. Most of the students were comfortable with the set builder notation, but when asked
More informationCS31: Introduction to Computer Science I Spring 2011
Final Practice TA: Brian Choi (schoi@cs.ucla.edu) Section Webpage: http://www.cs.ucla.edu/~schoi/cs31 1. Assume the following variable declarations: int foo = 0; int *ptr = &foo; Which of the following
More informationSpanning Trees. Lecture 20 CS2110 Spring 2015
1 Spanning Trees Lecture 0 CS110 Spring 01 1 Undirected trees An undirected graph is a tree if there is exactly one simple path between any pair of vertices Root of tree? It doesn t matter choose any vertex
More informationLesson 1.9 No learning goal mapped to this lesson Compare whole numbers up to 100 and arrange them in numerical. order.
Unit 1 Numbers and Routines 1 a D Find values of coin and bill combinations (Lessons 1.2, 1.6) 2.1.3 Identify numbers up to 100 in various combinations of tens and ones. ISTEP+ T1 #9-10 2.2.1 Model addition
More information(Refer Slide Time 3:31)
Digital Circuits and Systems Prof. S. Srinivasan Department of Electrical Engineering Indian Institute of Technology Madras Lecture - 5 Logic Simplification In the last lecture we talked about logic functions
More informationTOPIC 2 DECIMALS (and INTRODUCTION TO FRACTIONS) WEEK 3
TOPIC DECIMALS (and INTRODUCTION TO FRACTIONS) WEEK 3 Association between Fractions and Decimals is a fraction. It means divided by. If we divide by the result is not a whole number. It is a half of whole
More informationLinked Lists. College of Computing & Information Technology King Abdulaziz University. CPCS-204 Data Structures I
College of Computing & Information Technology King Abdulaziz University CPCS-204 Data Structures I What are they? Abstraction of a list: i.e. a sequence of nodes in which each node is linked to the node
More informationCS 112: Intro to Comp Prog
CS 112: Intro to Comp Prog Lecture Review Data Types String Operations Arithmetic Operators Variables In-Class Exercises Lab Assignment #2 Upcoming Lecture Topics Variables * Types Functions Purpose Parameters
More informationAlgebra of Sets. Aditya Ghosh. April 6, 2018 It is recommended that while reading it, sit with a pen and a paper.
Algebra of Sets Aditya Ghosh April 6, 2018 It is recommended that while reading it, sit with a pen and a paper. 1 The Basics This article is only about the algebra of sets, and does not deal with the foundations
More informationSolution: It may be helpful to list out exactly what is in each of these events:
MATH 5010(002) Fall 2017 Homework 1 Solutions Please inform your instructor if you find any errors in the solutions. 1. You ask a friend to choose an integer N between 0 and 9. Let A = {N 5}, B = {3 N
More information