Tree
A tree is a connected undirected
graph with no simple circuits
Which of these
graphs are trees?
Which of these
graphs are trees?
Solution: G1 and G2 are trees - both are
connected and have no simple circuits.
Because e, b, a, d, e is a simple circui

2016/10/20
CS 6003-INET (1 unread)
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note
Problem Set 4 Solution Guide
Problem 1
2
9
Problem 2
There are
2124 = 28
= 256 such strings.
Problem 3
Using the inclusive-exclusive rule:
The number of strings start with 11 is 210
The number of strings

ur Ozkan
Polytechnic Institute of NYU Prof. Ozg
CS6003Fall 2013
Final Exam. December 14th, 2013
You have four hours.
Use a word processor to write your responses. Clearly label your solutions. Once you
are done with the exam, submit the file as a File

2016/10/20
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note
Problem set 6 Solution Guide
Problem 1
1). Compare the rst and second integers in the sequence, set the temporary largest to the larger one and the temporary second-largest to the other.
2). Compare the nex

NYU School of Engineering
ur Ozkan
Prof. Ozg
CS6003Fall 2014
Sample Final Exam.
You have 2.5 hours.
You may not talk or otherwise communicate with other students during the exam. If
you try you get a zero for the exam on the spot.
Beepers, cell phones

CS6003: Foundations of Computer Science
Fall 2014
Problem Set 13.
You MUST show work to get credit.
Page:
1
2
Total
Points:
44
104
148
Score:
Reference
Recall thatP
if X1 , X2 , ., Xn are independent Poisson trials with P r[Xi = 1] = pi
where X = i Xi and

2016/10/22
CS 6003-INET
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note
Problem Set 7 Solution Guide
Problem 1
No. a=2, b=4, c=3,d=9.
Problem 2
Use values a=2, b=3, c=7 as an example. Now, 2|(3+7) but not 2|3 nor 2|7, so this will disprove the given statement.
Problem 3
a|c implies c = a

2016/10/20
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Problem Set 5 Solution Guide
Problem 1
Yes. c1 = 0.7 and c2 = 0.3. k=2.
Problem 2
No.
Problem 3
In this problem, we assume that the value of 1 coin is 1.
(1) an = an1 + an1 + an2 = 2an1 + an2, where a0
(2)

Midterm
October 18, 2016
1
1.1
1
a
x, y X, F (x, y) is true.
1.2
b
6 x X such that F (x, X) is true.
1.3
c
x, y X, F (y, x) is true.
1.4
d
x X, F (x, x) is not true.
2
2
x N abc(x 6= a2 b2 c2 )
1
3
3.1
3
a
n3 + n2 log(n) < n3 + n3 = O(n3 )
logn + 1 < logn

CS 6003: Foundations of Computer Science
Spring 2016
Name (PRINT):
Id:
Signature:
Midterm Exam. March 26th
You have 150 minutes for the exam. You will be allowed a total of 180 minutes to
ensure you have enough time to scan/etc. your solutions and submit

Final Exam
October 18, 2016
1
a
There is unique solution. C is knave, A is knight, B is spy.
b
Also a unique solution exists. A is knight. B is spy. C is knave.
2
It is not a tautology. Only false situation is when P is false and q is true.
3
a
xyF (x, y)

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Tree
Spanning Trees
Let G be a simple graph. A spanning tree of G
is a subgraph of G that is a tree containing
every vertex of G.
Example: Find the spanning tree of this
simple graph:
Spanning Trees (continued)
Theorem: A simple graph is connected if and

FCS Fall 2016 - Home Work
Due date: 11/29/2016
Problem 1
State two drawbacks of K-map. Suppose that a circuit is to be built that produces an output of 1
if the decimal digit is 5 or greater and an output of 0 if the decimal digit is less than 5. How can

Section 3.4
Recursive Definitions
1
Recursion
Recursion is the process of defining an object
in terms of itself
Technique can be used to define sequences,
functions and sets
To recursively define a sequence:
give first term
give rule for defining sub

Home Work 2
Due date: 09/21/16
Problem 1 (4 points)
Show the looping steps in order to find the number 15 with binary search in the list 7 8 10 12 12
15 16 18 20. Need to show the variables and update in each step.
Problem 2 (4 points)
Show that the sum o

CS 6003: Foundations of Computer Science
Spring 2016
Name (PRINT):
Id:
Signature:
Final Exam. May 14th, 2016
You have 150 minutes for the exam. You will be allowed a total of 180 minutes to
ensure you have enough time to scan/etc. your solutions and subm

2016/10/20
CS 6003-INET
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note
Problem Set 2 Solution Guide
1. A B = cfw_x|x A B = cfw_x|x A or x B = cfw_x|x A cfw_x|x
2. False. Draw Venn diagram to disprove it or give a counter example
3. False. Draw Venn diagram to disprove or give a counter e

Foundations of Computer Science CS-GY 6003
Assignment III
Name: Rahul Reddy Ajjaguttu
NetID : rra304
Q 1.
a)
a b (mod x) is equivalent to x (ba).
Thus, a b (mod m) m (ba), there is k such that km=ba.
Also as n m, there is a l such that ln=m.
So, k l n = b

Foundations of Computer Science CS-GY 6003
Assignment IV
Name: Rahul Reddy Ajjaguttu
NetID : rra304
Q 1.
a)
n=1 1/2
n=2 1/2 + 1/6 = 2/3
n=3 2/3 + 1/12 = 3/4
n=4 3/4 + 1/20 = 4/5
Looking at the values at each number n we can say the formula to be n/n+1.
i.

Chapter 7
Chapter Summary
Introduction to Discrete Probability
Probability Theory
Bayes Theorem
Expected Value and Variance
Section 7.1
Sec.on Summary
Finite Probability
Probabilities of Complements and Unions

Chapter 11
Chapter Summary
Introduction to Trees
Applications of Trees (not currently included in
overheads)
Tree Traversal
Spanning Trees
Minimum Spanning Trees (not currently included in
overheads)
Section 11.1

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Homework 5
Due Date: 02/28/2017
Problem 1 (8 points)
Consider the graph at the right.
(a) Does it have an Euler circuit?
(b) Does it have an Euler path?
(c) Does it have a Hamilton circuit?
(d) Does it have a Hamilton path?
Problem 2 (6 points)
Find a Ham

Home Work 1
Total: 60
Due date: 01/31/2017
Problem #1
Write these system specifications in symbols using the propositions
v: The user enters a valid password,
a: Access is granted to the user,
c: The user has contacted the network administrator,
and logic