Home Work 2
Submission Deadline: 10/06/2015
Problem #1
10 points
Problem #2
10 points
What will be big-Omega for Problem #1
Problem #3
10 points
Problem #4
10 points
Determine the complexity function that measures the number of print statements in an algo
Home Work 6
Student: Hanjie Shao
ID: N12875228
Problem 1 (10 points):
Suppose you have five coins three are good, but two are counterfeit. Assume that a counterfeit coin is
heavier than a good coin and that the two heavy coins have the same weight. A bala
NYU, Polytechnic School of Engineering
CS6033: Foundations of Computer Science Spring 2015, Itay Tal
Homework #7: Order of Growth
Due March 30th, 2015
Question 1
Rank the following functions by order of growth; that is, find an arrangement
g1, g2, g16 of
Tree
1.
2.
3.
4.
5.
6.
7.
8.
9.
10.
a connected graph which doesnt contain
simple circuit.
rooted tree: a tree in which one vertex has
been designated as the root and every edge is
directed away from the root. m
n n-1
m
N L=(N-1)/M L=[(M-1)N+1]/M
Suggested Syllabi
358
Suggested Syllabi
The text has been designed to be flexible. It can used in a variety of one-term and two-term courses, either
at a basic or at a more advanced level. A course designed to appeal to a diverse group of students can be
Java Middleware Overview
JMS
RMI
(c) Copyright Saeed Rahimi & Frank S. Haug
Slide: 1
The 3-Tier Model
Useful View of Distributed Application
Architecture
Subsystems assigned to one of 3 tiers based on
primary functionality
What are these 3-Tiers / Functio
Federated Databases
Copyright Saeed Rahimi
Page: 1
Degrees of Database Integration
Billing
Program
Purchasing
Program
Billing
Program
Billing &
Purchasing
Program
Purchasing
Program
Billing &
Purchasing
Program
Billing
Schema
Purchasing
Schema
Billing
Sc
Chapter 1, Part II: Predicate Logic
With Question/Answer Animations
Summary
Predicate Logic (First-Order Logic (FOL),
Predicate Calculus)
The Language of Quantifiers
Logical Equivalences
Nested Quantifiers
Translation from Predicate Logic to English
Trans
Chapter 1, Part I: Propositional Logic
With Question/Answer Animations
Chapter Summary
Propositional Logic
The Language of Propositions
Applications
Logical Equivalences
Predicate Logic
The Language of Quantifiers
Logical Equivalences
Nested Quantif
Chapter 1, Part III: Proofs
With Question/Answer
Animations
Summary
Valid Arguments and Rules of Inference
Proof Methods
Proof Strategies
Section 1.6
Section Summary
Valid Arguments
Inference Rules for Propositional
Logic
Using Rules of Inference to Build
Teaching Suggestions
362
Teaching Suggestions
In this part of the Instructors Resource Guide, I suggest how the text can be used effectively to teach an
introductory course in discrete mathematics. These views are based on my personal teaching experience
Chapter 2
With Question/Answer
Animations
Chapter Summary
Sets
The Language of Sets
Set Operations
Set Identities
Functions
Types of Functions
Operations on Functions
Computability
Sequences and Summations
Types of Sequences
Summation Formulae
464
Test Bank Questions and Answers
TEST BANK
Questions for Chapter 1
What is the negation of the propositions in 13?
1. Abby has more than 300 friends on facebook.
2. A messaging package for a cell phone costs less than $20 per month.
3. 4.5 + 2.5 = 6
In
NYU, Polytechnic School of Engineering
CS6033: Foundations of Computer Science Spring 2015, Itay Tal
Homework #2: Predicate Logic
Due February 9th, 2015
Answer the following questions from the textbook (Kenneth H. Rosen, Discrete
Mathematics and its Appli
NYU, Polytechnic School of Engineering
CS6033: Foundations of Computer Science Spring 2015, Itay Tal
Homework #5: Functions
Due March 9th, 2015
Answer the following questions from the textbook:
Page number
153
153
153
154
154
155
155
153
NYU, Polytechnic School of Engineering
CS6033: Foundations of Computer Science Spring 2015, Itay Tal
Homework #10
Due May 11th, 2015
Answer the following questions from the textbook:
Page number
406
406
422
422
422
432
432
432
433
557
Home Work 7
Deadline: 12/6/2015
Boolean Algebra
Problem 1-3 (30 points)
Exercise 11-13 Page 844 (textbook - by Rosen)
Problem 4 (10 points)
Using Quine McCluskey method simplify the circuit for f(w,x,y,z)= (0,4,5,7,8,11,12,15)
Counting
Problem 1 (5 points
Home Work 1
Submission deadline: 09/18/2015
Problem #1
5 points
The following proposition uses the English connective or. Determine from the context whether
or is intended to be used in the inclusive or exclusive sense.
If you do not wear a shirt or do no
Home Work 4
Student: Hanjie Shao
ID: N12875228
Problem #1
for n 2, and use the Principle of Mathematical Induction to prove that the formula is correct
Answer:
Assume the formula is
n+1
2n
Basic Step:
P(2) is true because P(2) =
2+1
22
=
3
4
= (1 -
1
22
)
Home Work 5
Student: Hanjie Shao
ID: N12875228
Problem #1 (3 points)
Let A be the set of all points in the plane with the origin removed. That is,
A = cfw_(x, y) | x, y R cfw_(0, 0).
Define a relation R on A by the rule:
(a, b)R(c, d) (a, b) and (c, d) li
Home Work 7
Student: Hanjie Shao
ID: N12875228
Boolean Algebra
Problem 1
a) Explain how K-maps can be used to simplify sum-of products expansions in four Boolean variables.
b) Use a K-map to simplify the sum-of-products expansion:
Answer:
a) K-map p
Name:
CS 6003: Foundation of Computer Science
Quiz 4
ID: .
Q.1.
Time: 1 hour 25 mins
State two drawbacks of Karnaugh map. A circuit is to be built that takes the numbers 0 through 9 as
inputs (1 = 0001, 2 = 0010, . . . , 9 = 1001). Let F(w, x, y, z) be t
NYU, Polytechnic School of Engineering
CS6033: Foundations of Computer Science Spring 2015, Itay Tal
Homework #3: Rules of Inference, Proof Methods
Due February 23th, 2015
Read pages 92-96 in the textbook, and answer the following questions:
Page number
NYU, Polytechnic School of Engineering
CS6033: Foundations of Computer Science Spring 2015, Itay Tal
Homework #4: Sets
Due March 2nd, 2015
Answer the following questions from the textbook:
Page number
125
125
136
136
136
137
137
126
126
NYU, Polytechnic School of Engineering
CS6033: Foundations of Computer Science Spring 2015, Itay Tal
Homework #6: Relations
Due March 23rd, 2015
Read pages 618-620 in the textbook (up to example 8 including this example),
and answer the following question
NYU, Polytechnic School of Engineering
CS6033: Foundations of Computer Science Spring 2015, Itay Tal
Homework #1: Propositional Logic
Due February 2nd, 2015
Answer the following questions from the textbook (Kenneth H. Rosen, Discrete
Mathematics and its A
NYU, Polytechnic School of Engineering
CS6033: Foundations of Computer Science Spring 2015, Itay Tal
Homework #8: Induction
Due April 13th, 2015
Answer the following questions from the textbook:
Page number Question number
329
6
329
8
330
NYU, Polytechnic School of Engineering
CS6033: Foundations of Computer Science Spring 2015, Itay Tal
Homework #9: Induction + Basic Counting Techniques
Due April 27th, 2015
Answer the following questions from the textbook:
Page number
342
344
358