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...Course Design Guide MTH/221 Version 1 1 Course Design Guide College of Information Systems & Technology MTH/221 Version 1 Discrete Math for Information Technology Copyright © 2010 by University of Phoenix. All rights reserved. Course Description Discrete (as opposed to continuous) mathematics is of direct importance to the fields of Computer Science and Information Technology. This branch of mathematics includes studying areas such as set theory, logic, relations, graph theory, and analysis of algorithms. This course is intended to provide students with an understanding of these areas and their use in the field of Information Technology. Policies Faculty and students/learners will be held responsible for understanding and adhering to all policies contained within the following two documents: University policies: You must be logged into the student website to view this document. Instructor policies: This document is posted in the Course Materials forum. University policies are subject to change. Be sure to read the policies at the beginning of each class. Policies may be slightly different depending on the modality in which you attend class. If you have recently changed modalities, read the policies governing your current class modality. Course Materials Grimaldi, R. P. (2004). Discrete and combinatorial mathematics: An applied introduction. (5th ed.). Boston, MA: Pearson Addison Wesley. Article References Albert, I. Thakar, J., Li, S., Zhang, R., & Albert, R...

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...operators , and , as is done in various programming languages. Information is often represented using bit strings, which are sequences of zeros and ones. When this is done, operations on the bit strings can be used to manipulate this information. A bit string is a sequence of zero or more bits. The length of this string is the number of bits in the string. We can extend bit operations to bit strings. We define the bitwise OR, bitwise AND and bitwise XOR of two strings of the same length to be the strings that have as their bits the OR, AND and XOR of the corresponding bits in the two strings, respectively. We use the symbols , and to represent the bitwise OR, bitwise AND and bitwise XOR operations respectively. Literature: Kenneth H. Rosen, Discrete Mathematics and Its Applications, fourth edition, 1999. Chapter 1, paragraph 1-4, pp. 6-18. Control questions: 1. Proposition. 2. Logical operations over propositions 3. Bit operations. Lecture 2. Propositional Equivalences An important type of step used in a mathematical argument is the replacement of a statement with another statement with the same truth value. Because of this, methods that produce propositions with the same truth value as a given compound proposition are used extensively in the construction of mathematical arguments. We begin our discussion with a classification of compound propositions according to their possible truth values. A compound proposition that is always true, no matter what the truth......

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...Discrete Math for Computer Science Students Ken Bogart Dept. of Mathematics Dartmouth College Scot Drysdale Dept. of Computer Science Dartmouth College Cliﬀ Stein Dept. of Industrial Engineering and Operations Research Columbia University ii c Kenneth P. Bogart, Scot Drysdale, and Cliﬀ Stein, 2004 Contents 1 Counting 1.1 Basic Counting . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . The Sum Principle . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . Abstraction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . Summing Consecutive Integers . . . . . . . . . . . . . . . . . . . . . . . . . . . . The Product Principle . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . Two element subsets . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . Important Concepts, Formulas, and Theorems . . . . . . . . . . . . . . . . . . . . Problems . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1.2 Counting Lists, Permutations, and Subsets. . . . . . . . . . . . . . . . . . . . . . Using the Sum and Product Principles . . . . . . . . . . . . . . . . . . . . . . . . Lists and functions . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . The Bijection Principle . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . k-element permutations of a set . . . . . . . . . . . . . . . . . . . . . . . . . . . . Counting......

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...Robert Gibbins MATH203-1401A-05 Application of Discrete Mathematics Phase 1 Individual Project January 12, 2014 Part I Demonstrate DeMorgan’s Laws using a Venn diagram: The portions below define 2 sets, and a universal set that exists within the 2 sets.. They state the union and intersection of the 2 sets and the complements of each set. The Venn Diagram gives a visual to give a demonstration of DeMorgan’s law of sets. Union The Union is the combined elements of both sets A and B: A U B = {Addison, Mabel, Leslie, Matt, Rick, Joel} or U = {Addison, Mabel, Leslie, Matt, Rick, Joel} Set A is expressed below in the shaded area of the Venn Diagram: A = {Addison, Leslie, Rick} Set B is expressed below n the shaded area of the Venn Diagram: B = {Mabel, Matt, Joel} Intersection The intersection are the elements both A and B have in common, in this case both softball and volleyball players. The intersection is expressed below and is represented in the shaded section of the Venn Diagram. A ∩ B = {Matt, Rick} Matt Rick Matt Rick Complements The Complement of a set contains everything in the universe minus what is in the set itself. The complement of Set A and Set B are expressed: A’ = {Mabel, Matt, Joel} B’ = {Addison, Leslie, Rick} De Morgan’s Law 1. The first portion of DeMorgan’s law says the complement of the union of sets A and B are the intersection of the...

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...MTH 221 (Discrete Math for Information Technology) CompleteClass IF You Want To Purchase A+ Work Then Click The Link Below , Instant Download http://hwnerd.com/Math-221-Discrete-Math-for-Information-Technology-Assignments-1491.htm?categoryId=-1 If You Face Any Problem E- Mail Us At Contact.Hwnerd@Gmail.Com MTH 221 Complete Class Week 1 – 5 All Assignments and Discussion Questions – A+ Graded Course Material Week 1 Individual Assignment Selected Textbook Exercises Complete 12 questions below by choosing at least four from each section. • Ch. 1 of Discrete and Combinatorial Mathematics o Supplementary Exercises 1, 2, 7, 8, 9, 10, 15(a), 18, 24, & 25(a & b) • Ch. 2 of Discrete and Combinatorial Mathematics o Exercise 2.1, problems 2, 3, 10, & 13, o Exercise 2.2, problems 3, 4, & 17 o Exercise 2.3, problems 1 & 4 o Exercise 2.4, problems 1, 2, & 6 o Exercise 2.5, problems 1, 2, & 4 • Ch. 3 of Discrete and Combinatorial Mathematics o Exercise 3.1, problems 1, 2, 18, & 21 o Exercise 3.2, problems 3 & 8 Exercise 3.3, problems 1, 2, 4, & 5 Week 1 DQ 1 Consider the problem of how to arrange a group of npeople so each person can shake hands with every other person. How might you organize this process? How many times will each person shake hands with someone else? How many handshakes will occur? How must your method vary according to whether or not n is even or odd? Week 1 DQ 2 There is an old joke that goes......

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...need 50 rows of seats. (a) Write the sequence for the number of seats for the first 5 rows C(1) = 16 + 4 (1) = 16 + 4 = 20 seats in the first row C(2) = 16 + 4 (2) = 16 + 8 = 24 seats in the first row C(3) = 16 + 4 (3) = 16 + 12 = 28 seats in the first row C(4) = 16 + 4 (4) = 16 + 16 = 32 seats in the first row C(5) = 16 + 4 (5) = 16 + 20 = 36 seats in the first row The sequence for the number of seats in the first 5 rows would be the following; 20, 24, 28, 32, 36 (b) How many seats will be in the last row? There are 50 rows, so n = 50 C(50) = 16 + 4 (50) = 16 + 200 = 216 seats in the last row The last row will have 216 seats. (c) What will be the total number of seats in the theater? From our MATH 203 Live Chat Session #4 on Wednesday evening 26 November 2014 we learned that the Sum of terms in a Sequence has the following formula; Sn = [ n (a1 + an ) ] / 2 So with that said n = 50 for the number of rows in the theater. S50 = [ 50 (a1 + an ) ] / 2 So in this case a1 is the first row which equals 20 seats in that row and an is the last row (50th row) which equals 216 seats in that row from (a) and (b) above.. S50 = [ 50 (20 + 216 ) ] / 2 Sum formula from results above S50 = [ 50 (236 ) ] / 2 20 plus 216 equals 236 S50 = [ 11800 ] / 2 50 times 236 equals 11,800 S50 = 5900 11,800 divided by 2 equals 5,900 The total number of seats in the theater will be 5900 seats....

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...MTH 221 Entire Course Discrete Math For Information To Buy this Tutorial Copy & paste below link in your Brower http://studentoffortune.biz/downloads/mth-221-entire-course-discrete-math-information/ Or Visit Our Website Visit : www.studentoffortune.biz Email Us : studentoffortunetutorials@gmail.com MTH 221 Entire Course Discrete Math For Information Individual – Selected Textbook Exercises : Chapter 1 Supplementary Exercises MTH 221 Week 1 DQs (A) Consider the problem of how to arrange a group of n people so each person can shake hands with every other person. How might you organize this process? How many times will each person shake hands with someone else? How many handshakes will occur? How must your method vary according to whether or not n is even or odd? (B) There is an old joke that goes something like this: “If God is love, love is blind, and Ray Charles is blind, then Ray Charles is God.” Explain, in the terms of first-order logic and predicate calculus, why this reasoning is incorrect. (C) There is an old joke, commonly attributed to Groucho Marx, which goes something like this: “I don’t want to belong to any club that will accept people like me as a member.” Does this statement fall under the purview of Russell’s paradox, or is there an easy semantic way out? Look up the term fuzzy set theory in a search engine of your choice or the University Library, and see if this theory can offer any insights into this statement MTH 221......

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...statements like “if 2+2=5 then the moon is made of green cheese” are technically true since whenever the antecedent (the part to the left of () is false, the entire implication is true irrespective of the truth value of the consequent (the part to the right of (). This feature of ( turns out to be very important, as we shall see later. Some definitions The CONVERSE of p(q is q(p The CONTRAPOSITIVE of p(q is (q ( (p The INVERSE of p(q is (p ( (q There are 16 (24) logically possible truth tables for two propositions, that is, two possible values in the four cells of the last column. We’ll look at one more although others may be of interest and occur elsewhere when logic is discussed. The expression “if and only if” occurs a lot in math and science, though not so much in daily life where we often say just “if” to mean “if and only if.” (When you say “If it rains I’ll cut classes” you usually mean “If it rains I’ll cut classes and if it doesn’t rain I won’t cut classes,” which amounts to “I’ll cut classes if and only if it rains,” but noone talks that way.) In any event we are interested in the logic of “if and only if” which is denoted by (. So consider: “I will leave tomorrow if and only if I get my car fixed.” Or: p ( q, where p symbolizes “I will leave tomorrow” and q symbolizes “I get my car fixed.” This compound proposition is true whenever both sides have the same truth value: If I leave tomorrow you would assume I got my car fixed and if you know I got......

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...MTH 221 Entire Course Discrete Math For Information To Buy this Tutorial Copy & paste below link in your Brower http://studentoffortune.biz/downloads/mth-221-entire-course-discrete-math-information/ Or Visit Our Website Visit : www.studentoffortune.biz Email Us : studentoffortunetutorials@gmail.com MTH 221 Entire Course Discrete Math For Information Individual – Selected Textbook Exercises : Chapter 1 Supplementary Exercises MTH 221 Week 1 DQs (A) Consider the problem of how to arrange a group of n people so each person can shake hands with every other person. How might you organize this process? How many times will each person shake hands with someone else? How many handshakes will occur? How must your method vary according to whether or not n is even or odd? (B) There is an old joke that goes something like this: “If God is love, love is blind, and Ray Charles is blind, then Ray Charles is God.” Explain, in the terms of first-order logic and predicate calculus, why this reasoning is incorrect. (C) There is an old joke, commonly attributed to Groucho Marx, which goes something like this: “I don’t want to belong to any club that will accept people like me as a member.” Does this statement fall under the purview of Russell’s paradox, or is there an easy semantic way out? Look up the term fuzzy set theory in a search engine of your choice or the University Library, and see if this theory can offer any insights into this statement MTH 221......

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...MTH 221 (Discrete Math for Information Technology) CompleteClass IF You Want To Purchase A+ Work Then Click The Link Below , Instant Download http://hwnerd.com/Math-221-Discrete-Math-for-Information-Technology-Assignments-1491.htm?categoryId=-1 If You Face Any Problem E- Mail Us At Contact.Hwnerd@Gmail.Com MTH 221 Complete Class Week 1 – 5 All Assignments and Discussion Questions – A+ Graded Course Material Week 1 Individual Assignment Selected Textbook Exercises Complete 12 questions below by choosing at least four from each section. • Ch. 1 of Discrete and Combinatorial Mathematics o Supplementary Exercises 1, 2, 7, 8, 9, 10, 15(a), 18, 24, & 25(a & b) • Ch. 2 of Discrete and Combinatorial Mathematics o Exercise 2.1, problems 2, 3, 10, & 13, o Exercise 2.2, problems 3, 4, & 17 o Exercise 2.3, problems 1 & 4 o Exercise 2.4, problems 1, 2, & 6 o Exercise 2.5, problems 1, 2, & 4 • Ch. 3 of Discrete and Combinatorial Mathematics o Exercise 3.1, problems 1, 2, 18, & 21 o Exercise 3.2, problems 3 & 8 Exercise 3.3, problems 1, 2, 4, & 5 Week 1 DQ 1 Consider the problem of how to arrange a group of npeople so each person can shake hands with every other person. How might you organize this process? How many times will each person shake hands with someone else? How many handshakes will occur? How must your method vary according to whether or not n is even or odd? Week 1 DQ 2 There is an old joke that goes......

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...MTH 221 (Discrete Math for Information Technology) CompleteClass IF You Want To Purchase A+ Work Then Click The Link Below , Instant Download http://hwnerd.com/Math-221-Discrete-Math-for-Information-Technology-Assignments-1491.htm?categoryId=-1 If You Face Any Problem E- Mail Us At Contact.Hwnerd@Gmail.Com MTH 221 Complete Class Week 1 – 5 All Assignments and Discussion Questions – A+ Graded Course Material Week 1 Individual Assignment Selected Textbook Exercises Complete 12 questions below by choosing at least four from each section. • Ch. 1 of Discrete and Combinatorial Mathematics o Supplementary Exercises 1, 2, 7, 8, 9, 10, 15(a), 18, 24, & 25(a & b) • Ch. 2 of Discrete and Combinatorial Mathematics o Exercise 2.1, problems 2, 3, 10, & 13, o Exercise 2.2, problems 3, 4, & 17 o Exercise 2.3, problems 1 & 4 o Exercise 2.4, problems 1, 2, & 6 o Exercise 2.5, problems 1, 2, & 4 • Ch. 3 of Discrete and Combinatorial Mathematics o Exercise 3.1, problems 1, 2, 18, & 21 o Exercise 3.2, problems 3 & 8 Exercise 3.3, problems 1, 2, 4, & 5 Week 1 DQ 1 Consider the problem of how to arrange a group of npeople so each person can shake hands with every other person. How might you organize this process? How many times will each person shake hands with someone else? How many handshakes will occur? How must your method vary according to whether or not n is even or odd? Week 1 DQ 2 There is an old joke that goes......

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Words: 1425 - Pages: 6

Words: 1425 - Pages: 6

Words: 1425 - Pages: 6

Words: 1425 - Pages: 6